NUMERICAL STUDY OF NATURAL-CONVECTION FROM DISCRETE HEAT-SOURCES IN A VERTICAL SQUARE ENCLOSURE

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 less-than-or-equal-to Ra less-than-or-equal-to 10(6) (Rayleigh number is based on the length of the heat source S divided by the aspect ratio A). The ratio-epsilon of the heat source size to the total height lies in the range 0.25 less-than-or-equal-to epsilon less-than-or-equal-to 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, epsilon, 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 S/A, are correlated as Nu = Nu (Ra, epsilon) and extrapolation equations are developed to cover the range of Ra from 0 less-than-or-equal-to Ra < 10(9).