Development of a mathematical model for a curved slat venetian blind with thickness

This article is about the development of a mathematical model for a venetian blind. The model is used for determining the performance of the glass window installed with a venetian blind in term of heat transmission. The blind, whose optical properties are considered nonspecular, is modeled as an effective layer. The optical properties of the effective layer are mainly dependent on the slat angle, slat properties and solar profile angle. The effect of slat curvature and the effect of slat thickness are included in the developed model. The shortwave optical properties of the effective layer, transmittance, reflectance and absorptance, are classified as the optical properties for direct radiation and the optical properties for diffuse radiation. The analysis for optical properties due to the interreflection of the direct radiation between the adjacent slat surfaces is done by using radiosity method on a 6 surface closed enclosure. The effect of the slat curvature and thickness causes the shaded area blocked by the blind itself increased in certain cases. The optical properties for diffuse radiation of the effective layer are determined considering the incident diffuse radiation from the sky and from the ground. The optical properties calculated from the developed model are also compared to the results obtained from the three previous models. The validation of the results predicted by the developed mathematical model is performed by comparing the predicted results with the experimental results. The results that used to validate in this study is the ratio of the transmitted radiation through the glass window installed with venetian blind to the incident radiation on the glass window. It is shown from the comparison that the developed mathematical model for the venetian blind included the curvature and thickness effect yields quite accurate predicted results.