Sol-air temperature

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

\frac{q}{A} = h_o(T_o - T_s)

where

q = rate of heat transfer [W]
A = heat transfer surface area [m²]
h_o = heat transfer coefficient for radiation (long wave) and convection [W/m²K]
T_o = outdoor surroundings' temperature [°C]
T_s = outside surface temperature [°C]

This equation only takes into account the temperature differences thus, ignoring solar radiative flux and infrared exchanges from the sky. The Tsol-air was then introduced to accommodate these two parameters.

T_\mathrm{sol-air} = T_o %2B \frac{ (a \cdot I - \Delta Q_{ir})}{h_o}

where

a = solar radiation absortivity of a surface [-]
I = global solar irradiance [W/m²]
\Delta Q_{ir} = extra infrared radiation due to difference between the external air temperature and the apparent sky temperature. = F_r * h_r * \Delta T_{o-sky} [W/m²]

and is to be used in

\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:

\frac{q}{A} = U_c(T_i - T_\mathrm{sol-air})

where

U_c = construction U-value, according to ISO 6946 [W/m²K].
T_i = indoor temperature [°C]
\Delta T_{o-sky} = difference between outside dry-bulb air temperature and sky mean radiant temperature [°C]

Expanding the above equation by substituting T_\mathrm{sol-air} gives the following heat loss equation:

\frac{q}{A}  =  U_c(T_i - T_o)  -  \frac{U_c}{h_o} {[a \cdot I - F_r  \cdot h_r \cdot \Delta T_{o-sky}]}

The above equation is used for opaque facades in [1], and renders intermediate calculation of T_\mathrm{sol-air} 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.

References

  1. ^ ISO 13790, Energy performance of buildings — Calculation of energy use for space heating and cooling
  1. Fundamentals volume of the ASHRAE Handbook, ASHRAE, Inc., Atlanta, GA, USA, 2005
  2. Heating and Cooling of Buildings, 2nd ed., Kreider, Curtiss, Rabl, McGraw-Hill, New York, USA, 2002

See also