Study of Heat Transfer in Porous Fin with Temperature Dependent Properties

Abstract

In this paper, mathematical model of heat transfer in a porous fin with internal heat generation, and thermal conductivity is influenced by both spatial factors and temperature are examined. These two concepts are integrated into the model, which highlighting the originality of the current study. The equations and conditions that govern the system are expressed in a dimensionless manner. We examine three scenarios for thermal conductivity: constant, linear, and exponential dependence on temperature. We have utilized three different techniques to solve the problem, including the Legendre Wavelet Collocation, Finite Difference, and Least Square. Due to the nonlinearity of the presented problem, it is not possible to find an exact analytical solution. In this specific scenario, we calculate exact solution, which is then compared to these three methods and found to have a good agreement. The findings and error assessment are displayed in figures and tables. The Legendre wavelet collocation approach yields high accuracy. The novelty of the research is the implantation of space and temperature dependent thermal conductivity and solution of a complex nonlinear problem using a hybrid numerical technique, specifically the collocation method with Legendre Wavelet basis functions.