Forced convection with viscous dissipation using a two-equation model in a channel filled by a porous medium

The effects of viscous dissipation on the temperature profiles for a fully developed forced convection flow between two parallel plates with a constant heat flux boundary condition are studied. A two-equation model that includes viscous dissipation in the fluid phase is solved analytically and exact solutions for the temperature fields are obtained. Based on the solutions, the effects of several parameters on the transverse temperature profiles and Nusselt number are studied. The solution reducing to two respective limiting situations of slug flow and clear fluid flow agrees with the literature. A comparison with a one-equation model is also presented.