Sol-air temperature

Sol-air temperature is a variable used to calculate cooling load of a building and determine the total heat gain through exterior surfaces. It is an improvement over:
Where:

= rate of heat transfer
= heat transfer surface area
= heat transfer coefficient for radiation and convection
= outdoor surroundings' temperature
= outside surface temperature

The above equation only takes into account the temperature differences and ignores two important parameters, being 1) solar radiative flux; and 2) infrared exchanges from the sky. The concept of T_sol-air was thus introduced to enable these parameters to be included within an improved calculation. The following formula results:
Where:

= solar radiation absorptivity
= global solar irradiance
= extra infrared radiation due to difference between the external air temperature and the apparent sky temperature. This can be written as

The product just found can now be used to calculate the amount of heat transfer per unit area, as below:
An equivalent, and more useful equation for the net heat loss across the whole construction is:
Where:

= construction U-value, according to ISO 6946 .
= indoor temperature
= difference between outside dry-bulb air temperature and sky mean radiant temperature
= Form factor between the element and the sky
* = 1 for an unshaded horizontal roof
* = 0,5 for an unshaded vertical wall
= external radiative heat transfer coefficient

By expanding the above equation through substituting the following heat loss equation is derived:
The above equation is used for opaque facades in, and renders intermediate calculation of unnecessary. The main advantage of this latter approach is that it avoids the need for a different outdoor temperature node for each facade. Thus, the solution scheme is kept simple, and the solar and sky radiation terms from all facades can be aggregated and distributed to internal temperature nodes as gains/losses.