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Nearly Explicit Solutions and Uniqueness for the Fluid Flow and Heat Transfer in Porous Media with Temperature-Dependent Viscosity

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Abstract

We present a method for reducing the PDE system of the flow of a viscous fluid in a porous medium with boundary conditions on the pressure to a simpler problem for the Laplacian. The viscosity and the thermal conductivity are allowed to depend on the temperature. In this way, existence, uniqueness and a nearly explicit computation of the solution are obtained.

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Authors and Affiliations

  1. Dipartimento di Matematica, Largo Bruno Pontecorvo 5, 56100, Pisa, Italy

    Giovanni Cimatti

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  1. Giovanni Cimatti
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Correspondence to Giovanni Cimatti.

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Communicated by G.P. Galdi

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Cimatti, G. Nearly Explicit Solutions and Uniqueness for the Fluid Flow and Heat Transfer in Porous Media with Temperature-Dependent Viscosity. J. Math. Fluid Mech. 13, 95–102 (2011). https://doi.org/10.1007/s00021-009-0011-4

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  • DOI: https://doi.org/10.1007/s00021-009-0011-4

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