Thermal development of forced convection in a channel or duct partly occupied by a porous medium

The classical Graetz methodology is applied to semi-analytically investigate the thermal development of forced convection in a parallel-plate channel or a circular tube partly filled by a porous medium. The Beavers-Joseph model for the interface is adopted, together with the Darcy model for the porous medium. For each of the two channel geometries, the cases of a porous core and a porous sheath are studied. For each of these, the variation of Nusselt number with axial coordinate is calculated for various values of the Darcy number and conductivity ratio, for a representative value of the interface position and a representative value of the Beavers-Joseph coefficient.