Numerical Simulation of Three-Dimensional Natural Convection in a Porous Box Heated from Below

ABSTRACT

Three-dimensional natural convection in a parallelepiped box filled with fluid saturated porous medium heated from below and cooled from top has been numerically simulated for wide range of parameters i.e. Rayleigh number, 0 < Ra ≤ 500 and two aspect ratios, 0.1 ≤ A_x ≤ 10.0 and 0.1 ≤ A_z ≤ 10.0. Governing equations in vector potential form are discretised using central finite difference scheme. Numerical code based on Successive Accelerated Replacement (SAR) has been developed and executed for wide range of parameters. The critical Rayleigh number at which onset of convection occurs depends on values of aspect ratios. If any of the two aspect ratios is equal or above unity, the critical Rayleigh number approaches 43. As both aspect ratios decrease below unity, the critical Rayleigh number increases above 43.

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