The steady two-dimensional laminar forced flow and heat transfer of a viscous incompressible electrically conducting and heat-generating fluid past a permeable wedge embedded in non-Darcy high-porosity ambient medium with uniform surface heat flux has been studied. The governing equations are derived using the usual boundary layer and Bossinesq approximations and accounting for the applied magnetic filed, permeability of porous medium, variable porosity, inertia and heat generation effects. These equations and boundary conditions are non-dimenstionalized and transformed using non-similarity transformation. The resulting non-linear partial differential equations are then solved numerically subject to the transformed boundary conditions by a finite difference method. Comparisons with previously published works are performed and the results are found to be in excellent agreement. Numerical and graphical results for the velocity and temperature profiles as well as the skin friction and Nusselt number are presented and discussed for various parametric conditions.