Thermal analysis of rectangular moving fins with temperature-variant properties by employing the Galerkin scheme

In the present study, the thermal behavior of a longitudinal fin considering three types of heat transfer mechanisms (conduction, convection, and radiation) is investigated. For this research, thermal conductivity, heat source, and heat transfer coefficient are assumed nonindependent. A semianalytical scheme called the Galerkin Method is utilized for solving the dimensionless governing equation. The impacts of important physical variables like Peclet number, gradient of thermal conductivity, thermo-geometric parameter, and radiation-conduction parameter on temperature profiles are analyzed comprehensively. The obtained results indicate that raising the thermo-geometric parameter from 0 to 2 leads to a 32% reduction in the temperature profile. Also from the results, it can be found that a 28% increment in the temperature is observed by changing the gradient of thermal conductivity from 0 to 2.