A mathematical model that predicts turbulent flow and heat transfer for plane two-dimensional channel flow in a porous medium in the limit as porosity approaches unity is developed. The development is carried out in two steps. The first is based on partial differential equations for momentum and energy conservation in the fluid and solid phases (two temperatures) in the channel derived from volume averaging theory (VAT) for a medium with a continuously changing of porosity and specific surface area. The second is to make changes to the porous layer morphology on the surfaces of the channel. After constructing closure models for the above equations, the features of momentum in the channel are shown to smoothly converge to the transport characteristics of a plane channel.