Galerkin’s Method of Weighted Residual for a Convective Straight Fin with Temperature-Dependent Conductivity and Internal Heat Generation

摘要

In this paper, Galerkin’s method of weighted residual was applied to study the heat transfer and thermal stability of a convective straight fin with temperature-dependent thermal conductivity and internal heat generation. The method of weighted residual provides a very powerful and accurate approximate analytical solution to the fin problem. The simple but highly accurate solution was validated by the exact solution for the linear problem. The developed heat transfer models were used to investigate the effects of thermo-geometric parameters, the 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 the basis for comparison of any other method of analysis of the problem and they also provide a platform for improvement in the design of fin in heat transfer equipment.