The current simulations treat impacts of the thermal radiation on some natural convective process and entropy generation along a vertical surface impeded in a non-Darcy porous medium. Various convective practicabilities are due to various thermal boundary conditions, namely, isothermal surface with horizontal leading edge C1, uniform surface with horizontal leading edge C2, an adiabatic surface with a concentrated heat source along the horizontal leading edge C3 and a plane plume rising from a horizontal thermal source C4. Beside the boundary conditions, these convection modes are characteristic with a power index n such that n=0 refers to C1, n=0.2 refers to C2 and n=-0.6 refers to C3 and C4. The worked mixture is Cu-water nanofluid. The dependent variables are expanded in terms of small parameters γ(x) and λ(x), those are function in the permeability parameter. Numerical imitations are …