MIXED CONVECTION ALONG A NONISOTHERMAL VERTICAL FLAT-PLATE EMBEDDED IN A POROUS-MEDIUM - THE ENTIRE REGIME

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(infinity) + 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 chi = [I + (Ra(x)/Pe(x))1/2]-1 and chi* = [1 + (Ra(x)*/Pe(x)3/2)1/3]-1, respectively, for VWT and VHF cases, from pure forced convection (chi = 1 or chi* = 1) to pure free convection (chi = 0 or chi* = 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 chi or chi* 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.