A numerical study of the convective heat transfer between a room and a window covered by a partially open plane blind with a gap at the top

Abstract

An approximate model of a window covered by a partially open plane blind has been considered. The window is represented by a vertical isothermal wall section which is exposed to a large surrounding room in which the mean temperature is lower than the window temperature. The blind is represented by a thin straight vertical wall which offers no resistance to heat transfer across it. The top of this thin section is aligned with the top of the heated wall section. There is a thin horizontal wall section at the top of the “blind”. This horizontal section does not fully reach to the vertical wall with the result that there is a small gap between the blind system and the vertical wall. The main purpose of this study was to determine the effect of the size of this gap on the heat transfer rate from the “window” to the room. The length of the thin vertical wall section is, in general, less than the height of the window and thus represents a partially open blind. Attention has only been given to the convective heat transfer from the window. The governing equations, written in dimensionless form, have been solved using a commercial finite-element based code. The solution has the following parameters: Rayleigh number, Prandtl number, dimensionless horizontal distance between the window and the blind, dimensionless distance of the bottom of the blind above the bottom of the window and dimensionless size of the gap at the top of the window. Results have only been obtained for a Prandtl number of 0.7.