Heating and cooling load calculations are the primary design basis for most heating and air-conditioning systems and components. These calculations affect the size of piping, ductwork, diffusers, air handlers, boilers, chillers, coils, compressors, fans, and every other component of systems that condition indoor environments. Cooling and heating load calculations can significantly affect first cost of building construction, comfort and productivity of occupants, and operating cost and energy consumption.
Simply put, heating and cooling loads are the rates of energy input (heating) or removal (cooling) required to maintain an indoor environment at a desired temperature and humidity condition. Heating and air conditioning systems are designed, sized, and controlled to accomplish that energy transfer. The amount of heating or cooling required at any particular time varies widely, depending on external (e.g., outdoor temperature) and internal (e.g., number of people occupying a space) factors.
Peak design heating and cooling load calculations, which are this chapter’s focus, seek to determine the maximum rate of heating and cooling energy transfer needed at any point in time. Similar principles, but with different assumptions, data, and application, can be used to estimate building energy consumption, as described in Chapter 19.
This chapter discusses common elements of cooling load calculation (e.g., internal heat gain, ventilation and infiltration, moisture migration, fenestration heat gain) and two methods of heating and cooling load estimation: heat balance (HB) and radiant time series (RTS).
1. COOLING LOAD CALCULATION PRINCIPLES
Cooling loads result from many conduction, convection, and radiation heat transfer processes through the building envelope and from internal sources and system components. Building components or contents that may affect cooling loads include the following:
External: Walls, roofs, windows, skylights, doors, partitions, ceilings, and floors
Internal: Lights, people, appliances, and equipment
Infiltration: Air leakage and moisture migration
System: Outdoor air, duct leakage and heat gain, reheat, fan and pump energy, and energy recovery
The variables affecting cooling load calculations are numerous, often difficult to define precisely, and always intricately interrelated. Many cooling load components vary widely in magnitude, and possibly direction, during a 24 h period. Because these cyclic changes in load components often are not in phase with each other, each component must be analyzed to establish the maximum cooling load for a building or zone. A zoned system (i.e., one serving several independent areas, each with its own temperature control) needs to provide no greater total cooling load capacity than the largest hourly sum of simultaneous zone loads throughout a design day; however, it must handle the peak cooling load for each zone at its individual peak hour. At some times of day during heating or intermediate seasons, some zones may require heating while others require cooling. The zones’ ventilation, humidification, or dehumidification needs must also be considered.
In air-conditioning design, the following four related heat flow rates, each of which varies with time, must be differentiated.
Space Heat Gain. This instantaneous rate of heat gain is the rate at which heat enters into and/or is generated within a space. Heat gain is classified by its mode of entry into the space and whether it is sensible or latent. Entry modes include (1) solar radiation through transparent surfaces; (2) heat conduction through exterior walls and roofs; (3) heat conduction through ceilings, floors, and interior partitions; (4) heat generated in the space by occupants, lights, and appliances; (5) energy transfer through direct-with-space ventilation and infiltration of outdoor air; and (6) miscellaneous heat gains. Sensible heat is added directly to the conditioned space by conduction, convection, and/or radiation. Latent heat gain occurs when moisture is added to the space (e.g., from vapor emitted by occupants and equipment). To maintain a constant humidity ratio, water vapor must condense on the cooling apparatus and be removed at the same rate it is added to the space. The amount of energy required to offset latent heat gain essentially equals the product of the condensation rate and latent heat of condensation. In selecting cooling equipment, distinguish between sensible and latent heat gain: every cooling apparatus has different maximum removal capacities for sensible versus latent heat for particular operating conditions. In extremely dry climates, humidification may be required, rather than dehumidification, to maintain thermal comfort.
Radiant Heat Gain. Radiant energy must first be absorbed by surfaces that enclose the space (walls, floor, and ceiling) and objects in the space (furniture, etc.). When these surfaces and objects become warmer than the surrounding air, some of their heat transfers to the air by convection. The composite heat storage capacity of these surfaces and objects determines the rate at which their respective surface temperatures increase for a given radiant input, and thus governs the relationship between the radiant portion of heat gain and its corresponding part of the space cooling load (Figure 1). The thermal storage effect is critical in differentiating between instantaneous heat gain for a given space and its cooling load at that moment. Predicting the nature and magnitude of this phenomenon to estimate a realistic cooling load for a particular set of circumstances has long been of interest to design engineers; the Bibliography lists some early work on the subject.
Space Cooling Load. This is the rate at which sensible and latent heat must be removed from the space to maintain a constant space air temperature and humidity. The sum of all space instantaneous heat gains at any given time does not necessarily (or even frequently) equal the cooling load for the space at that same time.
Space Heat Extraction Rate. The rates at which sensible and latent heat are removed from the conditioned space equal the space cooling load only if the room air temperature and humidity are constant. Along with the intermittent operation of cooling equipment, control systems usually allow a minor cyclic variation or swing in room temperature; humidity is often allowed to float, but it can be controlled. Therefore, proper simulation of the control system gives a more realistic value of energy removal over a fixed period than using values of the space cooling load. However, this is primarily important for estimating energy use over time; it is not needed to calculate design peak cooling load for equipment selection.
Cooling Coil Load. The rate at which energy is removed at a cooling coil serving one or more conditioned spaces equals the sum of instantaneous space cooling loads (or space heat extraction rate, if it is assumed that space temperature and humidity vary) for all spaces served by the coil, plus any system loads. System loads include fan heat gain, duct heat gain, and outdoor air heat and moisture brought into the cooling equipment to satisfy the ventilation air requirement.
Energy absorbed by walls, floor, furniture, etc., contributes to space cooling load only after a time lag. Some of this energy is still present and reradiating even after the heat sources have been switched off or removed, as shown in Figure 2.
There is always significant delay between the time a heat source is activated, and the point when reradiated energy equals that being instantaneously stored. This time lag must be considered when calculating cooling load, because the load required for the space can be much lower than the instantaneous heat gain being generated, and the space’s peak load may be significantly affected.
Accounting for the time delay effect is the major challenge in cooling load calculations. Several methods, including the two presented in this chapter, have been developed to take the time delay effect into consideration.
1.2 COOLING LOAD CALCULATION METHODS
This chapter presents two load calculation methods that vary significantly from previous methods. The technology involved, however (the principle of calculating a heat balance for a given space) is not new. The first of the two methods is the heat balance (HB) method; the second is radiant time series (RTS), which is a simplification of the HB procedure. Both methods are explained in their respective sections.
Cooling load calculation of an actual, multiple-room building requires a complex computer program implementing the principles of either method.
Cooling Load Calculations in Practice
Load calculations should accurately describe the building. All load calculation inputs should be as accurate as reasonable, without using safety factors. Introducing compounding safety factors at multiple levels in the load calculation results in an unrealistic and oversized load.
Variation in heat transmission coefficients of typical building materials and composite assemblies, differing motivations and skills of those who construct the building, unknown infiltration rates, and the manner in which the building is actually operated are some of the variables that make precise calculation impossible. Even if the designer uses reasonable procedures to account for these factors, the calculation can never be more than a good estimate of the actual load. Frequently, a cooling load must be calculated before every parameter in the conditioned space can be properly or completely defined. An example is a cooling load estimate for a new building with many floors of unleased spaces for which detailed partition requirements, furnishings, lighting, and layout cannot be predefined. Potential tenant modifications once the building is occupied also must be considered. Load estimating requires proper engineering judgment that includes a thorough understanding of heat balance fundamentals.
Perimeter spaces exposed to high solar heat gain often need cooling during sunlit portions of traditional heating months, as do completely interior spaces with significant internal heat gain. These spaces can also have significant heating loads during nonsunlit hours or after periods of nonoccupancy, when adjacent spaces have cooled below interior design temperatures. The heating loads involved can be estimated conventionally to offset or to compensate for them and prevent overheating, but they have no direct relationship to the spaces’ design heating loads.
Correct design and sizing of air-conditioning systems require more than calculation of the cooling load in the space to be conditioned. The type of air-conditioning system, ventilation rate, reheat, fan energy, fan location, duct heat loss and gain, duct leakage, heat extraction lighting systems, type of return air system, and any sensible or latent heat recovery all affect system load and component sizing. Adequate system design and component sizing require that system performance be analyzed as a series of psychrometric processes.
System design could be driven by either sensible or latent load, and both need to be checked. In a sensible-load-driven space (the most common case), the cooling supply air has surplus capacity to dehumidify, but this is usually permissible. For a space driven by latent load (e.g., an auditorium), supply airflow based on sensible load is likely not to have enough dehumidifying capability, so subcooling and reheating or some other dehumidification process is needed.
This chapter is primarily concerned with a given space or zone in a building. When estimating loads for a group of spaces (e.g., for an air-handling system that serves multiple zones), the assembled zones must be analyzed to consider (1) the simultaneous effects taking place; (2) any diversification of heat gains for occupants, lighting, or other internal load sources; (3) ventilation; and/or (4) any other unique circumstances. With large buildings that involve more than a single HVAC system, simultaneous loads and any additional diversity also must be considered when designing the central equipment that serves the systems. Methods presented in this chapter are expressed as hourly load summaries, reflecting 24 h input schedules and profiles of the individual load variables. Specific systems and applications may require different profiles.
Calculating space cooling loads requires detailed building design information and weather data at design conditions. Generally, the following information should be compiled.
Building Characteristics. Building materials, component size, external surface colors, and shape are usually determined from building plans and specifications.
Configuration. Determine building location, orientation, and external shading from building plans and specifications. Shading from adjacent buildings can be determined from a site plan or by visiting the proposed site, but its probable permanence should be carefully evaluated before it is included in the calculation. The possibility of abnormally high ground-reflected solar radiation (e.g., from adjacent water, sand, or parking lots) or solar load from adjacent reflective buildings should not be overlooked.
Outdoor Design Conditions. Obtain appropriate weather data, and select outdoor design conditions. Chapter 14 provides information for many weather stations; note, however, that these design dry-bulb and mean coincident wet-bulb temperatures may vary considerably from data traditionally used in various areas. Use judgment to ensure that results are consistent with expectations. Also, consider prevailing wind velocity and the relationship of a project site to the selected weather station.
Recent research projects have greatly expanded the amount of available weather data (e.g., ASHRAE 2012). In addition to the conventional dry bulb with mean coincident wet bulb, data are now available for wet bulb and dew point with mean coincident dry bulb. Peak space load generally coincides with peak solar or peak dry bulb, but peak system load often occurs at peak wet-bulb temperature. The relationship between space and system loads is discussed further in following sections of the chapter.
To estimate conductive heat gain through exterior surfaces and infiltration and outdoor air loads at any time, applicable outdoor dry- and wet-bulb temperatures must be used. Chapter 14 gives monthly cooling load design values of outdoor conditions for many locations. These are generally midafternoon conditions; for other times of day, the daily range profile method described in Chapter 14 can be used to estimate dry- and wet-bulb temperatures. Peak cooling load is often determined by solar heat gain through fenestration; this peak may occur in winter months and/or at a time of day when outdoor air temperature is not at its maximum.
Indoor Design Conditions. Select indoor dry-bulb temperature, indoor relative humidity, and ventilation rate. Include permissible variations and control limits. Consult ASHRAE Standard 90.1 for energy-savings conditions, and Standard 55 for ranges of indoor conditions needed for thermal comfort.
Internal Heat Gains and Operating Schedules. Obtain planned density and a proposed schedule of lighting, occupancy, internal equipment, appliances, and processes that contribute to the internal thermal load.
