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