Mixed convection along a nonisothermal vertical flat plate embedded in a porous medium: The entire regime

Abstract

The problem of mixed convection about a vertical flat plate embedded in a porous medium is analyzed. Nonsimilarity solutions are obtained for the cases of variable wall temperature (VWT) in the form T w (x) = T ∞+ ax n and variable surface heat flux (VHF) in the form q w (x) = bx m . The entire mixed convection regime is covered by two different nonsimilarity parameters χ = [1 + ( Ra x / Pe x ) 1/2] − and χ * = [1 + ( Ra x * / Pe x 3/2) 1/3] −1, respectively, for VWT and VHF cases, from pure forced convection (χ = 1 or χ * = 1) to pure free convection (χ = 0 or χ * = 0). A finite-difference scheme was used to solve the system of transformed governing equations. Velocity and temperature profiles, and local Nusselt numbers are presented. It is found that as χ or χ * decreases from 1 to 0, the thermal boundary layer thickness increases first and then decreases, but the local Nusselt number in the form Nu x ( Pe x 1/2 + Ra x 1/2) −1 or Nu x ( Pe x 1/2 + Ra x *1/3) −1 decreases first and then increases. The correlation equations for the local and average Nusselt numbers are also obtained for the two surface heating conditions.