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Convection in superposed fluid and porous layers

Published online by Cambridge University Press:  26 April 2006

Falin Chen  and
C. F. Chen
Falin Chen
Affiliation:
Institute of Applied Mechanics, National Taiwan University, Taipei, Taiwan 10764, ROC
C. F. Chen
Affiliation:
Department of Aerospace and Mechanical Engineering, The University of Arizona, Tucson, AZ 85721, USA
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Abstract

A nonlinear computational investigation of thermal convection due to heating from below in a porous layer underlying a fluid layer has been carried out. The motion of the fluid in the porous layer is governed by Darcy's equation with the Brinkman terms for viscous effects and the Forchheimer term for inertial effects included. The motion in the fluid layer is governed by the Navier-Stokes equation. The flow is assumed to be two-dimensional and periodic in the horizontal direction, with a wavelength equal to the critical value at onset as predicted by the linear stability theory. The numerical scheme used is a combined Galerkin and finite-difference method, and appropriate boundary conditions are applied at the interface. Results have been obtained for depth ratios $\hat{d}=0, 0.1, 0.2, 0.5 $ and 1.0, where $\hat{d}$ is the ratio of the thickness of the fluid layer to that of the porous layer. For $\hat{d}=0.1 $, up to Rm (Rayleigh number of the porous layer) equal to 20 times the critical $R_{{\rm m}_{\rm e}} $, the convection is dominated by the porous layer, similar to the situation at onset, even though the Rayleigh number for the fluid layer is well into the supercritical regime. The Nusselt number for $\hat{d}$ less than the critical value (0.13 in the present case) increases sharply with Rm, whereas at larger $\hat{d}$, the increase is very moderate. Heat transfer rates predicted by the numerical scheme for $\hat{d} = 0.1$ and 0.2 show good agreement with the experimental results of Chen & Chen (1989).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 234 , January 1992 , pp. 97 - 119
Copyright
© 1992 Cambridge University Press

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