Effect of radiative losses on the heat transfer from porous fins

The effect of radiation heat transfer on the natural convection heat transfer from a porous fin attached to a vertical isothermal surface has been investigated. The Rosseland approximation for the radiation heat exchange and the Darcy model for simulating the solid-fluid interactions in the porous medium have been adapted in this study. The governing equations are reduced to a single nonlinear ordinary differential equation. A closed form solution for the convection-radiation heat transfer from an infinite fin for low surface temperature parameter, θb, has been found and presented. The dimensionless temperature profiles, the effectiveness parameter, φBi, or the average Nusselt number are graphically displayed. The effect of varying Rayleigh number, Ra∗, the radiation-conduction parameter, Rd, the surface temperature parameter, θb, and the surface-ambient radiation parameter, R2, are presented. It is found that as the surface temperature parameters increases the radiation effect becomes important and as Ra∗ increases the radiation effects become less important.