Prediction of Temperature distribution in Straight Fin with variable Thermal Conductivity and Internal Heat Generation using Legendre Wavelet Collocation Method

Abstract

Due to increasing applications of extended surfaces as passive methods of cooling, study of thermal behaviors and development of mathematical solutions to nonlinear thermal models of extended surfaces have been the subjects of research in cooling technology over the years. In the thermal analysis of fin, various methods have been applied to solve the nonlinear thermal models. This paper focuses on the application of Legendre wavelet collocation method to the prediction of temperature distribution in longitudinal rectangular fin with temperature-dependent thermal conductivity and internal heat generation. The numerical approximations by the method are used to carry out parametric studies of the effects of the model parameters on the temperature distribution in the fin. The results show that the thermal performance of the fin is favoured at low values of thermogeometric parameter and internal heat generation decreases the performance of the fin. The results can serve as verification of the solutions of other methods of analysis of the component.