4. Design Conditions for Heating and Cooling

The size of a heating or cooling system for a building is determined on the basis of the desired indoor conditions that must be maintained based on the outdoor conditions that exist at that location. The desirable ranges of temperatures, humidities, and ventilation rates (the thermal comfort zone) discussed earlier constitute the typical indoor design conditions, and they remain fairly constant. For example, the recommended indoor temperature for general comfort heating is 22ºC (or 72ºF). The outdoor conditions at a location, on the other hand, vary greatly from year to year, month to month, and even hour to hour. The set of extreme outdoor conditions under which a heating or cooling system must be able to maintain a building at the indoor design conditions is called the outdoor design conditions (Fig. 17).

When designing a heating, ventilating, and air-conditioning (HVAC) system, perhaps the first thought that comes to mind is to select a system that is large enough to keep the indoors at the desired conditions at all times even under the worst weather conditions. But sizing an HVAC system on the basis of the most extreme weather on record is not practical since such an oversized system will have a higher initial cost, will occupy more space, and will probably have a higher operating cost because the equipment in this case will run at partial load most of time and thus at a lower efficiency. Most people would not mind experiencing an occasional slight discomfort under extreme weather conditions if it means a significant reduction in the initial and operating costs of the heating or cooling system. The question that arises naturally is what is a good compromise between economics and comfort?

To answer this question, we need to know what the weather will be like in the future. But even the best weather forecasters cannot help us with that.
Therefore, we turn to the past instead of the future and bet that the past weather data averaged over several years will be representative of a typical year in the future. The weather data in Tables 4 and 5 are based on the records of numerous weather stations in the United States that recorded various weather data in hourly intervals. For ordinary buildings, it turns out that the economics and comfort meet at the 97.5 percent level in winter. That is, the heating system will provide thermal comfort 97.5 percent of the time but may fail to do so during 2.5 percent of the time (Fig. 18). For example, the 97.5 percent winter design temperature for Denver, Colorado, is -17ºC, and thus the temperatures in Denver may fall below -17ºC about 2.5 percent of the time during winter months in a typical year. Critical applications such as health care facilities and certain process industries may require the more stringent 99 percent level.

Table 4 lists the outdoor design conditions for both cases as well as summer comfort levels. The winter percentages are based on the weather data for the months of December, January, and February while the summer percentages are based on the four months June through September. The three winter months have a total of 31 + 31 + 28 = 90 days and thus 2160 hours. Therefore, the conditions of a house whose heating system is based on the 97.5 percent level may fall below the comfort level for 2160 x 2.5% = 54 hours during the heating season of a typical year. However, most people will not even notice it because everything in the house will start giving off heat as soon as the temperature drops below the thermostat setting. This is especially the case in buildings with large thermal masses. The minimum temperatures usually occur between 6:00 AM and 8:00 AM solar time, and thus commercial buildings that open late (such as shopping centers) may even use less stringent outdoor design conditions (such as the 95 percent level) for their heating systems. This is also the case with the cooling systems of residences that are unoccupied during the maximum temperatures, which occur between 2:00 PM and 4:00 PM solar time in the summer.

The heating or cooling loads of a building represent the heat that must be supplied to or removed from the interior of a building to maintain it at the desired conditions. A distinction should be made between the design load and the actual load of heating or cooling systems. The design (or peak) heating load is usually determined with a steady-state analysis using the design conditions for the indoors and the outdoors for the purpose of sizing the heating system (Fig. 19). This ensures that the system has the required capacity to perform adequately at the anticipated worst conditions. But the energy use of a building during a heating or cooling season is determined on the basis of the actual heating or cooling load, which varies throughout the day.

The internal heat load (the heat dissipated off by people, lights, and appliances in a building) is usually not considered in the determination of the design heating load but is considered in the determination of the design cooling load. This is to ensure that the heating system selected can heat the building even when there is no contribution from people or appliances, and the cooling system is capable of cooling it even when the heat given off by people and appliances is at its highest level.

Wind increases heat transfer to or from the walls, roof, and windows of a building by increasing the convection heat transfer coefficient and also increasing the infiltration. Therefore, wind speed is another consideration when determining the heating and cooling loads. The recommended values of wind speed to be considered are 15 mph (6.7 m/s) for winter and 7.5 mph (3.4 m/s) for summer. The corresponding design values recommended by ASHRAE for heat transfer coefficients for combined convection and radiation on the outer surface of a building are 

The recommended heat transfer coefficient value for the interior surfaces of a building for both summer and winter is (Fig. 20)

For well-insulated buildings, the surface heat transfer coefficients constitute a small part of the overall heat transfer coefficients, and thus the effect of possible deviations from the above values is usually insignificant.

