Comments on two analyses of thermal non-equilibrium Darcy–Brinkman convection in cylindrical porous media

The problem of forced convection heat transfer in porous media using the non-thermal equilibrium two-equation model is revisited analytically. Darcy-extended Brinkman momentum equation is used to describe the velocity profile inside the porous medium. The solution steps for the volume-averaged equations are outlined concisely to allow easy comparison to existing solutions in the literature. Using a case of air flow in open-cell metal foam, the fluid temperature is obtained by the current solution and by a solution existing in the literature. The pre-existing solution produced a physically-unexplained behavior. What seemed to be an error in the pre-existing solution was identified and described in detail. Robust solutions are useful in parametric studies, initial engineering design and for calibration of numerical solutions of more complex cases.