The Effect of a Transition Layer Between a Fluid and a Porous Medium: Forced Convection in a Channel

Flow in a three-layer channel is modeled analytically. The channel consists of a transition layer sandwiched between a porous medium and a fluid clear of solid material. Within the transition layer, the reciprocal of the permeability varies linearly across the channel. The Brinkman model is used for the momentum equations for the porous medium layer and the transition layer. The velocity profile is obtained in closed form in terms of Airy, exponential, and polynomial functions and this is employed to find analytically the Nusselt number for fully developed forced convection with boundaries subject to uniform and constant heat flux.