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Local thermal non-equilibrium effects arising from the injection of a hot fluid into a porous medium

Published online by Cambridge University Press:  14 December 2007

D. ANDREW S. REES ,
ANDREW P. BASSOM  and
PRADEEP G. SIDDHESHWAR
D. ANDREW S. REES
Affiliation:
Department of Mechanical Engineering, University of Bath, Bath BA2 7AY, UK
ANDREW P. BASSOM
Affiliation:
School of Mathematics and Statistics, University of Western Australia, Crawley, WA 6009, Australia
PRADEEP G. SIDDHESHWAR
Affiliation:
Department of Mechanical Engineering, University of Bath, Bath BA2 7AY, UK Department of Mathematics, Bangalore University, Bangalore, India
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Abstract

We examine the effect of local thermal non-equilibrium on the infiltration of a hot fluid into a cold porous medium. The temperature fields of the solid porous matrix and the saturating fluid are governed by separate, but coupled, parabolic equations, forming a system governed by three dimensionless parameters. A scale analysis and numerical simulations are performed to determine the different manners in which the temperature fields evolve in time. These are supplemented by a large-time analysis showing that local thermal equilibrium between the phases is eventually attained. It is found that the thickness of the advancing thermal front is a function of the governing parameters rather than being independent of them. This has the implication that local thermal equilibrium is not equivalent to a single equation formulation of the energy equation as might have been expected. When the velocity of the infiltrating fluid is sufficiently large, the equations reduce to a hyperbolic system and a thermal shock wave is formed within the fluid phase. The strength of the shock decays exponentially with time, but the approach to local thermal equilibrium is slower and is achieved algebraically in time.

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Type
Papers
Information
Journal of Fluid Mechanics , Volume 594 , 10 January 2008 , pp. 379 - 398
Copyright
Copyright © Cambridge University Press 2008

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