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An equation for thermal dispersion flux transport and its mathematical modelling for heat and fluid flow in a porous medium

Published online by Cambridge University Press:  01 September 2006

A. NAKAYAMA
Affiliation:
Department of Mechanical Engineering, Shizuoka University 3-5-1 Johoku, Hamamatsu, 432-8561, Japan
F. KUWAHARA
Affiliation:
Department of Mechanical Engineering, Shizuoka University 3-5-1 Johoku, Hamamatsu, 432-8561, Japan
Y. KODAMA
Affiliation:
Department of Mechanical Engineering, Shizuoka University 3-5-1 Johoku, Hamamatsu, 432-8561, Japan

Abstract

It is shown for the first time that the gradient diffusion hypothesis often adopted for thermal dispersion heat flux in heat transfer within porous media can be derived from a transport equation for the thermal dispersion heat flux based on the Navier–Stokes and energy equations. The transport equation valid for both thermal equilibrium and non-equilibrium cases is mathematically modelled so that all unknown spatial correlation terms, associated with redistribution and dissipation of the dispersion heat flux, are expressed in terms of determinable variables. The unknown coefficients are determined analytically by considering of macroscopically unidirectional flow through a tube as treated by Taylor. Taylor's expression for the dispersion has been generated from the transport equation. Both laminar and turbulent flow cases are investigated to obtain two distinct limiting expressions for low- and high-Péclet-number regimes. The results obtained for the Taylor diffusion problem are translated to the case of heat and fluid flow in a packed bed, to obtain the corresponding expressions for the axial dispersion coefficient in a packed bed. The resulting expression for the high-Péclet-number case agrees well with the empirical formula, validating of the present transport analysis.

Type
Papers
Copyright
© 2006 Cambridge University Press

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