Areas. Use consistent methods for calculation of building areas. For fenestration, the definition of a component’s area must be consistent with associated ratings.
Gross surface area. It is efficient and conservative to derive gross surface areas from outer building dimensions, ignoring wall and floor thicknesses and avoiding separate accounting of floor edge and wall corner conditions. Measure floor areas to the outside of adjacent exterior walls or to the centerline of adjacent partitions. When apportioning to rooms, façade area should be divided at partition centerlines. Wall height should be taken as floor-to-floor height.
The outer-dimension procedure is expedient for load calculations, but it is not consistent with rigorous definitions used in building-related standards. The resulting differences do not introduce significant errors in this chapter’s procedures.
Fenestration area. As discussed in Chapter 15, fenestration ratings [U-factor and solar heat gain coefficient (SHGC)] are based on the entire product area, including frames. Thus, for load calculations, fenestration area is the area of the rough opening in the wall or roof.
Net surface area. Net surface area is the gross surface area less any enclosed fenestration area.
Internal heat gains from people, lights, motors, appliances, and equipment can contribute the majority of the cooling load in a modern building. As building envelopes have improved in response to more restrictive energy codes, internal loads have increased because of factors such as increased use of computers and the advent of dense-occupancy spaces (e.g., call centers). Internal heat gain calculation techniques are identical for both heat balance (HB) and radiant time series (RTS) cooling-load calculation methods, so internal heat gain data are presented here independent of calculation methods.
Table 1 gives representative rates at which sensible heat and moisture are emitted by humans in different states of activity. In high-density spaces, such as auditoriums, these sensible and latent heat gains comprise a large fraction of the total load. Even for short-term occupancy, the extra sensible heat and moisture introduced by people may be significant. See Chapter 9 for detailed information; however, Table 1 summarizes design data for common conditions.
The conversion of sensible heat gain from people to space cooling load is affected by the thermal storage characteristics of that space because some percentage of the sensible load is radiant energy. Latent heat gains are usually considered instantaneous, but research is yielding practical models and data for the latent heat storage of and release from common building materials.
Because lighting is often a major space cooling load component, an accurate estimate of the space heat gain it imposes is needed. Calculation of this load component is not straightforward; the rate of cooling load from lighting at any given moment can be quite different from the heat equivalent of power supplied instantaneously to those lights, because of heat storage.
Instantaneous Heat Gain from Lighting
The primary source of heat from lighting comes from light-emitting elements, or lamps, although significant additional heat may be generated from ballasts and other appurtenances in the luminaires. Generally, the instantaneous rate of sensible heat gain from electric lighting may be calculated from
where
| qel | = | heat gain, Btu/h
|
| W | = | total light wattage, W |
| Ful | = | lighting use factor |
| Fsa | = | lighting special allowance factor |
| 3.41 | = | conversion factor |
The total light wattage is obtained from the ratings of all lamps installed, both for general illumination and for display use. Ballasts are not included, but are addressed by a separate factor. Wattages of magnetic ballasts are significant; the energy consumption of high-efficiency electronic ballasts might be insignificant compared to that of the lamps.
The lighting use factor is the ratio of wattage in use, for the conditions under which the load estimate is being made, to total installed wattage. For commercial applications such as stores, the use factor is generally 1.0.
The special allowance factor is the ratio of the lighting fixtures’ power consumption, including lamps and ballast, to the nominal power consumption of the lamps. For incandescent lights, this factor is 1. For fluorescent lights, it accounts for power consumed by the ballast as well as the ballast’s effect on lamp power consumption. The special allowance factor can be less than 1 for electronic ballasts that lower electricity consumption below the lamp’s rated power consumption. Use manufacturers’ values for system (lamps + ballast) power, when available.
For high-intensity-discharge lamps (e.g. metal halide, mercury vapor, high- and low-pressure sodium vapor lamps), the actual lighting system power consumption should be available from the manufacturer of the fixture or ballast. Ballasts available for metal halide and high-pressure sodium vapor lamps may have special allowance factors from about 1.3 (for low-wattage lamps) down to 1.1 (for high-wattage lamps).
An alternative procedure is to estimate the lighting heat gain on a per-square-foot basis. Such an approach may be required when final lighting plans are not available. Table 2 shows the maximum lighting power density (LPD) (lighting heat gain per square foot) allowed by ASHRAE Standard 90.1-2013 for a range of space types.
In addition to determining the lighting heat gain, the fraction of lighting heat gain that enters the conditioned space may need to be distinguished from the fraction that enters an unconditioned space; of the former category, the distribution between radiative and convective heat gain must be established.
Fisher and Chantrasrisalai (2006) and Zhou et al. (2016) experimentally studied 12 luminaire types and recommended several categories of luminaires, as shown in Table 3. The table provides a range of design data for the conditioned space fraction, short-wave radiative fraction, and long-wave radiative fraction under typical operating conditions: airflow rate of 1 cfm/ft², supply air temperature between 59 and 62°F, and room air temperature between 72 and 75°F. The recommended fractions in Table 3 are based on lighting heat input rates range of 0.9 to 2.6 W/ft2. For higher design power input, the lower bounds of the space and short-wave fractions should be used; for design power input below this range, the upper bounds of the space and short-wave fractions should be used. The space fraction in the table is the fraction of lighting heat gain that goes to the room; the fraction going to the plenum can be computed as 1 – the space fraction. The radiative fraction is the radiative part of the lighting heat gain that goes to the room. The convective fraction of the lighting heat gain that goes to the room is 1 – the radiative fraction. Using values in the middle of the range yields sufficiently accurate results. However, values that better suit a specific situation may be determined according to the notes for Table 3.
Table 3’s data apply to both ducted and nonducted returns. However, application of the data, particularly the ceiling plenum fraction, may vary for different return configurations. For instance, for a room with a ducted return, although a portion of the lighting energy initially dissipated to the ceiling plenum is quantitatively equal to the plenum fraction, a large portion of this energy would likely end up as the conditioned space cooling load and a small portion would end up as the cooling load to the return air.
If the space airflow rate is different from the typical condition (i.e., about 1 cfm/ft2), Figure 3 can be used to estimate the lighting heat gain parameters. Design data shown in Figure 3 are only applicable for the recessed fluorescent luminaire without lens.
Although design data presented in Table 3 and Figure 3 can be used for a vented luminaire with side-slot returns, they are likely not applicable for a vented luminaire with lamp compartment returns, because in the latter case, all heat convected in the vented luminaire is likely to go directly to the ceiling plenum, resulting in zero convective fraction and a much lower space fraction. Therefore, the design data should only be used for a configuration where conditioned air is returned through the ceiling grille or luminaire side slots.
For other luminaire types, it may be necessary to estimate the heat gain for each component as a fraction of the total lighting heat gain by using judgment to estimate heat-to-space and heat-to-return percentages.
Because of the directional nature of downlight luminaires, a large portion of the short-wave radiation typically falls on the floor. When converting heat gains to cooling loads in the RTS method, the solar radiant time factors (RTFs) may be more appropriate than nonsolar RTFs. (Solar RTFs are calculated assuming most solar radiation is intercepted by the floor; nonsolar RTFs assume uniform distribution by area over all interior surfaces.) This effect may be significant for rooms where lighting heat gain is high and for which solar RTFs are significantly different from nonsolar RTFs.
Instantaneous sensible heat gain from equipment operated by electric motors in a conditioned space is calculated as
where
| qem |
= |
heat equivalent of equipment operation, Btu/h |
| P |
= |
motor power rating, hp |
| EM |
= |
motor efficiency, decimal fraction <1.0 |
| FUM |
= |
motor use factor, 1.0 or decimal fraction <1.0 |
| FLM |
= |
motor load factor, 1.0 or decimal fraction <1.0 |
| 2545 |
= |
conversion factor, Btu/h · hp |
The motor use factor may be applied when motor use is known to be intermittent, with significant nonuse during all hours of operation (e.g., overhead door operator). For conventional applications, its value is 1.0.
The motor load factor is the fraction of the rated load delivered under the conditions of the cooling load estimate. Equation (2) assumes that both the motor and driven equipment are in the conditioned space. If the motor is outside the space or airstream,
When the motor is inside the conditioned space or airstream but the driven machine is outside,
Equation (4) also applies to a fan or pump in the conditioned space that exhausts air or pumps fluid outside that space.
Table 4A and 4B gives minimum efficiencies and related data representative of typical electric motors from ASHRAE Standard 90.1-2013. If electric motor load is an appreciable portion of cooling load, the motor efficiency should be obtained from the manufacturer. Also, depending on design, maximum efficiency might occur anywhere between 75 to 110% of full load; if under- or overloaded, efficiency could vary from the manufacturer’s listing.
Overloading or Underloading
Heat output of a motor is generally proportional to motor load, within rated overload limits. Because of typically high no-load motor current, fixed losses, and other reasons, FLM is generally assumed to be unity, and no adjustment should be made for underloading or overloading unless the situation is fixed and can be accurately established, and reduced-load efficiency data can be obtained from the motor manufacturer.
Unless the manufacturer’s technical literature indicates otherwise, motor heat gain normally should be equally divided between radiant and convective components for the subsequent cooling load calculations.
A cooling load estimate should take into account heat gain from all appliances (electrical, gas, or steam). Because of the variety of appliances, applications, schedules, use, and installations, estimates can be very subjective. Often, the only information available about heat gain from equipment is that on its nameplate, which can overestimate actual heat gain for many types of appliances, as discussed in the section on Office Equipment.
These appliances include common heat-producing cooking equipment found in conditioned commercial kitchens. Marn (1962) concluded that appliance surfaces contributed most of the heat to commercial kitchens and that when appliances were installed under an effective hood, the cooling load was independent of the fuel or energy used for similar equipment performing the same operations.
Gordon et al. (1994) and Smith et al. (1995) found that gas appliances may exhibit slightly higher heat gains than their electric counterparts under wall-canopy hoods operated at typical ventilation rates. This is because heat contained in combustion products exhausted from a gas appliance may increase the temperatures of the appliance and surrounding surfaces, as well as the hood above the appliance, more so than the heat produced by its electric counterpart. These higher-temperature surfaces radiate heat to the kitchen, adding moderately to the radiant gain directly associated with the appliance cooking surface.
Marn (1962) confirmed that, where appliances are installed under an effective hood, only radiant gain adds to the cooling load; convective and latent heat from cooking and combustion products are exhausted and do not enter the kitchen. Gordon et al. (1994) and Smith et al. (1995) substantiated these findings. Chapter 33 of the 2015 ASHRAE Handbook—HVAC Applications has more information on kitchen ventilation.
Sensible Heat Gain for Hooded Cooking Appliances. To establish a heat gain value, nameplate energy input ratings may be used with appropriate usage and radiation factors. Where specific rating data are not available (nameplate missing, equipment not yet purchased, etc.), representative heat gains listed in Tables 5A to 5E (Swierczyna et al. 2008, 2009) for a wide variety of commonly encountered equipment items. In estimating appliance load, probabilities of simultaneous use and operation for different appliances located in the same space must be considered.
