Three-dimensional natural convection in a porous layer locally heated from below

Three-dimensional natural convection in a porous, cubic, horizontal enclosure is numerically studied using a vector potential formulation, and a finite difference solution of the equations. The enclosure is isothermally heated along part of its lower boundary at an isothermal hot temperature, and at an isothermal temperature along all of its upper boundary. The remaining surfaces are adiabatic. It is found that, if the Rayleigh number is sufficiently large, three-dimensional motion leads to significantly higher heat transfer rates than those obtained from two-dimensional solution. At low Rayleigh number, two-dimensional analysis provides adequate estimates of the heat transfer rate across the enclosure. At very small heated lengths, two-dimensional analysis gives values of heat transfer coefficients slightly higher than those computed by three-dimensional analyses.