Exploration of Temperature Distribution through a Longitudinal Rectangular Fin with Linear and Exponential Temperature-Dependent Thermal Conductivity Using DTM-Pade Approximant

Abstract

The present study elaborates on the thermal distribution and efficiency of a longitudinal rectangular fin with exponentially varying temperature-dependent thermal conductivity and heat transfer coefficient concerning internal heat generation. Also, the thermal distribution of a fin is comparatively studied for both exponentially varying temperature-dependent thermal conductivity and linearly varying temperature-dependent thermal conductivity. Further, the thermal distribution of a longitudinal fin is examined by using ANSYS software with different fin materials. Many physical mechanisms can be explained by ordinary differential equations (ODEs) with symmetrical behavior, the significance of which varies based on the perspective. The governing equation of the considered problem is reduced to a non-linear ODE with the assistance of dimensionless terms. The resultant equation is solved analytically using the DTM-Pade approximant and is also solved numerically using Runge-Kutta Fehlberg’s fourth-fifth (RKF-45) order method. The features of dimensionless parameters influencing the fin efficiency and temperature profile are discussed through graphical representation for exponentially and linearly varying temperature-dependent thermal conductivity. This study ensures that the temperature field enhances for the higher magnitude of thermal conductivity parameter, whereas it diminishes for diverse values of the thermo-geometric parameter. Also, greater values of heat generation and heat transfer parameters enhance the temperature profile. Highlight: Thermal distribution through a rectangular profiled straight fin is examined. Linear and non-linear thermal properties are considered. The combined impact of conduction, convection, and internal heat generation is taken for modeling the energy equation of the fin. Thermal simulation is performed for Aluminum Alloy 6061 (AA 6061) and Cast Iron using ANSYS.