Radiant heat gain from hooded cooking equipment can range from 15 to 45% of the actual appliance energy consumption (Gordon et al. 1994; Smith et al. 1995; Swierczyna et al. 2008; Talbert et al. 1973). This ratio of heat gain to appliance energy consumption may be expressed as a radiation factor, and it is a function of both appliance type and fuel source. The radiation factor FR is applied to the average rate of appliance energy consumption, determined by applying usage factor FU to the nameplate or rated energy input. Marn (1962) found that radiant heat temperature rise can be substantially reduced by shielding the fronts of cooking appliances. Although this approach may not always be practical in a commercial kitchen, radiant gains can also be reduced by adding side panels or partial enclosures that are integrated with the exhaust hood.
Heat Gain from Meals. For each meal served, approximately 50 Btu/h of heat, of which 75% is sensible and 25% is latent, is transferred to the dining space.
Heat Gain for Generic Appliances. The average rate of appliance energy consumption can be estimated from the nameplate or rated energy input qinput by applying a duty cycle or usage factor FU. Thus, sensible heat gain qs for generic electric, steam, and gas appliances installed under a hood can be estimated using one of the following equations:
or
where FL is the ratio of sensible heat gain to the manufacturer’s rated energy input. However, ASHRAE research (Swierczyna et al. 2008, 2009) showed the design value for heat gain from a hooded appliance at idle (ready-to-cook) conditions based on its energy consumption rate is, at best, a rough estimate. When appliance heat gain measurements during idle conditions were regressed against energy consumption rates for gas and electric appliances, the appliances’ emissivity, insulation, and surface cooling (e.g., through ventilation rates) scattered the data points widely, with large deviations from the average values. Because large errors could occur in the heat load calculation for specific appliance lines by using a general radiation factor, heat gain values in Table 5 should be applied in the HVAC design.
Table 5 lists usage factors, radiation factors, and load factors based on appliance energy consumption rate for typical electrical, steam, and gas appliances under standby (idle or ready-to-cook) and cooking conditions, hooded and unhooded.
Warewashing Applications. Typically, hot-water sanitizing and conveyor-type dish machines have either a dishwasher/condensing hood or direct-connected ductwork. If the ventilation is not operating properly, there are significant sensible and latent gains to the space. Chemical sanitizing and vapor reduction models are typically unhooded; consequently, the dish machines produce internal gains that must be accounted for and managed by the building HVAC system.
Sensible radiant and convective gains are affected by dishwasher insulation, and latent convective gains are affected by door seals. Heat loads may vary.
Recirculating Systems. Cooking appliances ventilated by recirculating systems or “ductless” hoods should be treated as unhooded appliances when estimating heat gain. In other words, all energy consumed by the appliance and all moisture produced by cooking is introduced to the kitchen as a sensible or latent cooling load.
Recommended Heat Gain Values. Table 5 lists recommended rates of heat gain from typical commercial cooking appliances. Data in the “hooded” columns assume installation under a properly designed exhaust hood connected to a mechanical fan exhaust system operating at an exhaust rate for complete capture and containment of the thermal and effluent plume. Improperly operating hood systems load the space with a significant convective component of the heat gain.
Hospital and Laboratory Equipment
Hospital and laboratory equipment items are major sources of sensible and latent heat gains in conditioned spaces. Care is needed in evaluating the probability and duration of simultaneous usage when many components are concentrated in one area, such as a laboratory, an operating room, etc. Commonly, heat gain from equipment in a laboratory ranges from 15 to 70 Btu/h · ft2 or, in laboratories with outdoor exposure, as much as four times the heat gain from all other sources combined.
Medical Equipment. It is more difficult to provide generalized heat gain recommendations for medical equipment than for general office equipment because medical equipment is much more varied in type and in application. Some heat gain testing has been done, but the equipment included represents only a small sample of the type of equipment that may be encountered.
Data presented for medical equipment in Table 6 are relevant for portable and bench-top equipment. Medical equipment is very specific and can vary greatly from application to application. The data are presented to provide guidance in only the most general sense. For large equipment, such as MRI, heat gain must be obtained from the manufacturer.
Laboratory Equipment. Equipment in laboratories is similar to medical equipment in that it varies significantly from space to space. Chapter 16 of the 2019 ASHRAE Handbook—HVAC Applications discusses heat gain from equipment, which may range from 5 to 25 W/ft2 in highly automated laboratories. Table 7 lists some values for laboratory equipment, but, as with medical equipment, it is for general guidance only. Wilkins and Cook (1999) also examined laboratory equipment heat gains.
Computers, printers, copiers, etc., can generate very significant heat gains, sometimes greater than all other gains combined. ASHRAE research project RP-822 developed a method to measure the actual heat gain from equipment in buildings and the radiant/convective percentages (Hosni et al. 1998; Jones et al. 1998). This methodology was then incorporated into ASHRAE research project RP-1055 and applied to a wide range of equipment (Hosni et al. 1999) as a follow-up to independent research by Wilkins and McGaffin (1994) and Wilkins et al. (1991). Komor (1997) found similar results. Analysis of measured data showed that results for office equipment could be generalized, but results from laboratory and hospital equipment proved too diverse. The following general guidelines for office equipment are a result of these studies
Nameplate Versus Measured Energy Use. Nameplate data rarely reflect the actual power consumption of office equipment. Actual power consumption is assumed to equal total (radiant plus convective) heat gain, but its ratio to the nameplate value varies widely. ASHRAE research project RP-1055 (Hosni et al. 1999) found that, for general office equipment with nameplate power consumption of less than 1000 W, the actual ratio of total heat gain to nameplate ranged from 25 to 50%, but when all tested equipment is considered, the range is broader. Generally, if the nameplate value is the only information known and no actual heat gain data are available for similar equipment, it is conservative to use 50% of nameplate as heat gain and more nearly correct if 25% of nameplate is used. Much better results can be obtained, however, by considering heat gain to be predictable based on the type of equipment. However, if the device has a mainly resistive internal electric load (e.g., a space heater), the nameplate rating may be a good estimate of its peak energy dissipation.
Computers. Based on tests by Hosni et al. (1999) and Wilkins and McGaffin (1994), nameplate values on computers should be ignored when performing cooling load calculations. Tables 8A, 8B, and 8C (Bach and Sarfraz 2017) present typical heat gain values for computers of varying types and models.
Monitors. Table 8D shows typical values for various sizes and types.
Flat-panel monitors have replaced CRT monitors in almost all workplaces. Power consumption, and thus heat gain, for flat-panel displays are significantly lower than for CRTs.
Laser Printers. Hosni et al. (1999) found that power consumption, and therefore the heat gain, of laser printers depended largely on the level of throughput for which the printer was designed. Smaller printers tend to be used more intermittently, and larger printers may run continuously for longer periods.
Table 9 presents data on typical printers. These data can be applied by taking the value for continuous operation and then applying an appropriate diversity factor. This would likely be most appropriate for larger open office areas. Another approach, which may be appropriate for a single room or small area, is to take the value that most closely matches the expected operation of the printer with no diversity.
Copiers. Bach and Sarfraz (2017) also tested photocopy machines, including desktop and office (freestanding high-volume copiers) models. Larger machines used in production environments were not addressed. Table 9 summarizes the results. Desktop copiers rarely operate continuously, but office copiers frequently operate continuously for periods of an hour or more. Large, high-volume photocopiers often include provisions for exhausting air outdoors; if so equipped, the direct-to-space or system makeup air heat gain needs to be included in the load calculation. Also, when the air is dry, humidifiers are often operated near copiers to limit static electricity; if this occurs during cooling mode, their load on HVAC systems should be considered.
Miscellaneous Office Equipment. Table 10 presents data on miscellaneous office equipment such as vending machines and other equipment tested by Bach and Sarfraz (2017).
Diversity. The ratio of measured peak electrical load at equipment panels to the sum of the maximum electrical load of each individual item of equipment is the usage diversity. A small, one- or two-person office containing equipment listed in Tables 8 to 10 usually contributes heat gain to the space at the sum of the appropriate listed values. Progressively larger areas with many equipment items always experience some degree of usage diversity resulting from whatever percentage of such equipment is not in operation at any given time.
Wilkins and McGaffin (1994) measured diversity in 23 areas within five different buildings totaling over 275,000 ft2. Diversity was found to range between 37 and 78%, with the average (normalized based on area) being 46%. Figure 4 shows the relationship between nameplate, sum of peaks, and actual electrical load with diversity accounted for, based on the average of the total area tested. Data on actual diversity can be used as a guide, but diversity varies significantly with occupancy. The proper diversity factor for an office of call center operators is different from that for an office of sales representatives who travel regularly.
ASHRAE research project RP-1093 derived diversity profiles for use in energy calculations (Abushakra et al. 2004; Claridge et al. 2004). Those profiles were derived from available measured data sets for a variety of office buildings, and indicated a range of peak weekday diversity factors for lighting ranging from 70 to 85% and for receptacles (appliance load) between 42 and 89%.
Heat Gain per Unit Area. Bach and Sarfraz (2017), Wilkins and Hosni (2000, 2011) and Wilkins and McGaffin (1994) summarized research on a heat gain per unit area basis. Diversity testing showed that the actual heat gain per unit area, or load factor, ranged from 0.44 to 1.08 W/ft2, with an average (normalized based on area) of 0.81 W/ft2. Spaces tested were fully occupied and highly automated, comprising 21 unique areas in five buildings, with a computer and monitor at every workstation. Table 11 presents a range of load factors with a subjective description of the type of space to which they would apply. The medium load density is likely to be appropriate for most standard office spaces. Medium/heavy or heavy load densities may be encountered but can be considered extremely conservative estimates even for densely populated and highly automated spaces. Table 12 indicates applicable diversity factors.
Radiant/Convective Split. ASHRAE research project RP-1482 (Hosni and Beck 2008) examined the radiant/convective split for common office equipment; the most important differentiating feature is whether the equipment had a cooling fan. Footnotes in Tables 8 and 9 summarize those results.
Cooling load estimation involves calculating a surface-by-surface conductive, convective, and radiative heat balance for each room surface and a convective heat balance for the room air. These principles form the foundation for all methods described in this chapter. The heat balance (HB) method solves the problem directly instead of introducing transformation-based procedures. The advantages are that it contains no arbitrarily set parameters, and no processes are hidden from view.
Some computations required by this rigorous approach require the use of computers. The heat balance procedure is not new. Many energy calculation programs have used it in some form for many years. The first implementation that incorporated all the elements to form a complete method was NBSLD (Kusuda 1967). The heat balance procedure is also implemented in both the BLAST and TARP energy analysis programs (Walton 1983). Before ASHRAE research project RP-875, the method had never been described completely or in a form applicable to cooling load calculations. The papers resulting from RP-875 describe the heat balance procedure in detail (Liesen and Pedersen 1997; McClellan and Pedersen 1997; Pedersen et al. 1997).
The HB method is codified in the software called Hbfort that accompanies Cooling and Heating Load Calculation Principles (Pedersen et al. 1998).
ASHRAE research project RP-1117 constructed two model rooms for which cooling loads were physically measured using extensive instrumentation (Chantrasrisalai et al. 2003; Eldridge et al. 2003; Iu et al. 2003). HB calculations closely approximated measured cooling loads when provided with detailed data for the test rooms.
All calculation procedures involve some kind of model; all models require simplifying assumptions and, therefore, are approximate. The most fundamental assumption is that air in the thermal zone can be modeled as well mixed, meaning its temperature is uniform throughout the zone. ASHRAE research project RP-664 (Fisher and Pedersen 1997) established that this assumption is valid over a wide range of conditions.
