Viscous dissipation and local non-equilibrium in a Darcy-Graetz problem with axially periodic boundary conditions

The thermal entrance region in a plane-parallel channel filled by a fluid saturated porous medium is investigated, with reference to steady forced convection and to a thermal boundary condition given by a wall temperature longitudinally varying with a sinusoidal law. The effect of viscous dissipation in the fluid is taken into account, and a two temperature model is employed in order to evaluate separately the local fluid and solid matrix temperatures. The asymptotic temperature distributions are determined analytically. The governing equations in the thermal entrance region are solved numerically by a finite element method and by the method of lines.