Darcy boundary layer in forced convection regime using Local Thermal Non Equilibrium model: analytical and numerical solution

A steady two-dimensional forced convection thermal boundary layer flow in a porous medium is studied. The solid and fluid phases are assumed to be in local thermal nonequilibrium and therefore two coupled heat transport equations are studied. A system of parabolic equations is obtained which is analysed both analytically and numerically. The forced convection regime implies taking an asymptotically large Péclet number, Pe >> 1, so that the boundary layer approximation may be applied. Local thermal nonequilibrium between the phases is found to be at its strongest near the leading edge, but the maximum difference between the temperatures of the phases decreases with distance from the leading edge, and local thermal equilibrium is attained at large distances.