The next major assumption is that the surfaces of the room (walls, windows, floor, etc.) can be treated as having
Uniform surface temperatures
Uniform long-wave (LW) and short-wave (SW) irradiation
Diffuse radiating surfaces
One-dimensional heat conduction within
The resulting formulation is called the heat balance (HB) model. Note that the assumptions, although common, are quite restrictive and set certain limits on the information that can be obtained from the model.
Within the framework of the assumptions, the HB can be viewed as four distinct processes:
Outdoor-face heat balance
Wall conduction process
Indoor-face heat balance
Air heat balance
Figure 5 shows the relationship between these processes for a single opaque surface. The top part of the figure, inside the shaded box, is repeated for each surface enclosing the zone. The process for transparent surfaces is similar, but the absorbed solar component appears in the conduction process block instead of at the outdoor face, and the absorbed component splits into inward- and outward-flowing fractions. These components participate in the surface heat balances.
Outdoor-Face Heat Balance
The heat balance on the outdoor face of each surface is
where
| q˝αsol | = | absorbed direct and diffuse solar radiation flux (q/A), Btu/h · ft2 |
| q˝LWR | = | net long-wave radiation flux exchange with air and surroundings, Btu/h · ft2 |
| q˝conv | = | convective exchange flux with outdoor air, Btu/h · ft2 |
| q˝ko | = | conductive flux (q/A) into wall, Btu/h · ft2 |
All terms are positive for net flux to the face except q˝ko, which is traditionally taken to be positive from outdoors to inside the wall.
Each term in Equation (16) has been modeled in several ways, and in simplified methods the first three terms are combined by using the sol-air temperature.
The wall conduction process has been formulated in more ways than any of the other processes. Techniques include
This process introduces part of the time dependence inherent in load calculation. Figure 6 shows surface temperatures on the indoor and outdoor faces of the wall element, and corresponding conductive heat fluxes away from the outer face and toward the indoor face. All four quantities are functions of time. Direct formulation of the process uses temperature functions as input or known quantities, and heat fluxes as outputs or resultant quantities.
In some models, surface heat transfer coefficients are included as part of the wall element, making the temperatures in question the indoor and outdoor air temperatures. This is not a desirable formulation, because it hides the heat transfer coefficients and prohibits changing them as airflow conditions change. It also prohibits treating the internal long-wave radiation exchange appropriately.
Because heat balances on both sides of the element induce both the temperature and heat flux, the solution must deal with this simultaneous condition. Two computational methods that have been used widely are finite difference and conduction transfer function methods. Because of the computational time advantage, the conduction transfer function formulation has been selected for presentation here.
The heart of the HB method is the internal heat balance involving the inner faces of the zone surfaces. This heat balance has many heat transfer components, and they are all coupled. Both long-wave (LW) and short-wave (SW) radiation are important, as well as wall conduction and convection to the air. The indoor-face heat balance for each surface can be written as follows:
where
| q˝LWX | = | net long-wave radiant flux exchange between zone surfaces, Btu/h · ft2 |
| q˝SW | = | net short-wave radiation flux to surface from lights, Btu/h · ft2 |
| q˝LWS | = | long-wave radiation flux from equipment in zone, Btu/h · ft2 |
| q˝ki | = | conductive flux through wall, Btu/h · ft2 |
| q˝sol | = | transmitted solar radiative flux absorbed at surface, Btu/h · ft2 |
| q˝conv | = | convective heat flux to zone air, Btu/h · ft2 |
These terms are explained in the following paragraphs.
LW Radiation Exchange Among Zone Surfaces. The limiting cases for modeling internal LW radiation exchange are
Most HB models treat air as completely transparent and not participating in LW radiation exchange among surfaces in the zone. The second model is attractive because it can be formulated simply using a combined radiative and convective heat transfer coefficient from each surface to the zone air and thus decouples radiant exchange among surfaces in the zone. However, because the transparent air model allows radiant exchange and is more realistic, the second model is inferior.
Furniture in a zone increases the amount of surface area that can participate in radiative and convective heat exchanges. It also adds thermal mass to the zone. These two changes can affect the time response of the zone cooling load.
SW Radiation from Lights. The short-wavelength radiation from lights is usually assumed to be distributed over the surfaces in the zone in some manner. The HB procedure retains this approach but allows the distribution function to be changed.
LW Radiation from Internal Sources. The traditional model for this source defines a radiative/convective split for heat introduced into a zone from equipment. The radiative part is then distributed over the zone’s surfaces in some manner. This model is not completely realistic, and it departs from HB principles. In a true HB model, equipment surfaces are treated just as other LW radiant sources in the zone. However, because information about the surface temperature of equipment is rarely known, it is reasonable to keep the radiative/convective split concept even though it ignores the true nature of the radiant exchange. ASHRAE research project RP-1055 (Hosni et al. 1999) determined radiative/convective splits for many additional equipment types, as listed in footnotes for Tables 8 and 9.
Transmitted Solar Heat Gain. Chapter 15’s calculation procedure for determining transmitted solar energy through fenestration uses the solar heat gain coefficient (SHGC) directly rather than relating it to double-strength glass, as is done when using a shading coefficient (SC). The difficulty with this plan is that the SHGC includes both transmitted solar and inward-flowing fraction of the solar radiation absorbed in the window. With the HB method, this latter part should be added to the conduction component so it can be included in the indoor-face heat balance.
Transmitted solar radiation is also distributed over surfaces in the zone in a prescribed manner. It is possible to calculate the actual position of beam solar radiation, but this involves partial surface irradiation, which is inconsistent with the rest of the zone model, which assumes uniform conditions over an entire surface.
Using SHGC to Calculate Solar Heat Gain
The total solar heat gain through fenestration consists of directly transmitted solar radiation plus the inward-flowing fraction of solar radiation that is absorbed in the glazing system. Both parts contain beam and diffuse contributions. Transmitted radiation goes directly onto surfaces in the zone and is accounted for in the surface indoor heat balance. The zone heat balance model accommodates the resulting heat fluxes without difficulty. The second part, the inward-flowing fraction of the absorbed solar radiation, interacts with other surfaces of the enclosure through long-wave radiant exchange and with zone air through convective heat transfer. As such, it depends both on geometric and radiative properties of the zone enclosure and convection characteristics inside and outside the zone. The solar heat gain coefficient (SHGC) combines the transmitted solar radiation and the inward-flowing fraction of the absorbed radiation. The SHGC is defined as
where
| τ | = | solar transmittance of glazing |
| αk | = | solar absorptance of the k th layer of the glazing system |
| n | = | number of layers |
| Nk | = | inward-flowing fraction of absorbed radiation in the kth layer |
Note that Equation (18) is written generically. It can be written for a specific incidence angle and/or radiation wavelength and integrated over the wavelength and/or angle, but the principle is the same in each case. Refer to Chapter 15 for the specific expressions.
Unfortunately, the inward-flowing fraction N interacts with the zone in many ways. This interaction can be expressed as
| N | = | f (indoor convection coefficient, outdoor convection coefficient, glazing system overall heat transfer coefficient, zone geometry, zone radiation properties) |
The only way to model these interactions correctly is to combine the window model with the zone heat balance model and solve both simultaneously. This has been done recently in some energy analysis programs, but is not generally available in load calculation procedures. In addition, the SHGC used for rating glazing systems is based on specific values of the indoor, outdoor, and overall heat transfer coefficients and does not include any zonal long-wavelength radiation considerations. So, the challenge is to devise a way to use SHGC values within the framework of heat balance calculation in the most accurate way possible, as discussed in the following paragraphs.
Using SHGC Data. The normal incidence SHGC used to rate and characterize glazing systems is not sufficient for determining solar heat gain for load calculations. These calculations require solar heat gain as a function of the incident solar angle to determine the hour-by-hour gain profile. Thus, it is necessary to use angular SHGC values and also diffuse SHGC values. These can be obtained from the WINDOW 7.4.6 program (LBL 2015). This program does a detailed optical and thermal simulation of a glazing system and, when applied to a single clear layer, produces the information shown in Table 13.
Table 13 shows the parameters as a function of incident solar angle and also the diffuse values. The specific parameters shown are
| Vtc | = | transmittance in visible spectrum |
| Rfv and Rbv | = | front and back surface visible reflectances |
| Tsol | = | solar transmittance [τ in Equations (18), (19), and (20)] |
| Rf and Rb | = | front and back surface solar reflectances |
| Abs1 | = | solar absorptance for layer 1, which is the only layer in this case [α in Equations (18), (19), and (20)] |
| SHGC | = | solar heat gain coefficient at center of glazing |
The parameters used for heat gain calculations are Tsol, Abs, and SHGC. For the specific convective conditions assumed in WINDOW 7.4.6 program, the inward-flowing fraction of the absorbed solar can be obtained by rearranging Equation (18) to give
This quantity, when multiplied by the appropriate incident solar intensity, provides the amount of absorbed solar radiation that flows inward. In the heat balance formulation for zone loads, this heat flux is combined with that caused by conduction through glazing and included in the surface heat balance.
The outward-flowing fraction of absorbed solar radiation is used in the heat balance on the outdoor face of the glazing and is determined from
If there is more than one layer, the appropriate summation of absorptances must be done.
There is some potential inaccuracy in using the WINDOW 7.4.6 SHGC values because the inward-flowing fraction part was determined under specific conditions for the indoor and outdoor heat transfer coefficients. However, the program can be run with indoor and outdoor coefficients of one’s own choosing. Normally, however, this effect is not large, and only in highly absorptive glazing systems might cause significant error.
For solar heat gain calculations, then, it seems reasonable to use the generic window property data that comes from WINDOW 7.4.6. Considering Table 13, the procedure is as follows:
Determine angle of incidence for the glazing.
Determine corresponding SHGC.
Evaluate Nkαk using Equation (18).
Multiply Tsol by incident beam radiation intensity to get transmitted beam solar radiation.
Multiply Nkαk by incident beam radiation intensity to get inward-flowing absorbed heat.
Repeat steps 2 to 5 with diffuse parameters and diffuse radiation.
Add beam and diffuse components of transmitted and inward-flowing absorbed heat.
This procedure is incorporated into the HB method so the solar gain is calculated accurately for each hour.
Table 10 in Chapter 15 contains SHGC information for many additional glazing systems. That table is similar to Table 13 but is slightly abbreviated. Again, the information needed for heat gain calculations is Tsol, SHGC, and Abs.
The same caution about the indoor and outdoor heat transfer coefficients applies to the information in Table 10 in Chapter 15. Those values were also obtained with specific indoor and outdoor heat transfer coefficients, and the inward-flowing fraction N is dependent upon those values.
Convection to Zone Air. Indoor convection coefficients presented in past editions of this chapter and used in most load calculation procedures and energy programs are based on very old, natural convection experiments and do not accurately describe heat transfer coefficients in a mechanically ventilated zone. In previous load calculation procedures, these coefficients were buried in the procedures and could not be changed. A heat balance formulation keeps them as working parameters. In this way, research results such as those from ASHRAE research project RP-664 (Fisher 1998) can be incorporated into the procedures. It also allows determining the sensitivity of the load calculation to these parameters.
In HB formulations aimed at determining cooling loads, the capacitance of air in the zone is neglected and the air heat balance is done as a quasisteady balance in each time period. Four factors contribute to the air heat balance:
where
| qconv | = | convective heat transfer from surfaces, Btu/h |
| qCE | = | convective parts of internal loads, Btu/h |
| qIV | = | sensible load caused by infiltration and ventilation air, Btu/h |
| qsys | = | heat transfer to/from HVAC system, Btu/h |
Convection from zone surfaces qconv is the sum of all the convective heat transfer quantities from the indoor-surface heat balance. This comes to the air through the convective heat transfer coefficient on the surfaces.
