Mixed convection flow in a narrow vertical duct filled with a porous medium

This paper presents a theoretical study of mixed convection flow in a vertical duct filled with a fluid-saturated porous medium under the assumption that E. the ratio of the duct width to the heated length, is small, i.e., that the duct is narrow. It is assumed that a fully developed flow has already been set up in the duct before localised heating on one wall causes the flow to be changed by the action of buoyancy forces, as measured by the mixed convection parameter, lambda. An analytical solution is derived for the case when both the Peclet number, Pe, and lambda are of O(1). It is found that reversed flow appears at leading order when lambda > 2. This is confirmed by numerical integrations of the governing equations, for P = epsilonPe = 100 and a range of values of lambda, where epsilon --> 0 and Pe = O (epsilon(-1)). The limiting cases of P 1 (boundary layer) with lambda variable and lambda --> infinity (free convection limit) are also studied. The numerical results show very good agreement with the analytical and asymptotic solutions. (C) 2003 Elsevier SAS. All rights reserved.