Thermal analysis of longitudinal fin with temperature-dependent properties and internal heat generation using Galerkin's method of weighted residual

In this study, heat transfer in a longitudinal rectangular fin with temperature-dependent thermal properties and internal heat generation is analysed using Galerkin's method of weighted residual. The simple, but highly accurate solution was validated by the exact solution for the linear problem, and also by numerical method and differential transformation method in the case of the non-linear problem. The developed heat transfer models were used to investigate the effects of thermo-geometric parameters, coefficient of heat transfer and thermal conductivity (non-linear) parameters on the temperature distribution, heat transfer and thermal performance of the longitudinal rectangular fin. From the results, it shows that the fin temperature distribution, the total heat transfer, the fin effectiveness, and the fin efficiency are significantly affected by the thermo-geometric and thermal parameters of the fin. The analysis revealed that the operational parameters must be carefully chosen to ensure that the fin retains its primary purpose of removing heat from the primary surface. Therefore, the results obtained in this analysis serve as basis for comparison of any other method of analysis of the problem, and they also provide a platform for improvement in fin design of fin in heat transfer equipment.