Non-Darcian Effects in Open-Ended Cavities Filled With a Porous Medium

[+] Author and Article Information
J. Ettefagh, K. Vafai, S. J. Kim

Department of Mechanical Engineering, The Ohio State University, Columbus, OH 43210

J. Heat Transfer 113(3), 747-756 (Aug 01, 1991) (10 pages) doi:10.1115/1.2910627 History: Received January 30, 1990; Revised July 24, 1990; Online May 23, 2008


The importance and relevance of non-Darcian effects associated with the buoyancy driven convection in open-ended cavities filled with fluid-saturated porous medium is analyzed in this work. Several different flow models for porous media, such as Brinkman-extended Darcy, Forchheimer-extended Darcy, and generalized flow models, are considered. The significance of inertia and boundary effects, and their crucial influence on the prediction of buouancy-induced flow and heat transfer in open-ended cavities, are investigated. Analysis is made on the proper choice of parameters that can fully determine the criteria for the range of validity of Darcy’s law in this type of configuration. Critical values of the inertial parameter, Λcrit , below which, for any given modified Rayleigh number, the Darcy flow model breaks down, have been investigated. It is shown that the critical value of the inertial parameter depends on the modified Rayleigh number and that this critical value increases as Ra* increases. It is also observed that for higher modified Rayleigh number, the deviation from a Darcian formulation appears at Darcy numbers greater than 1×10−4 . The Prandtl number effects on convective flow and heat transfer are shown to be quite significant for small values of Pr. The Prandtl number effects are reduced significantly for higher values of the Prandtl number.

Copyright © 1991 by The American Society of Mechanical Engineers
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