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Local thermal non-equilibrium effects arising from the injection of a hot fluid into a porous medium
journal contribution
posted on 2023-05-18, 15:48 authored by Rees, DAS, Andrew BassomAndrew Bassom, Siddheshwar, PGWe 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.
History
Publication title
Journal of Fluid MechanicsVolume
594Pagination
379-398ISSN
0022-1120Department/School
School of Natural SciencesPublisher
Cambridge Univ PressPlace of publication
40 West 20Th St, New York, USA, Ny, 10011-4211Rights statement
Copyright 2008 Cambridge University PressRepository Status
- Restricted