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

Abstract

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 ε, 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, λ. An analytical solution is derived for the case when both the Péclet number, Pe, and λ are of O(1). It is found that reversed flow appears at leading order when λ>2. This is confirmed by numerical integrations of the governing equations, for P= εPe=100 and a range of values of λ, where ε→0 and Pe= O( ε −1). The limiting cases of P⪡1 and P⪢1 (boundary layer) with λ variable and λ→∞ (free convection limit) are also studied. The numerical results show very good agreement with the analytical and asymptotic solutions.