A numerical analysis has been performed for the steady-state temperature and stream function distributions in a short cylinder, having an isothermal side and top, an insulated bottom, for a uniform heat generating porous medium. The analysis uses the stream function formulation of Darcy's equation in cylindrical coordinates and the Boussinesq approximation. A single energy equation was used for the fluid and solid. Fluid currents formed in a fluid saturated porous media during conduction heat transfer has many important applications, such as in oil and gas production, cereal grain storage, geothermal energy, and porous insulation.