An Effective Analytical Approach to Study Heat Transfer in Porous Fin with Uniform Magnetic Field

Abstract

The objective of the manuscript is to propose a robust analytical method for evaluating the thermal performance of porous fins subjected to a uniform magnetic a problem characterized by strong nonlinearities. In this study, we propose a Differential Transform Method (DTM) that transforms highly nonlinear governing equations into a solvable system of algebraic equations, thereby overcoming the limitations of conventional numerical approaches. A significant novelty of the method is its ability to provide both analytical insight and computational efficiency, making it an ideal alternative for solving complex heat transfer problems. Thorough analysis is conducted on the thermal characteristics of the fin in relation to critical physical parameters, such as the modified Rayleigh number, radiation-conduction parameter, convection parameter, and Hartmann number. The proposed method’s reliability and accuracy are demonstrated through validation against existing numerical and analytical solutions. A MATLAB-based technique is also provided to facilitate real-world implementations. For the accurate and effective thermal design of extended surfaces in sophisticated engineering systems, this framework offers a new tool.