The convective parts of the internal loads qCE is the companion to q˝LWS, the radiant contribution from internal loads [Equation (17)]. It is added directly to the air heat balance. This also violates the tenets of the HB approach, because surfaces producing internal loads exchange heat with zone air through normal convective processes. However, once again, this level of detail is generally not included in the heat balance, so it is included directly into the air heat balance instead.
In keeping with the well-mixed model for zone air, any air that enters directly to a space through infiltration or ventilation qIV is immediately mixed with the zone’s air. The amount of infiltration or natural ventilation air is uncertain. Sometimes it is related to the indoor/outdoor temperature difference and wind speed; however it is determined, it is added directly to the air heat balance.
Conditioned air that enters the zone from the HVAC system and provides qsys is also mixed directly with the zone air. For commercial HVAC systems, ventilation air is most often provided using outdoor air as part of this mixed-in conditioned air; ventilation air is thus normally a system load rather than a direct-to-space load. An exception is where infiltration or natural ventilation is used to provide all or part of the ventilation air, as discussed in Chapter 16.
5.3 GENERAL ZONE FOR LOAD CALCULATION
The HB procedure is tailored to a single thermal zone, shown in Figure 7. The definition of a thermal zone depends on how the fixed temperature is controlled. If air circulated through an entire building or an entire floor is uniformly well stirred, the entire building or floor could be considered a thermal zone. On the other hand, if each room has a different control scheme, each room may need to be considered as a separate thermal zone. The framework needs to be flexible enough to accommodate any zone arrangement, but the heat balance aspect of the procedure also requires that a complete zone be described. This zone consists of four walls, a roof or ceiling, a floor, and a “thermal mass surface” (described in the section on Input Required). Each wall and the roof can include a window (or skylight in the case of the roof). This makes a total of 12 surfaces, any of which may have zero area if it is not present in the zone to be modeled.
The heat balance processes for this general zone are formulated for a 24 h steady-periodic condition. The variables are the indoor and outdoor temperatures of the 12 surfaces plus either the HVAC system energy required to maintain a specified air temperature or the air temperature, if system capacity is specified. This makes a total of 25 × 24 = 600 variables. Although it is possible to set up the problem for a simultaneous solution of these variables, the relatively weak coupling of the problem from one hour to the next allows a double iterative approach. One iteration is through all the surfaces in each hour, and the other is through the 24 h of a day. This procedure automatically reconciles nonlinear aspects of surface radiative exchange and other heat flux terms.
5.4 MATHEMATICAL DESCRIPTION
Because it links the outdoor and indoor heat balances, the wall conduction process regulates the cooling load’s time dependence. For the HB procedure presented here, wall conduction is formulated using conduction transfer functions (CTFs), which relate conductive heat fluxes to current and past surface temperatures and past heat fluxes. The general form for the indoor heat flux is
For outdoor heat flux, the form is
where
| Xj | = | outdoor CTF, j = 0,1, …nz |
| Yj | = | cross CTF, j = 0,1, …nz |
| Zj | = | indoor CTF, j = 0,1, …nz |
| Φj | = | flux CTF, j = 1,2, …nq |
| θ | = | time |
| δ | = | time step |
| Tsi | = | indoor-face temperature, °F |
| Tso | = | outdoor-face temperature, °F |
| q˝ki | = | conductive heat flux on indoor face, Btu/h · ft2 |
| q˝ko | = | conductive heat flux on outdoor face, Btu/h · ft2 |
The subscript following the comma indicates the time period for the quantity in terms of time step δ. Also, the first terms in the series have been separated from the rest to facilitate solving for the current temperature in the solution scheme.
The two summation limits nz and nq depend on wall construction and also somewhat on the scheme used for calculating the CTFs. If nq = 0, the CTFs are generally referred to as response factors, but then theoretically nz is infinite. Values for nz and nq are generally set to minimize the amount of computation. A development of CTFs can be found in Hittle and Pedersen (1981).
The primary variables in the heat balance for the general zone are the 12 indoor face temperatures and the 12 outdoor face temperatures at each of the 24 h, assigning i as the surface index and j as the hour index, or, in the case of CTFs, the sequence index. Thus, the primary variables are
In addition, qsysj = cooling load, j = 1,2, …, 24.
Equations (16) and (23) are combined and solved for Tso to produce 12 equations applicable in each time step:
where
| To | = | outdoor air temperature |
| hco | = | outdoor convection coefficient, introduced by using q˝conv = hco(To – Tso) |
Equation (24) shows the need to separate Zi,0, because the contribution of current surface temperature to conductive flux can be collected with the other terms involving that temperature.
Equations (17) and (22) are combined and solved for Tsi to produce the next 12 equations:
where
| Ta | = | zone air temperature |
| hci | = | convective heat transfer coefficient indoors, obtained from q˝conv = hci (Ta – Tsi) |
Note that in Equations (24) and (25), the opposite surface temperature at the current time appears on the right-hand side. The two equations could be solved simultaneously to eliminate those variables. Depending on the order of updating the other terms in the equations, this can have a beneficial effect on solution stability.
The remaining equation comes from the air heat balance, Equation (21). This provides the cooling load qsys at each time step:
In Equation (26), the convective heat transfer term is expanded to show the interconnection between the surface temperatures and the cooling load.
Overall HB Iterative Solution
The iterative HB procedure consists of a series of initial calculations that proceed sequentially, followed by a double iteration loop, as shown in the following steps:
Initialize areas, properties, and face temperatures for all surfaces, 24 h.
Calculate incident and transmitted solar flux for all surfaces and hours.
Distribute transmitted solar energy to all indoor faces, 24 h.
Calculate internal load quantities for all 24 h.
Distribute LW, SW, and convective energy from internal loads to all surfaces for all hours.
Calculate infiltration and direct-to-space ventilation loads for all hours.
Iterate the heat balance according to the following scheme:
Display results.
Generally, four or six surface iterations are sufficient to provide convergence. The convergence check on the day iteration should be based on the difference between the indoor and outdoor conductive heat flux terms qk. A limit, such as requiring the difference between all indoor and outdoor flux terms to be less than 1% of either flux, works well.
Previous methods for calculating cooling loads attempted to simplify the procedure by precalculating representative cases and grouping the results with various correlating parameters. This generally tended to reduce the amount of information required to apply the procedure. With heat balance, no precalculations are made, so the procedure requires a fairly complete description of the zone.
Global Information. Because the procedure incorporates a solar calculation, some global information is required, including latitude, longitude, time zone, month, day of month, directional orientation of the zone, and zone height (floor to floor). Additionally, to take full advantage of the flexibility of the method to incorporate, for example, variable outdoor heat transfer coefficients, things such as wind speed, wind direction, and terrain roughness may be specified. Normally, these variables and others default to some reasonable set of values, but the flexibility remains.
Wall Information (Each Wall). Because the walls are involved in three of the fundamental processes (external and internal heat balance and wall conduction), each wall of the zone requires a fairly large set of variables. They include
Facing angle with respect to solar exposure
Tilt (degrees from horizontal)
Area
Solar absorptivity outdoors
Long-wave emissivity outdoors
Short-wave absorptivity indoors
Long-wave emissivity indoors
Exterior boundary temperature condition (solar versus nonsolar)
External roughness
Layer-by-layer construction information
Again, some of these parameters can be defaulted, but they are changeable, and they indicate the more fundamental character of the HB method because they are related to true heat transfer processes.
Window Information (Each Window). The situation for windows is similar to that for walls, but the windows require some additional information because of their role in the solar load. Necessary parameters include
Area
Normal solar transmissivity
Normal SHGC
Normal total absorptivity
Long-wave emissivity outdoors
Long-wave emissivity indoor
Surface-to-surface thermal conductance
Reveal (for solar shading)
Overhang width (for solar shading)
Distance from overhang to window (for solar shading)
Roof and Floor Details. The roof and floor surfaces are specified similarly to walls. The main difference is that the ground outdoor boundary condition will probably be specified more often for a floor.
Thermal Mass Surface Details. An “extra” surface, called a thermal mass surface, can serve several functions. It is included in radiant heat exchange with the other surfaces in the space but is only exposed to the indoor air convective boundary condition. As an example, this surface would be used to account for movable partitions in a space. Partition construction is specified layer by layer, similar to specification for walls, and those layers store and release heat by the same conduction mechanism as walls. As a general definition, the extra thermal mass surface should be sized to represent all surfaces in the space that are exposed to the air mass, except the walls, roof, floor, and windows. In the formulation, both sides of the thermal mass participate in the exchange.
Internal Heat Gain Details. The space can be subjected to several internal heat sources: people, lights, electrical equipment, and infiltration. Infiltration energy is assumed to go immediately into the air heat balance, so it is the least complicated of the heat gains. For the others, several parameters must be specified. These include the following fractions:
Radiant Distribution Functions. As mentioned previously, the generally accepted assumptions for the HB method include specifying the distribution of radiant energy from several sources to surfaces that enclose the space. This requires a distribution function that specifies the fraction of total radiant input absorbed by each surface. The types of radiation that require distribution functions are
Other Required Information. Additional flexibility is included in the model so that results of research can be incorporated easily. This includes the capability to specify such things as
The amount of input information required may seem extensive, but many parameters can be set to default values in most routine applications. However, all parameters listed can be changed when necessary to fit unusual circumstances or when additional information is obtained.
6. RADIANT TIME SERIES (RTS) METHOD
The radiant time series (RTS) method is a simplified method for performing design cooling load calculations that is derived from the heat balance (HB) method. It effectively replaces all other simplified (non-heat-balance) methods, such as the transfer function method (TFM), the cooling load temperature difference/cooling load factor (CLTD/CLF) method, and the total equivalent temperature difference/time averaging (TETD/TA) method.
This method was developed to offer an approach that is rigorous, yet does not require iterative calculations, and that quantifies each component’s contribution to the total cooling load. In addition, it is desirable for the user to be able to inspect and compare the coefficients for different construction and zone types in a form showing their relative effect on the result. These characteristics of the RTS method make it easier to apply engineering judgment during cooling load calculation.
The RTS method is suitable for peak design load calculations, but it should not be used for annual energy simulations because of its inherent limiting assumptions. Although simple in concept, RTS involves too many calculations for practical use as a manual method, although it can easily be implemented in a simple computerized spreadsheet, as shown in the examples. For a manual cooling load calculation method, refer to the CLTD/CLF method in Chapter 28 of the 1997 ASHRAE Handbook—Fundamentals.
6.1 ASSUMPTIONS AND PRINCIPLES
Design cooling loads are based on the assumption of steady-periodic conditions (i.e., the design day’s weather, occupancy, and heat gain conditions are identical to those for preceding days such that the loads repeat on an identical 24 h cyclical basis). Thus, the heat gain for a particular component at a particular hour is the same as 24 h prior, which is the same as 48 h prior, etc. This assumption is the basis for the RTS derivation from the HB method.
Cooling load calculations must address two time-delay effects inherent in building heat transfer processes:
Delay of conductive heat gain through opaque massive exterior surfaces (walls, roofs, or floors)
Delay of radiative heat gain conversion to cooling loads.
Exterior walls and roofs conduct heat because of temperature differences between outdoor and indoor air. In addition, solar energy on exterior surfaces is absorbed, then transferred by conduction to the building interior. Because of the mass and thermal capacity of the wall or roof construction materials, there is a substantial time delay in heat input at the exterior surface becoming heat gain at the interior surface.
