Steady finite Rayleigh number convective flows in a porous medium with internal heat generation

The steady convective flow within a square region filled with a fluid-saturated porous medium having internal heat generation at a rate proportional to a power of the temperature difference is considered. Three dimensionless parameters are identified, a Rayleigh number Ra, a heating rate parameter γ and the exponent p in the local heating term. The case Ra=0 is considered first, where a critical value γc is found, such that there are solutions possible only for γ⩽γc. This case also identifies a value γ0, where there is a change in the maximum temperatures Tmax achieved. For γ>γ0, Tmax>1 and temperatures above the heated wall value can be generated. Numerical results for Ra>0 are obtained, also showing the existence of a critical value γc and a value γ0. These results show that, for larger values of Ra, boundary layers develop on the vertical walls with a weak eddy flow in the central region. They also show that significantly higher temperatures than the heated wall can be generated by the internal heating, particularly for the larger values of γ.