Appling Eqs. (14) and (18) to each surface of the closed enclosure shown in Fig. 1, yields 12 related equations.
The view factors for every surface in the closed enclosure shown in Fig. 1 can be solved from the Hottel’s cross string
method in Eq. (10) and the reciprocity relation in Eq. (8).
Solving these 12 equations, one can get the longwave optical properties of the effective layer.
To solve the longwave optical properties, transmittance, reflectance, absorptance and emittance from the 12 governing equations there are several methods that can be used.
In this study we chose to follow the externally imposed radiation or imposed surface temperature of the slats and note the portion of the radiation flux that is transmitted through the effective layer, reflected from the effective layer and absorbed at the effective layer.
Fig. 3 shows the radiant exchange between the surfaces in the closed enclosure.