Sol-air temperature (Tsol-air) 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:
q A = h o ( T o − T s ) {\displaystyle {\frac {q}{A}}=h_{o}(T_{o}-T_{s})}
Where:
q {\displaystyle q} = rate of heat transfer [W]
A {\displaystyle A} = heat transfer surface area [m2]
h o {\displaystyle h_{o}} = heat transfer coefficient for radiation (long wave) and convection [W/m2K]
T o {\displaystyle T_{o}} = outdoor surroundings' temperature [°C]
T s {\displaystyle T_{s}} = outside surface temperature [°C] 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 Tsol-air was thus introduced to enable these parameters to be included within an improved calculation. The following formula results:
T s o l − a i r = T o + ( a ⋅ I − Δ Q i r ) h o {\displaystyle T_{\mathrm {sol-air} }=T_{o}+{\frac {(a\cdot I-\Delta Q_{ir})}{h_{o}}}}
Where:
a {\displaystyle a} = solar radiation absorptivity (surface solar absorptance or the inverse of the solar reflectance of a material) [-]
I {\displaystyle I} = global solar irradiance (i.e. total solar radiation incident on the surface) [W/m2]
Δ Q i r {\displaystyle \Delta Q_{ir}} = extra infrared radiation due to difference between the external air temperature and the apparent sky temperature. This can be written as Δ Q i r = F r ∗ h r ∗ Δ T o − s k y {\displaystyle \Delta Q_{ir}=F_{r}*h_{r}*\Delta T_{o-sky}} [W/m2] The product T s o l − a i r {\displaystyle T_{\mathrm {sol-air} }} just found can now be used to calculate the amount of heat transfer per unit area, as below:
q A = h o ( T s o l − a i r − T s ) {\displaystyle {\frac {q}{A}}=h_{o}(T_{\mathrm {sol-air} }-T_{s})}
An equivalent, and more useful equation for the net heat loss across the whole construction is:
q A = U c ( T i − T s o l − a i r ) {\displaystyle {\frac {q}{A}}=U_{c}(T_{i}-T_{\mathrm {sol-air} })}
Where:
U c {\displaystyle U_{c}} = construction U-value, according to ISO 6946 [W/m2K].
T i {\displaystyle T_{i}} = indoor temperature [°C]
Δ T o − s k y {\displaystyle \Delta T_{o-sky}} = difference between outside dry-bulb air temperature and sky mean radiant temperature [°C]
F r {\displaystyle F_{r}} = Form factor between the element and the sky [-]
F r {\displaystyle F_{r}} = 1 for an unshaded horizontal roof
F r {\displaystyle F_{r}} = 0,5 for an unshaded vertical wall
… excerpt ends here. Continue reading the full article.
