Abstract
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, σ 1 = 0(1) and 0( 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 σ 1. The results of the analysis show that the heat transfer rate varies as Ra 1 2 for a given σ 1. The results are in agreement with the experimental results of Schneider.
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