Conjugate heat transfer in enclosures with openings for ventilation

Conjugate heat transfer by natural convection and conduction in enclosures with openings has been studied by a numerical method. The enclosure contained a chimney consisting of a vertical solid wall, which was insulated on one side and a constant heat flux applied on the other. Vertical boundaries with openings were isothermal and horizontal boundaries adiabatic. These problems are encountered in heat transfer in buildings and heat management in electronic equipment. Two dimensional equations of conservation of mass, momentum and energy, with the Boussinesq approximation are solved using the Simpler method. Various geometrical parameters were: aspect ratio, A from 0.5 to 2.0, openings' heights, h ₁ and h ₂ from 0.10 to 0.30, orifice height, h ₃ from 0.05 to 0.15, insulation thickness, w ₁ from 0 to 0.10, wall thickness, w ₂ from 0.05 to 0.15 and chimney width, w ₃ from 0.05 to 0.15. Rayleigh number, Ra was varied from 10 ⁸ to 10 ¹² and the conductivity ratio, k _r was from 1 to 40. The results are reduced in terms of the normalized Nusselt number, Nu and volume flow rate, V? as a function of Ra number, and other non dimensional geometrical parameters. The isotherms and streamlines are produced for various Ra numbers and geometrical conditions. It is found that Nu and V? are both an increasing function of Ra, h ₁ at high Ra numbers, h ₃, and k _r. They are a decreasing function of h ₁ at low Ra numbers, h ₂, and w ₂. Nu and V? have optima with respect to w ₁, w ₃ and A.