Glazing solar heat gain analysis and optimization at varying orientations and placements in aspect of distributed radiation at the interior surfaces

This paper aims at introducing a novel methodology to calculate the distribution of incoming solar energy on the internal surfaces of closed spaces with an opening at various orientations and placements. While the incoming diffuse solar radiation and the reflected solar radiation are as usually distributed with the use of absorptance–weighted area ratios the penetrating direct radiation is distributed according to the formed sunlit areas on the interior surfaces. The determination of the sunlit areas into the enclosure is accomplished by forming at each time step a, so-called, “sunlit pattern” with four letter-characters specifying the particular illuminated interior surfaces that are stricken by the sun’s rays. Though this study is carried out for the Mediterranean climatic conditions, the methodology is general and can be applied to other regions. Following this methodology the optimum glazing setup to maximize the solar heat gain per square meter during the heating period is formulated and solved as a constrained optimization problem. To this effect, the well-known pattern search methodology has been appropriately adapted to deal with the highly nonlinear nature of this problem, particularly when the glazing distance from the right sidewall is variable. Representative computer results are provided showing the optimization problem complexity by varying the glazing width to height and the floor width to floor depth ratios.