Non-Linear Model for a Spiral Porous Fin Subjected to Darcy Flow

Abstract

In this study, the temperature distribution equation for a spiral porous fin is presented. Based on Darcy’s model, a mathematical equation of the energy is derived and a suitable dimensionless form is outlined to highlight some characteristic parameters, namely, the spiral fin pitch, the porosity, and the modified Rayleigh number. The behavior of the solution is analyzed for two cases of interest, taking into account the temperature-dependent thermal conductivity of the fin encountered in a hostile environment. A Numerical method is applied to solve this non-linear problem. It is found that the thermal transfer is not affected by the change of the spiral fin pitch, whereas increasing the porosity or the parameter β* makes higher fin temperature and improve the fin efficiency.