Numerical analysis of heat transfer in porous fin with non-homogeneous porosity and considering thermal radiation effect

In this study, the analysis of heat transfer in porous fin considering thermal radiation and natural convection is investigated. In order to model radiation, discrete ordinates method is used. Also, Darcy–Brinkman–Forchheimer model is applied for simulating porous media. A Least square method and numerical simulation (computational fluid dynamics) are applied to obtain the solution of governing equations. In addition, accuracy of LSM results is compared with the numerical simulation results. Moreover, the effects of homogeneous and non-homogeneous porosity along the porous media, Rayleigh number, Darcy number, porosity, surface emissivity, on temperature distribution along the length of porous fin and Nusselt number are investigated. Results show that the numerical simulation and LSM results are in good agreement with each other (With average error of 3.39%). Also neglecting thermal radiation effect in heat transfer analysis of porous fin leads to 10- 20% error in the Nusselt number value. Moreover, by applying nonlinear variable porosity along the porous media, the Nusselt number will increase up to 23% with respect to the homogeneous porosity. So in order to enhance heat transfer rate, porosity profile should be applied appropriately along the porous media.