As described in the section on Cooling Load Principles, most heat sources transfer energy to a room by a combination of convection and radiation. The convective part of heat gain immediately becomes cooling load. The radiative part must first be absorbed by the finishes and mass of the interior room surfaces, and becomes cooling load only when it is later transferred by convection from those surfaces to the room air. Thus, radiant heat gains become cooling loads over a delayed period of time.
Figure 8 gives an overview of the RTS method. When calculating solar radiation, transmitted solar heat gain through windows, sol-air temperature, and infiltration, RTS is exactly the same as previous simplified methods (TFM and TETD/TA). Important areas that differ from previous simplified methods include
Computation of conductive heat gain
Splitting of all heat gains into radiant and convective portions
Conversion of radiant heat gains into cooling loads
The RTS method accounts for both conduction time delay and radiant time delay effects by multiplying hourly heat gains by 24 h time series. The time series multiplication, in effect, distributes heat gains over time. Series coefficients, which are called radiant time factors and conduction time factors, are derived using the HB method. Radiant time factors reflect the percentage of an earlier radiant heat gain that becomes cooling load during the current hour. Likewise, conduction time factors reflect the percentage of an earlier heat gain at the exterior of a wall or roof that becomes heat gain indoors during the current hour. By definition, each radiant or conduction time series must total 100%.
These series can be used to easily compare the time-delay effect of one construction versus another. This ability to compare choices is of particular benefit during design, when all construction details may not have been decided. Comparison can show the magnitude of difference between the choices, allowing the engineer to apply judgment and make more informed assumptions in estimating the load.
Figure 9 shows conduction time series (CTS) values for three walls with similar U-factors but with light to heavy construction. Figure 10 shows CTS for three walls with similar construction but with different amounts of insulation, thus with significantly different U-factors. Figure 11 shows RTS values for zones varying from light to heavy construction.
The general procedure for calculating cooling load for each load component (lights, people, walls, roofs, windows, appliances, etc.) with RTS is as follows:
Calculate 24 h profile of component heat gains for design day (for conduction, first account for conduction time delay by applying conduction time series).
Split heat gains into radiant and convective parts (see Table 14 for radiant and convective fractions).
Apply appropriate radiant time series to radiant part of heat gains to account for time delay in conversion to cooling load.
Sum convective part of heat gain and delayed radiant part of heat gain to determine cooling load for each hour for each cooling load component.
After calculating cooling loads for each component for each hour, sum those to determine the total cooling load for each hour and select the hour with the peak load for design of the air-conditioning system. Repeat this process for multiple design months to determine the month when the peak load occurs, especially with windows on southern exposures (northern exposure in southern latitudes), which can result in higher peak room cooling loads in winter months than in summer.
6.4 HEAT GAIN THROUGH EXTERIOR SURFACES
Heat gain through exterior opaque surfaces is derived from the same elements of solar radiation and thermal gradient as that for fenestration areas. It differs primarily as a function of the mass and nature of the wall or roof construction, because those elements affect the rate of conductive heat transfer through the composite assembly to the interior surface.
Sol-air temperature is the outdoor air temperature that, in the absence of all radiation changes gives the same rate of heat entry into the surface as would the combination of incident solar radiation, radiant energy exchange with the sky and other outdoor surroundings, and convective heat exchange with outdoor air.
Heat Flux into Exterior Sunlit Surfaces. The heat balance at a sunlit surface gives the heat flux into the surface q/A as
where
| α | = | absorptance of surface for solar radiation |
| Et | = | total solar radiation incident on surface, Btu/h · ft2 |
| ho | = | coefficient of heat transfer by long-wave radiation and convection at outer surface, Btu/h · ft2 · °F |
| to | = | outdoor air temperature, °F |
| ts | = | surface temperature, °F |
| ε | = | hemispherical emittance of surface |
| ΔR | = | difference between long-wave radiation incident on surface from sky and surroundings and radiation emitted by blackbody at outdoor air temperature, Btu/h · ft2 |
Assuming the rate of heat transfer can be expressed in terms of the sol-air temperature te ,
and from Equations (27) and (28),
For horizontal surfaces that receive long-wave radiation from the sky only, an appropriate value of ΔR is about 20 Btu/h · ft2, so that if ε = 1 and ho = 3.0 Btu/h · ft2 · °F, the long-wave correction term is about 7°F (Bliss 1961).
Because vertical surfaces receive long-wave radiation from the ground and surrounding buildings as well as from the sky, accurate ΔR values are difficult to determine. When solar radiation intensity is high, surfaces of terrestrial objects usually have a higher temperature than the outdoor air; thus, their long-wave radiation compensates to some extent for the sky’s low emittance. Therefore, it is common practice to assume ε Δ R = 0 for vertical surfaces.
Tabulated Temperature Values. The sol-air temperatures in Example Cooling and Heating Load Calculations section have been calculated based on ε Δ R/ho values of 7°F for horizontal surfaces and 0°F for vertical surfaces; total solar intensity values used for the calculations were calculated using equations in Chapter 14.
Surface Colors. Sol-air temperature values are given in the Example Cooling and Heating Load Calculations section for two values of the parameter α/ho; the value of 0.15 is appropriate for a light-colored surface, whereas 0.30 represents the usual maximum value for this parameter (i.e., for a dark-colored surface or any surface for which the permanent lightness cannot reliably be anticipated). Solar absorptance values of various surfaces are included in Table 15.
This procedure was used to calculate the sol-air temperatures included in the Examples section. Because of the tedious solar angle and intensity calculations, using a simple computer spreadsheet or other software for these calculations can reduce the effort involved.
Calculating Conductive Heat Gain Using Conduction Time Series
In the RTS method, conduction through exterior walls and roofs is calculated using CTS values. Wall and roof conductive heat input at the exterior is defined by the familiar conduction equation as
where
| qi,θ−n | = | conductive heat input for surface n hours ago, Btu/h |
| U | = | overall heat transfer coefficient for surface, Btu/h · ft2 · °F |
| A | = | surface area, ft2 |
| te,θ-n | = | sol-air temperature n hours ago, °F |
| trc | = | presumed constant room air temperature, °F |
Conductive heat gain through walls or roofs can be calculated using conductive heat inputs for the current hours and past 23 h and conduction time series:
where
| qθ | = | hourly conductive heat gain for surface, Btu/h |
| qi,θ | = | heat input for current hour |
| qi,θ-n | = | heat input n hours ago |
| c0, c1, etc. | = | conduction time factors |
Conduction time factors for representative wall and roof types are included in Tables 16 and 17. Those values were derived by first calculating conduction transfer functions for each example wall and roof construction. Assuming steady-periodic heat input conditions for design load calculations allows conduction transfer functions to be reformulated into periodic response factors, as demonstrated by Spitler and Fisher (1999a). The periodic response factors were further simplified by dividing the 24 periodic response factors by the respective overall wall or roof U-factor to form the conduction time series. The conduction time factors can then be used in Equation (31) and provide a way to compare time delay characteristics between different wall and roof constructions. Construction material data used in the calculations for walls and roofs in Tables 16 and 17 are listed in Table 18.
Heat gains calculated for walls or roofs using periodic response factors (and thus CTS) are identical to those calculated using conduction transfer functions for the steady periodic conditions assumed in design cooling load calculations. The methodology for calculating periodic response factors from conduction transfer functions was originally developed as part of ASHRAE research project RP-875 (Spitler and Fisher 1999b; Spitler et al. 1997). For walls and roofs that are not reasonably close to the representative constructions in Tables 16 and 17, CTS coefficients may be computed with a computer program such as that described by Iu and Fisher (2004). For walls and roofs with thermal bridges, the procedure described by Karambakkam et al. (2005) may be used to determine an equivalent wall construction, which can then be used as the basis for finding the CTS coefficients. When considering the level of detail needed to make an adequate approximation, remember that, for buildings with windows and internal heat gains, the conduction heat gains make up a relatively small part of the cooling load. For heating load calculations, the conduction heat loss may be more significant.
The tedious calculations involved make a simple computer spreadsheet or other computer software a useful labor saver.
6.5 HEAT GAIN THROUGH INTERIOR SURFACES
Whenever a conditioned space is adjacent to a space with a different temperature, heat transfer through the separating physical section must be considered. The heat transfer rate is given by
where
| q | = | heat transfer rate, Btu/h |
| U | = | coefficient of overall heat transfer between adjacent and conditioned space, Btu/h · ft2 · °F |
| A | = | area of separating section concerned, ft2 |
| tb | = | average air temperature in adjacent space, °F |
| ti | = | air temperature in conditioned space, °F |
U-values can be obtained from Chapter 27. Temperature tb may differ greatly from ti. The temperature in a kitchen or boiler room, for example, may be as much as 15 to 50°F above the outdoor air temperature. Actual temperatures in adjoining spaces should be measured, when possible. Where nothing is known except that the adjacent space is of conventional construction, contains no heat sources, and itself receives no significant solar heat gain, tb – ti may be considered the difference between the outdoor air and conditioned space design dry-bulb temperatures minus 5°F. In some cases, air temperature in the adjacent space corresponds to the outdoor air temperature or higher.
For floors directly in contact with the ground or over an underground basement that is neither ventilated nor conditioned, sensible heat transfer may be neglected for cooling load estimates because usually there is a heat loss rather than a gain. An exception is in hot climates (i.e., where average outdoor air temperature exceeds indoor design condition), where the positive soil-to-indoor temperature difference causes sensible heat gains (Rock 2005). In many climates and for various temperatures and local soil conditions, moisture transport up through slabs-on-grade and basement floors is also significant, and contributes to the latent heat portion of the cooling load.
6.6 CALCULATING COOLING LOAD
The instantaneous cooling load is the rate at which heat energy is convected to the zone air at a given point in time. Computation of cooling load is complicated by the radiant exchange between surfaces, furniture, partitions, and other mass in the zone. Most heat gain sources transfer energy by both convection and radiation. Radiative heat transfer introduces a time dependency to the process that is not easily quantified. Radiation is absorbed by thermal masses in the zone and then later transferred by convection into the space. This process creates a time lag and dampening effect. The convective portion, on the other hand, is assumed to immediately become cooling load in the hour in which that heat gain occurs.
Heat balance procedures calculate the radiant exchange between surfaces based on their surface temperatures and emissivities, but they typically rely on estimated “radiative/convective splits” to determine the contribution of internal loads, including people, lighting, appliances, and equipment, to the radiant exchange. RTS further simplifies the HB procedure by also relying on an estimated radiative/convective split of wall and roof conductive heat gain instead of simultaneously solving for the instantaneous convective and radiative heat transfer from each surface, as in the HB procedure.
Thus, the cooling load for each load component (lights, people, walls, roofs, windows, appliances, etc.) for a particular hour is the sum of the convective portion of the heat gain for that hour plus the time-delayed portion of radiant heat gains for that hour and the previous 23 h. Table 14 contains recommendations for splitting each of the heat gain components into convective and radiant portions.
