Heat transfer on a naturally cross-driven ventilated triangular cavity with openings

Abstract

This work addresses the problem of heat transfer through the roof of a family home with the purpose of improving air-conditioning energy savings during hot summer days. To this end, the air natural convection in a right-angle triangular cavity, resembling an attic, is numerically analyzed. The air cavity is assumed as naturally ventilated through two openings that induce an external air-stream flowing into and out of the cavity. The governing equations for both flow and heat transfer are simultaneously solved with appropriate boundary conditions. Finite element technique is employed to transform the original set of differential equations into a non-linear discrete one, which is finally solved by Newton iteration. Two major assumptions are made, namely: radiation heat transfer is negligible and the air flow is in laminar regime; in addition, the usual Boussinesq approximation is employed. Under these assumptions the numerical predictions show that the amount of heat transferred through the ceiling rapidly diminishes as the flow through the cavity increases. Therefore; whether or not the ceiling is insulated, the energy transfer is reduced by more than 50% and energy savings are considerably improved.