Analytical solution for the effect of viscous dissipation on mixed convection in saturated porous media

A new analytical solution is introduced for the effect of viscous dissipation on mixed convection flow and heat transfer about an isothermal vertical wall embedded in Darcy and non-Darcy porous media with uniform free stream velocity. The effect of viscous dissipation on mixed convection in both regimes has been analyzed for both the aiding and opposing flows using Gebhart number, Ge-x = g beta x/c(p). The governing parameters are Re, Ra, Pe and Ge-x. The case of Re = 0 corresponds to Darcy mixed convection region and Re/Pe is identified as the mixed convection governing parameter, Ra = 0 leading to pure forced convection. A good agreement was found between the numerical and analytical solutions. It was found from the Nusselt number results that viscous dissipation lowers the heat transfer rate in both Darcy and Forchheimer flow regimes for aiding as well as opposing flows.