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A systematic approximation for the equations governing convection-diffusion in a porous medium. (English) Zbl 1194.35336
Summary: In order to take into account thermal effects in flows through porous media, one makes ad hoc modifications to Darcy’s equation by appending a term that is similar to the one that is obtained in the Oberbeck-Boussinesq approximation for a fluid. In this short paper, we outline a systematic procedure for obtaining an Oberbeck-Boussinesq type of approximation for the flow of a fluid through a porous medium. In addition to establishing the appropriate equation for a flow governed by Darcy’s equation, we proceed to obtain the approximations for flows governed by equations due to Forchheimer and Brinkman.

35Q35 PDEs in connection with fluid mechanics
76S05 Flows in porous media; filtration; seepage
35A35 Theoretical approximation in context of PDEs
80A20 Heat and mass transfer, heat flow (MSC2010)
Full Text: DOI
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