In this study, the curved venetian blind is modeled as an effective layer with the following assumptions; each slat surface is isothermal, uniformly irradiated, and is a diffuse reflector and emitter.
The whole blind assembly is represented by two consecutive slats.
The two adjacent slat curved surfaces, with the imaginary surfaces at the front and back openings, constitute an enclosure.
The blind enclosure is then split into six surfaces as shown in Fig. 1.
The surfaces are as follows; surface 3 is the curved surface ab, surface 4 is the curved surface de, surface 5 is the curved surface bc, surface 6 is the curved surface ef, surface 1 is the imaginary surface ad, and surface 2 is the imaginary
surface cf.
The distance between the two adjacent slats is defined as h.
The width of the curved slat is defined as sw (measured along the curved surface) while the projected width of the slat on the flat plane is defined as s.
When the blind has a ratio of the distance between two adjacent slats to the projected slat width less than one (h=s < 1), it is found that, when the blind is closed, the slats will overlap.
The length of the slat subsurfaces, ab and ef, are defined as the overlapped length of the slat.
In the case of the blind with a flat slat, the length of the surfaces defined in the enclosure can be simply determined, but
for the blind with the curved slat, to find the length of the surfaces in the enclosure shown in Fig. 1 is not quite
so straight forward. Certain relationships and parameters are needed.
Fig. 2 shows the curved slat with a slat angle of phi(b) and its related parameters.
The critical angle of the curved slat is defined as the half of the curvature angle of the slat width, sw.
This critical angle can be expressed as