This model computes the radiative temperature in the room. For a room with windows but no shade, the radiative temperature is computed as
Trad = ∑i (Ai εi Ti) ⁄ ∑i (Ai εi)
where Trad is the radiative temperature of the room, Ai are the surface areas of the room, εi are the infrared emissivities of the surfaces, and Ti are the surface temperatures.
If a the windows have a shade, then the equation is modified to take the actual shaded and non-shaded surface area into account. In this situation, the shaded part of a window has a infrared radiative power of
E = A ( u εs Ts + (1-u) εg τs Tgs)
where A is the surface area of the glass, u is the control signal of the shade, εs is the infrared absorptivity of the shade, Ts is the temperature of the shade, εg is the infrared absorptivity of the glass, τs is the infrared transmittance of the shade, and Tgs is the glass temperature behind the shade.
For the unshaded part of the window, the radiative power is
E = A (1-u) εg Tgn
where Tgn is the glass temperature of the non-shaded part of the window.