J. Fluid Alech. zyxwvutsrqp (1996), zyxwvutsrqp rol. zyxwvutsr 322, zyxwvuts pp. 201-214 Copyright 0 1996 Cambridge University Press 20 1 zy Forced convection in a fluid-saturated porous-medium channel with isothermal or isoflux boundaries By D. A. NIELD', S. L. M. JUNQUEIRA2 AND J. L. LAGE2 Department of Engineering Science, University of Auckland, Auckland, New Zealand Mechanical Engineering Department, Southern Methodist University, Dallas, TX 75375-0337, USA (Received 9 August 1995 and in revised form 14 March 1996) We present a fresh theoretical analysis of fully developed forced convection in a fluid- saturated porous-medium channel bounded by parallel plates, with imposed uniform heat flux or isothermal condition at the plates. As a preliminary step, we obtain an 'exact zyxwvuts ' solution of the Brinkman-Forchheimer extension of Darcy's momentum equation for flow in the channel. This uniformly valid solution permits a unified treatment of forced convection heat transfer, provides the means for a deeper explanation of the physical phenomena, and also leads to results which are valid for highly porous materials of current practical importance. 1. Introduction Because of its relevance to a variety of situations (e.g. geothermal systems, thermal insulation, coal and grain storage, solid matrix heat exchangers, nuclear waste disposal), convection in porous media is a well-developed field of investigation. The literature on the topic of forced convection is surveyed in chapter 4 of Nield & Bejan (1992). Studies on forced convection in a channel progressed chronologically towards complex models. The groundbreaking study by Kaviany ( 1985) presented an analytical solution of the transport equations based on the Brinkman-extended Darcy flow model. An important step towards predicting transport phenomena in more general and complex situations was taken by Vafai & Kim (1989), who presented a closed form solution of the Brinkman-Forchheimer-extended Darcy momentum equation and the associated heat transfer equation for the case of fully developed flow with uniform heat flux at the boundaries. The analysis was limited to the case of effective viscosity equal to fluid viscosity. (It is true that one can extend their solution to an effective viscosity model; this involves redefining their Darcy number and inertia parameter.) Vafai & Kim assumed a boundary-layer-type developed flow and as a consequence their solution is inaccurate when the inertia parameter is small and the Darcy number approaches and exceeds the value unity. In the absence of an accurate general theoretical solution one has to rely on direct numerical simulation. Noteworthy in this line are the numerical (and experimental) studies by Poulikakos & Renken (1987) and Renken & Poulikakos ( 1988), who employed a finite-difference formulation of the differential equations. These authors allowed for viscosity variations, and they were able to deal with developing flow and to incorporate expressions for the permeability and Forchheimer coefficient pertinent for packed beds of spheres, and they performed