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Journal of Porous Media
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ISSN Imprimir: 1091-028X
ISSN En Línea: 1934-0508

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Journal of Porous Media

DOI: 10.1615/JPorMedia.v1.i1.30
pages 31-46

Heat Transfer at the Boundary Between a Porous Medium and a Homogeneous Fluid: The One-Equation Model

J Alberto Ochoa-Tapia
Departamento de I.P.H., Universidad Autonoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, 09340, Mexico, D.F., Mexico
Stephen Whitaker
Department of Chemical Engineering and Material Science, University of California, Davis, California, USA


The heat transfer condition at the boundary between a porous medium (the ω region) and a homogeneous fluid {the η region) is developed as a flux jump condition based on the "nonlocal form" of the volume-averaged thermal energy equation that is valid within the "boundary region." Away from the boundary region, we impose the condition of "local thermal equilibrium" so that the nonlocal form simplifies to the classic one-equation model for thermal energy transport. The derived jump condition for the energy flux contains terms representing the accumulation, conduction, and convection of "excess surface thermal energy," in addition to an "excess nonequilibrium thermal source" that results from the potential failure of local thermal equilibrium in the boundary region. When the transport of excess surface thermal energy is negligible, the analysis indicates that the jump condition reduces to

nωη · Κω* · ∇ (T)ω = nωη · kβ(T)η + Φs, at the ω−η boundary

Because local thermal equilibrium will fail in the boundary region before it fails in the homogeneous region of the porous medium, the nonequilibrium thermal source, Φs represents an important term in the transition from a one-equation model to a two-equation model.

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