Analysis of natural convection about a vertical plate embedded in a porous medium (Q1123760)

Buoyancy-driven fluid flow and heat transfer about a vertical flat plate embedded in a porous medium are analyzed in depth for two general cases. These are the constant wall temperature case and the constant wall heat flux case. By an order of magnitude analysis it is shown that there are two governing dimensionless parameters which are related to the thermal and viscous effects. The governing equations are solved analytically using the method of matched asymptotic expansions along with the modified Oseen method. The numerical solution of the governing equations based on the similarity transformations is also obtained. A complete physical description of the problem is presented throughout the analysis.