Numerical study of the natural convection in cavity heated from the lower corner and cooled from the ceiling

This work enters within the frame work of general study dealing with passive cooling air conditioning systems. Steady laminar natural convection of air in an enclosed cavity with localized heating and cooling ceiling has been investigated numerically. The ceiling is cooled at a constant temperature and portion vertical wall is isothermally heated, while the remaining portion of the boundary is adiabatic. This study states the problem in Cartesian coordinates system, involves the use of a control volume method and solves the full vorticity transport equation together with the stream function and energy equations. The velocity and temperature fields are determined for various combinations of Rayleigh numbers, and geometrical parameters to show some of the flow field characteristics. The results are reduced in terms of the Nusselt number as a function of Ra.