In most of the previous works, the developed mathematical model for a venetian blind was based on the venetian blind of straight blade without thickness.
The slats of the real venetian blinds usually have some curvature and thickness.
The effect of slat curvature and slat thickness cause the shaded area blocked by the slat increasing in certain slat angle and solar incident angle.
In the analysis, the whole blind assembly is then represented by two consecutive slats.
Fig. 1 shows the side view of one of the cell of a flat blind composed of two adjacent slats and the side view of one of the cell of a curved blind composed of two adjacent slats at different solar profile angle (profile angle is the angle of incidence in a plane that is perpendicular to the window and perpendicular to the slat direction).
Fig. 1a and c show the case of the blind in which the direct radiation is incident on the slat surfaces.
Fig. 1b and d show the case of the blind in which some of the direct radiation is passing through the blind without touching the slat surfaces.
From the geometry shown in the Fig. 1b, the shaded area being blocked by the flat slat is defined as