Integral transform analysis of natural convection in porous enclosures

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Abstract
A hybrid numerical‐analytical solution for steady‐state natural convection in a porous cavity is proposed, based on application of the ideas in the generalized integral transform technique. The integral transformation process reduces the original coupled partial differential equations, for temperature and stream function, into an infinite system of non‐linear ordinary differential equations for the transformed potentials, which is adaptively truncated and numerically solved through well‐established algorithms. The approach is applied to a vertical rectangular enclosure subjected to uniform internal heat generation. The convergence characteristics of the explicit inversion formulae are illustrated and critical comparisons with previously reported purely numerical solutions are performed.

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