A steady incompressible fully developed laminar viscous flow is investigated analytically in a channel partially filled with a porous medium attached to the wall. A new mathematical model is presented to better understand the behavior of various types of wicking materials in heat pipes and enhancement heat transfer in thermal systems. Also, the model can be used to optimize the utilization of basic energy resources in the major energy consuming sectors. The effects of Darcy number, thickness of porous layer and porosity are investigated. The modeling and solution of the conservation equations provide velocity and shear stress distribution in two domains. The results show that under a constant pressure gradient, the velocity profile in the porous layer is nearly linear. The shear stress depends on the porous thickness and has a non-monotonic behavior for large Darcy numbers. This trend can be changed to a monotonic function if the Darcy numbers is decreased.