A COMPUTATIONAL METHOD TO SOLVE NONLINEAR ELLIPTIC EQUATIONS FOR NATURAL CONVECTION IN ENCLOSURES

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Abstract
A simple and rapidly converging method has been developed to study laminar natural convection in enclosures. The method is a combination of the Gauss-Seidel iterative technique and optimum under-relaxation with ω < 1. Three nonlinear elliptic equations for the conservation of mass, momentum, and energy in an enclosure are solved simultaneously in the finite-difference form on a computer. The results are in very good agreement with experimental data. An internal checking procedure, based on the physics of the problem, is strongly recommended. This computational method can probably be applied to other engineering problems involving more than three elliptic equations. The effect of the Prandtl number on the heat transfer across the enclosure is discussed. Correlations are presented for the Nusselt number as a function of the Prandtl number, Rayleigh number, and enclosure height-to-width ratio.