RTS converts the radiant portion of hourly heat gains to hourly cooling loads using radiant time factors, the coefficients of the radiant time series. Radiant time factors are used to calculate the cooling load for the current hour on the basis of current and past heat gains. The radiant time series for a particular zone gives the time-dependent response of the zone to a single pulse of radiant energy. The series shows the portion of the radiant pulse that is convected to zone air for each hour. Thus, r0 represents the fraction of the radiant pulse convected to the zone air in the current hour r1 in the previous hour, and so on. The radiant time series thus generated is used to convert the radiant portion of hourly heat gains to hourly cooling loads according to the following equation:
where
| Qr,θ |
= |
radiant cooling load Qr for current hour θ, Btu/h |
| qr,θ |
= |
radiant heat gain for current hour, Btu/h |
| qr,θ–n |
= |
radiant heat gain n hours ago, Btu/h |
| r0, r1, etc. |
= |
radiant time factors |
The radiant cooling load for the current hour, which is calculated using RTS and Equation (33), is added to the convective portion to determine the total cooling load for that component for that hour.
Radiant time factors are generated by a heat-balance-based procedure. A separate series of radiant time factors is theoretically required for each unique zone and for each unique radiant energy distribution function assumption. For most common design applications, RTS variation depends primarily on the overall massiveness of the construction and the thermal responsiveness of the surfaces the radiant heat gains strike.
One goal in developing RTS was to provide a simplified method based directly on the HB method; thus, it was deemed desirable to generate RTS coefficients directly from a heat balance. A heat balance computer program was developed to do this: Hbfort, which is included as part of Cooling and Heating Load Calculation Principles (Pedersen et al. 1998). The RTS procedure is described by Spitler et al. (1997). The procedure for generating RTS coefficients may be thought of as analogous to the custom weighting factor generation procedure used by DOE 2.1 (Kerrisk et al. 1981; Sowell 1988a, 1988b). In both cases, a zone model is pulsed with a heat gain. With DOE 2.1, the resulting loads are used to estimate the best values of the transfer function method weighting factors to most closely match the load profile. In the procedure described here, a unit periodic heat gain pulse is used to generate loads for a 24 h period. As long as the heat gain pulse is a unit pulse, the resulting loads are equivalent to the RTS coefficients.
Two different radiant time series are used: solar, for direct transmitted solar heat gain (radiant energy assumed to be distributed to the floor and furnishings only) and nonsolar, for all other types of heat gains (radiant energy assumed to be uniformly distributed on all internal surfaces). Nonsolar RTS apply to radiant heat gains from people, lights, appliances, walls, roofs, and floors. Also, for diffuse solar heat gain and direct solar heat gain from fenestration with indoor shading (blinds, drapes, etc.), the nonsolar RTS should be used. Radiation from those sources is assumed to be more uniformly distributed onto all room surfaces. Effect of beam solar radiation distribution assumptions is addressed by Hittle (1999).
Representative solar and nonsolar RTS data for light, medium, and heavyweight constructions are provided in Tables 19 and 20. Those were calculated using the Hbfort computer program (Pedersen et al. 1998) with zone characteristics listed in Table 21. Customized RTS values may be calculated using the HB method where the zone is not reasonably similar to these typical zones or where more precision is desired.
ASHRAE research project RP-942 compared HB and RTS results over a wide range of zone types and input variables (Rees et al. 2000; Spitler et al. 1998). In general, total cooling loads calculated using RTS closely agreed with or were slightly higher than those of the HB method with the same inputs. The project examined more than 5000 test cases of varying zone parameters. The dominating variable was overall thermal mass, and results were grouped into lightweight, U.S. medium-weight, U.K. medium-weight, and heavyweight construction. Best agreement between RTS and HB results was obtained for light- and medium-weight construction. Greater differences occurred in heavyweight cases, with RTS generally predicting slightly higher peak cooling loads than HB. Greater differences also were observed in zones with extremely high internal radiant loads and large glazing areas or with a very lightweight exterior envelope. In this case, heat balance calculations predict that some of the internal radiant load will be transmitted to the outdoor environment and never becomes cooling load in the space. RTS does not account for energy transfer out of the space to the environment, and thus predicted higher cooling loads.
ASHRAE research project RP-1117 built two model rooms for which cooling loads were physically measured using extensive instrumentation. The results agreed with previous simulations (Chantrasrisalai et al. 2003; Eldridge et al. 2003; Iu et al. 2003). HB calculations closely approximated measured cooling loads when provided with detailed data for the test rooms. RTS overpredicted measured cooling loads in tests with large, clear, single-glazed window areas with bare concrete floor and no furnishings or internal loads. Tests under more typical conditions (venetian blinds, carpeted floor, office-type furnishings, and normal internal loads) provided good agreement between HB, RTS, and measured loads.
7. HEATING LOAD CALCULATIONS
Techniques for estimating design heating load for commercial, institutional, and industrial applications are essentially the same as for those estimating design cooling loads for such uses, with the following exceptions:
Temperatures outdoor conditioned spaces are generally lower than maintained space temperatures.
Credit for solar or internal heat gains is not included
Thermal storage effect of building structure or content is ignored.
Thermal bridging effects on wall and roof conduction are greater for heating loads than for cooling loads, and greater care must be taken to account for bridging effects on U-factors used in heating load calculations.
Heat losses (negative heat gains) are thus considered to be instantaneous, heat transfer essentially conductive, and latent heat treated only as a function of replacing space humidity lost to the exterior environment.
This simplified approach is justified because it evaluates worst-case conditions that can reasonably occur during a heating season. Therefore, the near-worst-case load is based on the following:
Design interior and exterior conditions
Including infiltration and/or ventilation
No solar effect (at night or on cloudy winter days)
Before the periodic presence of people, lights, and appliances has an offsetting effect
Typical commercial and retail spaces have nighttime unoccupied periods at a setback temperature where little to no ventilation is required, building lights and equipment are off, and heat loss is primarily through conduction and infiltration. Before being occupied, buildings are warmed to the occupied temperature (see the following discussion). During occupied time, building lights, equipment, and people cooling loads can offset conduction heat loss, although some perimeter heat may be required, leaving infiltration and ventilation as the primary heating loads. Ventilation heat load may be offset with heat recovery equipment. These loads (conduction loss, warm-up load, and ventilation load) may not be additive when sizing building heating equipment, and it is prudent to analyze each load and their interactions to arrive at final equipment sizing for heating.
7.1 HEAT LOSS CALCULATIONS
The general procedure for calculation of design heat losses of a structure is as follows:
Select outdoor design conditions: temperature, humidity, and wind direction and speed.
Select indoor design conditions to be maintained.
Estimate temperature in any adjacent unheated spaces.
Select transmission coefficients and compute heat losses for walls, floors, ceilings, windows, doors, and foundation elements.
Compute heat load through infiltration and any other outdoor air introduced directly to the space.
Sum the losses caused by transmission and infiltration.
Outdoor Design Conditions
The ideal heating system provides enough heat to match the structure’s heat loss. However, weather conditions vary considerably from year to year, and heating systems designed for the worst weather conditions on record would have a great excess of capacity most of the time. A system’s failure to maintain design conditions during brief periods of severe weather usually is not critical. However, close regulation of indoor temperature may be critical for some occupancies or industrial processes. Design temperature data and discussion of their application are given in Chapter 14. Generally, the 99% temperature values given in the tabulated weather data are used. However, caution is needed, and local conditions should always be investigated. In some locations, outdoor temperatures are commonly much lower and wind velocities higher than those given in the tabulated weather data.
The main purpose of the heating system is to maintain indoor conditions that make most of the occupants comfortable. Keep in mind, however, that the purpose of heating load calculations is to obtain data for sizing the heating system components. In many cases, the system will rarely be called upon to operate at the design conditions. Therefore, the use and occupancy of the space are general considerations from the design temperature point of view. Later, when the building’s energy requirements are computed, the actual conditions in the space and outdoor environment, including internal heat gains, must be considered.
The indoor design temperature should be selected at the lower end of the acceptable temperature range, so that the heating equipment will not be oversized. Even properly sized equipment operates under partial load, at reduced efficiency, most of the time; therefore, any oversizing aggravates this condition and lowers overall system efficiency. A maximum design dry-bulb temperature of 70°F is recommended for most occupancies. The indoor design value of relative humidity should be compatible with a healthful environment and the thermal and moisture integrity of the building envelope. A minimum relative humidity of 30% is recommended for most situations.
Calculation of Transmission Heat Losses
Exterior Surface Above Grade. All above-grade surfaces exposed to outdoor conditions (walls, doors, ceilings, fenestration, and raised floors) are treated identically, as follows:
where HF is the heating load factor in Btu/h · ft2.
Below-Grade Surfaces. An approximate method for estimating below-grade heat loss [based on the work of Latta and Boileau (1969)] assumes that the heat flow paths shown in Figure 12 can be used to find the steady-state heat loss to the ground surface, as follows:
where
| Uavg | = | average U-factor for below-grade surface from Equation (38) or (39), Btu/h · ft2·°F |
| tin | = | below-grade space air temperature, °F |
| tgr | = | design ground surface temperature from Equation (37), °F |
The effect of soil heat capacity means that none of the usual external design air temperatures are suitable values for tgr. Ground surface temperature fluctuates about an annual mean value by amplitude A, which varies with geographic location and surface cover. The minimum ground surface temperature, suitable for heat loss estimates, is therefore
where
| t̅gr | = | mean ground temperature, °F, estimated from the annual average air temperature or from well-water temperatures, shown in Figure 18 of Chapter 34 in the 2011 ASHRAE Handbook—HVAC Applications |
| A | = | ground surface temperature amplitude, °F, from Figure 13 for North America |
Figure 14 shows depth parameters used in determining Uavg. For walls, the region defined by z1 and z2 may be the entire wall or any portion of it, allowing partially insulated configurations to be analyzed piecewise.
The below-grade wall average U-factor is given by
where
| Uavg,bw | = | average U-factor for wall region defined by z1 and z2, Btu/h · ft2 · °F |
| ksoil | = | soil thermal conductivity, Btu/h · ft ·°F |
| Rother | = | total resistance of wall, insulation, and indoor surface resistance, h · ft2 · °F/Btu |
| z1, z2 | = | depths of top and bottom of wall segment under consideration, ft (Figure 14) |
The value of soil thermal conductivity k varies widely with soil type and moisture content. A typical value of 0.8 Btu/h · ft · °F has been used previously to tabulate U-factors, and Rother is approximately 1.47 h · ft2 · °F/Btu for uninsulated concrete walls. For these parameters, representative values for Uavg,bw are shown in Table 22.
The average below-grade floor U-factor (where the entire basement floor is uninsulated or has uniform insulation) is given by
where
| wb | = | basement width (shortest dimension), ft |
| zf | = | floor depth below grade, ft (see Figure 14) |
Representative values of Uavg,bf for uninsulated basement floors are shown in Table 23.
At-Grade Surfaces. Concrete slab floors may be (1) unheated, relying for warmth on heat delivered above floor level by the heating system, or (2) heated, containing heated pipes or ducts that constitute a radiant slab or portion of it for complete or partial heating of the house.
The simplified approach that treats heat loss as proportional to slab perimeter allows slab heat loss to be estimated for both unheated and heated slab floors:
where
| q | = | heat loss through perimeter, Btu/h |
| Fp | = | heat loss coefficient per foot of perimeter, Btu/h · ft · °F, Table 24 |
| p | = | perimeter (exposed edge) of floor, ft |
Surfaces Adjacent to Buffer Space. Heat loss to adjacent unconditioned or semiconditioned spaces can be calculated using a heating factor based on the partition temperature difference:
Infiltration of outdoor air through openings into a structure is caused by thermal forces, wind pressure, and negative pressure (planned or unplanned) with respect to the outdoors created by mechanical systems. Typically, in building design, if the mechanical systems are designed to maintain positive building pressure, infiltration need not be considered except in ancillary spaces such as entryways and loading areas.
