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Rajagopal, K. R.; Saccomandi, G.; Vergori, L.

A systematic approximation for the equations governing convection-diffusion in a porous medium. (English) Zbl 1194.35336

Nonlinear Anal., Real World Appl. 11, No. 4, 2366-2375 (2010).
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.

Cited in 12 Documents

MSC:

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)

Keywords:

pressure dependent viscosity; Oberbeck-Boussinesq approximation; porous media; Darcy’s equation
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Full Text: DOI

References:

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