Effect of local thermal non-equilibrium on thermally developing forced convection in a porous medium

The classical Graetz methodology is applied to investigate the effect of local thermal non-equilibrium on the thermal development of forced convection in a parallel-plate channel filled by a saturated porous medium, with walls held at constant temperature. The Brinkman model is employed. The analysis leads to an expression for the local Nusselt number, as a function of the dimensionless longitudinal coordinate, the Péclet number, the Darcy number, the solid–fluid heat exchange parameter, the solid/fluid thermal conductivity ratio, and the porosity.