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Fluids 2017, 2(3), 48; doi:10.3390/fluids2030048

Modelling Bidispersive Local Thermal Non-Equilibrium Flow

1
Department of Mathematics, University of Bologna, 5 Piazza di Porta S. Donato, 40126 Bologna, Italy
2
Department of Mathematics, University of Durham, Durham DH1 3LE, UK
*
Author to whom correspondence should be addressed.
Received: 1 August 2017 / Revised: 12 September 2017 / Accepted: 13 September 2017 / Published: 18 September 2017
(This article belongs to the Special Issue Convective Instability in Porous Media)
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Abstract

In this work, we present a system of equations which describes non-isothermal flow in a bidispersive porous medium under conditions of local thermal non-equilibrium. The porous medium consists of macro pores, and in the solid skeleton are cracks or fissures which give rise to micro pores. The temperatures in the solid skeleton and in the fluids in the macro and micro pores are all allowed to be independent. After presenting the general model, we derive a result of universal stability, which guarantees exponential decay of the solution for all initial data. We further present a concrete example by specializing the model to the problem of thermal convection in a layer heated from below. View Full-Text
Keywords: bidispersive porous flows; local thermal non-equilibrium; universal stability; thermal convection bidispersive porous flows; local thermal non-equilibrium; universal stability; thermal convection
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Franchi, F.; Nibbi, R.; Straughan, B. Modelling Bidispersive Local Thermal Non-Equilibrium Flow. Fluids 2017, 2, 48.

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