Infiltration is treated as a room load and has both sensible and latent components. During winter, this means heat and humidity loss because cold, dry air must be heated to design temperature and moisture must be added to increase the humidity to design condition. Typically, during winter, controlling indoor humidity is not a factor and infiltration is reduced to a simple sensible component. Under cooling conditions, both sensible and latent components are added to the space load to be treated by the air conditioning system. Procedures for estimating the infiltration rate are discussed in Chapter 16. The infiltration rate is reduced to a volumetric flow rate at a known dry bulb/wet bulb condition. Along with indoor air condition, the following equations define the infiltration sensible and latent loads.
where
| cfm | = | volume flow rate of infiltrating air |
| cp | = | specific heat capacity of air, Btu/lbm · °F |
| v | = | specific volume of infiltrating air, ft3/lbm |
Assuming standard air conditions (59°F and sea-level conditions) for v and cp, Equation (43) may be written as
The infiltrating air also introduces a latent heating load given by
where
| Win | = | humidity ratio for indoor space air, lbw/lba |
| Wo | = | humidity ratio for outdoor air, lbw/lba |
| Dh | = | change in enthalpy to convert 1 lb water from vapor to liquid, Btu/lbw |
For standard air and nominal indoor comfort conditions, the latent load may be expressed as
The coefficients 1.10 in Equation (44) and 4840 in Equation (46) are given for standard conditions. They depend on temperature and altitude (and, consequently, pressure).
7.2 HEATING SAFETY FACTORS AND LOAD ALLOWANCES
Before mechanical cooling became common in the second half of the 1900s, and when energy was less expensive, buildings included much less insulation; large, operable windows; and generally more infiltration-prone assemblies than the energy-efficient and much tighter buildings typical of today. Allowances of 10 to 20% of the net calculated heating load for piping losses to unheated spaces, and 10 to 20% more for a warm-up load, were common practice, along with other occasional safety factors reflecting the experience and/or concern of the individual designer. Such measures are less conservatively applied today with newer construction. A combined warm-up/safety allowance of 20 to 25% is fairly common but varies depending on the particular climate, building use, and type of construction. Engineering judgment must be applied for the particular project. Armstrong et al. (1992a, 1992b) provide a design method to deal with warm-up and cooldown load.
7.3 OTHER HEATING CONSIDERATIONS
Calculation of design heating load estimates has essentially become a subset of the more involved and complex estimation of cooling loads for such spaces. Chapter 19 discusses using the heating load estimate to predict or analyze energy consumption over time. Special provisions to deal with particular applications are covered in the 2015 ASHRAE Handbook—HVAC Applications and the 2016 ASHRAE Handbook—HVAC Systems and Equipment.
The 1989 ASHRAE Handbook—Fundamentals was the last edition to contain a chapter dedicated only to heating load. Its contents were incorporated into this volume’s Chapter 17, which describes steady-state conduction and convection heat transfer and provides, among other data, information on losses through basement floors and slabs.
10. PREVIOUS COOLING LOAD CALCULATION METHODS
Procedures described in this chapter are the most current and scientifically derived means for estimating cooling load for a defined building space, but methods in earlier editions of the ASHRAE Handbook are valid for many applications. These earlier procedures are simplifications of the heat balance principles, and their use requires experience to deal with atypical or unusual circumstances. In fact, any cooling or heating load estimate is no better than the assumptions used to define conditions and parameters such as physical makeup of the various envelope surfaces, conditions of occupancy and use, and ambient weather conditions. Experience of the practitioner can never be ignored.
The primary difference between the HB and RTS methods and the older methods is the newer methods’ direct approach, compared to the simplifications necessitated by the limited computer capability available previously.
The transfer function method (TFM), for example, required many calculation steps. It was originally designed for energy analysis with emphasis on daily, monthly, and annual energy use, and thus was more oriented to average hourly cooling loads than peak design loads.
The total equivalent temperature differential method with time averaging (TETD/TA) has been a highly reliable (if subjective) method of load estimating since its initial presentation in the 1967 Handbook of Fundamentals. Originally intended as a manual method of calculation, it proved suitable only as a computer application because of the need to calculate an extended profile of hourly heat gain values, from which radiant components had to be averaged over a time representative of the general mass of the building involved. Because perception of thermal storage characteristics of a given building is almost entirely subjective, with little specific information for the user to judge variations, the TETD/TA method’s primary usefulness has always been to the experienced engineer.
The cooling load temperature differential method with solar cooling load factors (CLTD/CLF) attempted to simplify the two-step TFM and TETD/TA methods into a single-step technique that proceeded directly from raw data to cooling load without intermediate conversion of radiant heat gain to cooling load. A series of factors were taken from cooling load calculation results (produced by more sophisticated methods) as “cooling load temperature differences” and “cooling load factors” for use in traditional conduction (q = UA Δ t) equations. The results are approximate cooling load values rather than simple heat gain values. The simplifications and assumptions used in the original work to derive those factors limit this method’s applicability to those building types and conditions for which the CLTD/CLF factors were derived; the method should not be used beyond the range of applicability.
Although the TFM, TETD/TA, and CLTD/CLF procedures are not republished in this chapter, those methods are not invalidated or discredited. Experienced engineers have successfully used them in millions of buildings around the world. The accuracy of cooling load calculations in practice depends primarily on the availability of accurate information and the design engineer’s judgment in the assumptions made in interpreting the available data. Those factors have much greater influence on a project’s success than does the choice of a particular cooling load calculation method.
The primary benefit of HB and RTS calculations is their somewhat reduced dependency on purely subjective input (e.g., determining a proper time-averaging period for TETD/TA; ascertaining appropriate safety factors to add to the rounded-off TFM results; determining whether CLTD/CLF factors are applicable to a specific unique application). However, using the most up-to-date techniques in real-world design still requires judgment on the part of the design engineer and care in choosing appropriate assumptions, just as in applying older calculation methods.
ASHRAE members can access ASHRAE Journal articles and ASHRAE research project final reports at technologyportal.ashrae.org. Articles and reports are also available for purchase by nonmembers in the online ASHRAE Bookstore at www.ashrae.org/bookstore.
Abushakra, B., J.S. Haberl, and D.E. Claridge. 2004. Overview of literature on diversity factors and schedules for energy and cooling load calculations (1093-RP). ASHRAE Transactions 110(1):164-176.
Armstrong, P.R., C.E. Hancock, III, and J.E. Seem. 1992a. Commercial building temperature recovery—Part I: Design procedure based on a step response model. ASHRAE Transactions 98(1):381-396.
Armstrong, P.R., C.E. Hancock, III, and J.E. Seem. 1992b. Commercial building temperature recovery—Part II: Experiments to verify the step response model. ASHRAE Transactions 98(1):397-410.
ASHRAE. 2013. Thermal environmental conditions for human occupancy. ANSI/ASHRAE Standard 55-2013.
ASHRAE. 2016. Ventilation for acceptable indoor air quality. ANSI/ASHRAE Standard 62.1-2016.
ASHRAE. 2016. Energy standard for building except low-rise residential buildings. ANSI/ASHRAE/IES Standard 90.1-2016.
ASHRAE. 2012. Updating the climatic design conditions in the ASHRAE Handbook—Fundamentals (RP-1613). ASHRAE Research Project, Final Report.
ASHRAE. 2013. Underfloor air distribution (UFAD) design guide, 2nd ed.
ASTM. 2008. Practice for estimate of the heat gain or loss and the surface temperatures of insulated flat, cylindrical, and spherical systems by use of computer programs. Standard C680-08. American Society for Testing and Materials, West Conshohocken, PA.
Bach, C., and O. Sarfraz. 2017. Update to measurements of office heat gain data. ASHRAE Research Project RP-1742, Progress Report.
Bauman, F., S. Schiavon, T. Webster, and K.H. Lee. 2010. Cooling load design tool for UFAD systems. ASHRAE Journal (September):62-71. escholarship.org/uc/item/9d8430v3.
Bliss, R.J.V. 1961. Atmospheric radiation near the surface of the ground. Solar Energy 5(3):103.
CFR. Annual. Energy efficiency program for certain commercial and industrial equipment. Code of Federal Regulations 10 CFR 431. U.S. Government Publishing Office, Washington, D.C. www.ecfr.gov.
Chantrasrisalai, C., D.E. Fisher, I. Iu, and D. Eldridge. 2003. Experimental validation of design cooling load procedures: The heat balance method. ASHRAE Transactions 109(2):160-173.
Claridge, D.E., B. Abushakra, J.S. Haberl, and A. Sreshthaputra. 2004. Electricity diversity profiles for energy simulation of office buildings (RP-1093). ASHRAE Transactions 110(1):365-377.
Eldridge, D., D.E. Fisher, I. Iu, and C. Chantrasrisalai. 2003. Experimental validation of design cooling load procedures: Facility design (RP-1117). ASHRAE Transactions 109(2):151-159.
Feng, J., S. Schiavon, and F. Bauman. 2012. Comparison of zone cooling load for radiant and air conditioning systems. Proceedings of the International Conference on Building Energy and Environment. Boulder, CO. escholarship.org/uc/item/9g24f38j.
Fisher, D.R. 1998. New recommended heat gains for commercial cooking equipment. ASHRAE Transactions 104(2):953-960.
Fisher, D.E., and C. Chantrasrisalai. 2006. Lighting heat gain distribution in buildings (RP-1282). ASHRAE Research Project, Final Report.
Fisher, D.E., and C.O. Pedersen. 1997. Convective heat transfer in building energy and thermal load calculations. ASHRAE Transactions 103(2): 137-148.
Gordon, E.B., D.J. Horton, and F.A. Parvin. 1994. Development and application of a standard test method for the performance of exhaust hoods with commercial cooking appliances. ASHRAE Transactions 100(2).
Hittle, D.C. 1999. The effect of beam solar radiation on peak cooling loads. ASHRAE Transactions 105(2):510-513.
Hittle, D.C., and C.O. Pedersen. 1981. Calculating building heating loads using the frequency of multi-layered slabs. ASHRAE Transactions 87(2): 545-568.
Hosni, M.H., and B.T. Beck. 2008. Update to measurements of office equipment heat gain data (RP-1482). ASHRAE Research Project, Progress Report.
Hosni, M.H., B.W. Jones, J.M. Sipes, and Y. Xu. 1998. Total heat gain and the split between radiant and convective heat gain from office and laboratory equipment in buildings. ASHRAE Transactions 104(1A):356-365.
Hosni, M.H., B.W. Jones, and H. Xu. 1999. Experimental results for heat gain and radiant/convective split from equipment in buildings. ASHRAE Transactions 105(2):527-539.
Incropera, F.P., and D.P. DeWitt. 1990. Fundamentals of heat and mass transfer, 3rd ed. Wiley, New York.
Iu, I., and D.E. Fisher. 2004. Application of conduction transfer functions and periodic response factors in cooling load calculation procedures. ASHRAE Transactions 110(2):829-841.
Iu, I., C. Chantrasrisalai, D.S. Eldridge, and D.E. Fisher. 2003. Experimental validation of design cooling load procedures: The radiant time series method (RP-1117). ASHRAE Transactions 109(2):139-150.
Jones, B.W., M.H. Hosni, and J.M. Sipes. 1998. Measurement of radiant heat gain from office equipment using a scanning radiometer. ASHRAE Transactions 104(1B):1775-1783.
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