In summer, the moisture level of the outdoor air is much higher than that of indoor air. Therefore, the excess moisture that enters a house from the outside with infiltrating air needs to be condensed and removed by the cooling system. But this requires the removal of the latent heat from the moisture, and the cooling system must be large enough to handle this excess cooling load. To size the cooling system properly, we need to know the moisture level of the outdoor air at design conditions. This is usually done by specifying the wet-bulb temperature, which is a good indicator of the amount of moisture in the air. The moisture level of the cold outside air is very low in winter, and thus normally it does not affect the heating load of a building.

Solar radiation plays a major role on the , and you may think that it should be an important consideration in the evaluation of the design heating and cooling loads. Well, it turns out that peak heating loads usually occur early in the mornings just before sunrise. Therefore, solar radiation does not affect the peak or design heating load and thus the size of a heating system. However, it has a major effect on the actual heating load, and solar radiation can reduce the annual heating energy consumption of a building considerably.

Sol-Air Temperature

The sun is the main heat source of the earth, and without the sun, the environment temperature would not be much higher than the deep space temperature of -270ºC. The solar energy stored in the atmospheric air, the ground, and the structures such as buildings during the day is slowly released at night, and thus the variation of the outdoor temperature is governed by the incident solar radiation and the thermal inertia of the earth. Heat gain from the sun is the primary reason for installing cooling systems, and thus solar radiation has a major effect on the peak or design cooling load of a building, which usually occurs early in the afternoon as a result of the solar radiation entering through the glazing directly and the radiation absorbed by the walls and the roof that is released later in the day.

The effect of solar radiation for glazing such as windows is expressed in terms of the solar heat gain factor (SHGF), discussed later in this chapter. For opaque surfaces such as the walls and the roof, on the other hand, the effect of solar radiation is conveniently accounted for by considering the outside temperature to be higher by an amount equivalent to the effect of solar radiation. This is done by replacing the ambient temperature in the heat transfer relation through the walls and the roof by the sol-air temperature, which is defined as the equivalent outdoor air temperature that gives the same rate of heat transfer to a surface as would the combination of incident solar radiation, convection with the ambient air, and radiation exchange with the sky and the surrounding surfaces (Fig.22).

Heat flow into an exterior surface of a building subjected to solar radiation can be expressed as

where a_s is the solar absorptivity and ε is the emissivity of the surface, h_o is the combined convection and radiation heat transfer coefficient,q_solar is the solar radiation incident on the surface (in W/m² or Btu/h · ft²) and

is the sol-air temperature. The first term in Equation 15 represents the convection and radiation heat transfer to the surface when the average surrounding surface and sky temperature is equal to the ambient air temperature, T_surr = T_ambient, and the last term represents the correction for the radiation heat transfer when T_surr ≠ T_ambient. The last term in the sol-air temperature relation represents the equivalent change in the ambient temperature corresponding to this radiation correction effect and ranges from about zero for vertical wall surfaces to 4ºC (or 7ºF) for horizontal or inclined roof surfaces facing the sky. This difference is due to the low effective sky temperature.

The sol-air temperature for a surface obviously depends on the absorptivity of the surface for solar radiation, which is listed in Table 6 for common exterior surfaces. Being conservative and taking h_o = 17 W/m² · ºC = 3.0 Btu/h · ft² · ºF, the summer design values of the ratio a_s/h_o for light- and dark-colored surfaces are determined to be (Fig. 23)

where we have assumed conservative values of 0.45 and 0.90 for the solar absorptivities of light- and dark-colored surfaces, respectively. The sol-air temperatures for light- and dark-colored surfaces are listed in Table 7 for July 21 at 40º N latitude versus solar time. Sol-air temperatures for other dates and latitudes can be determined from Equation 16 by using appropriate temperature and incident solar radiation data.

Once the sol-air temperature is available, heat transfer through a wall (or similarly through a roof ) can be expressed as

where A_s is the wall area and U is the overall heat transfer coefficient of the wall. Therefore, the rate of heat transfer through the wall will go up by UA for each degree rise in equivalent outdoor temperature due to solar radiation. Noting that the temperature rise due to solar radiation is

the rate of additional heat gain through the wall becomes

The total solar radiation incident on the entire wall is Q_solar = A_sq_solar Therefore, the fraction of incident solar heat transferred to the interior of the house is