Nonsimilarity solutions for mixed convection from vertical surfaces in porous media: variable surface temperature or heat flux

Abstract

Nonsimilarity solutions for mixed convection from a vertical flat plate embedded in a porous medium are reported for two surface heating conditions: variable wall temperature (VWT) and variable surface heat flux (VHF) of the power-law form. The entire mixed convection regime is divided into two regions. One region covers the forced convection dominated regime and the other one covers the free convection dominated regime. The governing equations are first transformed into a dimensionless form by the nonsimilar transformation and then solved by a finite-difference scheme. Four nonsimilarity parameters are introduced. The parameters Ra x/Pe x and Ra x */Pe x 3/2 characterize the effect of buoyancy forces on the forced convection for the VWT and VHF cases, respectively; while the parameters Pe x/Ra x and Pe x/Ra x *2/3 characterize the effect of forced flow on the free convection for VWT and VHF cases, respectively. Numerical results for both heating conditions are presented. Correlation equations for the local and average Nusselt numbers are also presented.