Thermal analysis of convective fin with temperature-dependent thermal conductivity and heat generation

In this study, a simple and highly accurate semi-analytical method called the Differential Transformation Method (DTM) is used for solving the nonlinear temperature distribution equation in a longitudinal fin with temperature dependent internal heat generation and thermal conductivity. The problem is solved for two main cases. In the first case, heat generation is assumed variable by fin temperature and in the second case, both thermal conductivity and heat generation vary with temperature. Results are presented for the temperature distribution for a range of values of parameters appeared in the mathematical formulation (e.g. N, εG, and G). Results reveal that DTM is very effective and convenient. Also, it is found that this method can achieve more suitable results compared to numerical methods.