Physical background
The intensity of radiation (energy density of radiation - physical unit is W/m3) is a function of its wave length and the temperature. The energy density of radiation increases with higher temperatures and it shows a distinctive maximum between 1 ... 3 μm that shifts toward lower wave length. This dependency is called Max Planck's radiation law of black bodies. As an practical approach in building physics, one differentiates between short wave radiation and long wave radiation. Short wave radiation comprises the visible sun radiation and a certain range above (0.2 ... 3 μm). The long wave radiation (3 ..30 μm) is commonly denoted as heat radiation.
The integration of Max Planck's radiation law of black bodies over the wave length delivers a radiation flux density as function of temperature to the power of four. This dependency is called Stefan Boltzmann's radiation law; its proportionality factor is the Boltzmann constant. Knowing the surface temperature of bodies, it is then possible to establish radiation balances.
General remarks about radiation components
Beside the air temperature, the short wave radiation and long wave radiation are two climate components having major influence on the thermal behavior of the building envelope and the building as whole. Both, the short wave radiation and long wave radiation consist of two components, the direct and diffuse sun radiation as well as the long wave emission and atmospheric counter (sky) radiation. For a proper modeling of the heat balance at building surfaces, all these radiation components have to be taken into account.
While the direct short wave radiation is a directed radiation, all other radiation components are not directed. The mechanisms of transformation of direct radiation into diffuse radiation are adsorption and dispersion (extinction) in the atmosphere (by ozone, carbon dioxide, water vapor, dust, pollution). The short wave radiation is a net influx (gain) of energy from the viewpoint of the building. The long wave radiation is always expressed as a balance, a difference between adsorption and emission.
The building establishes radiation equilibrium with the sky and the surrounding ground. While the sky can be modeled as an spheric half-infinite room, the ground can be seen as an flat plane perpendicular to vertical building surfaces. From the viewpoint of the building, there is a net gain of energy by direct and diffuse reflection of short wave radiation from the ground. At the same time, as the building itself, the ground acts as an long wave radiator.
Radiation balances at the building surface
Radiation balances can be established at the exterior surface of the building or the building component. According the absorption coefficient of the wall surface, the short wave sun radiation is divided into an adsorbed part and a reflected part. The absorbed radiation flux is taken up by the building element but only a part of it, the heat load contribution from the building element can be transferred to the indoor room. The heat load is reduced by convective heat transport (ventilation of the building element) and by higher long wave emission with higher surface temperature.
The long wave radiation balance is determined by the building component's emission coefficient and the surface temperature, the albedo and temperature of the surrounding ground and the cloudiness, relative humidity and temperature of the sky. For sake of simplification, the ground temperature and the sky temperature are usually set equal to the outdoor air temperature.
