Asymptotic solutions for nonlinear thermal convection in porous media (Q761322)

Nonlinear thermal convection in a saturated porous medium is studied under different approximations. Asymptotic solutions for free boundaries are obtained for two limiting cases: Ra large, \(\sigma_ 1=O(1)\) and O(Ra) using the method of matched asymptotic expansions. The analytical approximation method is also used to study the convection problem over a wide range of Ra and \(\sigma_ 1\). The results of the analysis show that the heat transfer rate varies as \(Ra^{1/3}\) for a given \(\sigma_ 1\).