Numerical study of natural convection from discrete heat sources in a vertical square enclosure

Abstract

A numerical finite difference technique based on the Marker and Cell (MAC) method is used to obtain solutions of a two-dimensional model of a square enclosure with laminar natural convection heat transfer from discrete heat sources. A discrete heat source is located in the center of one vertical side representing a high- power integrated circuit (IC). The conservation equations are solved using the primitive variables: velocity, pressure, and temperature. Computations are carried out for Pr = 0.72, A = 1 and 0 5 Ra 5 lo6 (Rayleigh number is based on the length of the heat source S divided by the aspect ratio A). The ratio E of the heat source size to the total height lies in the range 0.25 5 E 5 1.0. Verification of numerical results are obtained at Ra = 0 (conduction limit) with an analytical conduction solution, and the dependence of Nu and total resistance on Ra, E , and boundary conditions are studied. Relationships between Nu and Ra based on different scale lengths are examined. In addition, a relationship between Nu and Ra, based on SIA, are correlated as Nu = Nu (Ra, E ) and extrapolation equations are developed to cover the range of Ra from 0 5 Ra < lo9.