Antiderivative approach to radiative free convection past a vertically raised surface in a porous material with entropy analysis

This study investigates free convective heat and mass transfer over a vertically raised surface embedded in a fluid-saturated porous medium subjected to Rosseland-approximated radiative heat flux, for the case of constant wall heat and mass flux ( \(n=1/3\) ). An antiderivative (Von Kármán integral) approach is used to reduce the governing boundary-layer equations to closed algebraic relations for the boundary-layer-thickness ratio, local Nusselt number, and local Sherwood number. The governing parameters are the buoyancy ratio N , the Lewis number Le , and the radiation parameter Rd . At the reference point \(N=0\) , \(Le=1\) , the method is calibrated against the classical similarity solution of Lai and Kulacki (giving \(Nu/Ra_x1/2=Sh/Ra_x1/2=0.6777\) ); away from this point the closed-form predictions are compared against the benchmark to within the deviations reported in Table. Across the tested range \(Le∈ [1,100]\) , the Nusselt number is found to fall by roughly a factor of 3 while the Sherwood number rises by more than an order of magnitude, reflecting the disparate diffusion regimes captured by Le . Velocity, temperature, concentration, entropy generation, and Bejan-number profiles are analysed for varying N , Rd , and Le , together with skin friction, Nusselt, and Sherwood numbers.