Comments on ‘forced convection with slip-flow in a channel or duct occupied by a hyper-porous medium saturated by a rarefied gas’, Transport in Porous Media, 64, 161–170, 2006

Abstract

In a recent paper in this Journal (Nield and Kuznetsov 2006) analytical solution is obtained for forced convection flow in channels occupied by a hyper-porous medium saturated with a rarefied gas in the slip-flow regime, for the case of uniform flux boundary conditions. The convective heat transfer in channels occupied by porous media saturated with rarefied gases (or in micro-channels filled with porous media) is a new and a vitally important subject. This motivated us to write the present letter which focuses on many important issues that have emerged after reading of Nield and Kuznetsov, the above referenced work. Our comments will be offered in the following manner (not ordered based on importance): 1. In thefirst paragraph of Nield and Kuznetsov (2006), the authors state: “It seems no studies have been made on forced convection in a duct or channel occupied by a porous medium when the fluid saturating the porous medium is a rarefied gas” In this regard, we would like to inform the authors about our recent work in this research area. During the last two years, we have worked on many papers that investigate the hydrodynamic and thermal behavior of gaseous slip-flow through micro-channels occupied by porous media (Haddad et al. 2005a, b, c, 2006), and the first of these has been published before the submission of Nield’s and Kuznetsov’s while the rest have been in the press for about one year. It is worth mentioning here that gaseous slip-flow in micro-channels (or equivalently rarefied gas flow in macro-channels) may be described mathematically by the same flow model provided that both have Knudsen number, Kn (defined as the ratioofthemean-free-pathtothecharacteristicmacroscopiclengthscale),inthe range 0.001 <Kn< 0.1. For the slip-flow regime, the Navier-Stokes equations arestillapplicableifvelocityslipboundaryconditionsareusedattheboundaries. IntheworkofHaddadetal.(2005a,b,c,2006),Knwasassumedtofallwithinthe “slip-flow regime” in order to use the classical Darcy–Brinkman–Forchhiemer