An optimization study to investigate non-linearity in thermal behaviour of porous fin having temperature dependent internal heat generation with and without tip loss

Abstract

This work is devoted to study the temperature distribution, efficiency and optimization of rectangular porous fins for insulated and convective tip conditions. The governing differential equations obtained in the analysis of porous fins are highly non linear in kind. Two approximate analytical techniques, Adomian Decomposition method (ADM) and Differential transformation method (DTM) are adopted to predict the temperature distribution in the porous fin with temperature dependent heat generation, and temperature dependent thermal conductivities of fin material and fluid passing through fin pores. A numerical scheme using finite difference method has been applied to validate the analytical results. The analytical results obtained have been found in accordance with the numerical results. The role of different important parameters have been discussed to understand their importance in the heat transfer through porous fins. Also, a comparison has been presented between solid and porous fins and the results indicate that by selecting an appropriate value of porosity higher heat transfer rate can be achieved.