Insight into variable thermophysical features of the functionally graded porous annular fin influenced by internal heat and thermal radiation

Abstract

The present analysis considers a functionally graded porous fin of radiating shape. The fin is subject to thermal-dependent internal heat generation and radiation. Two different cases are performed where the thermal conductivity varies linearly and exponentially with temperature. For simplicity, it is assumed that the material properties of the porous fin change along the fin radius based on a power-law function, with a consistent Poisson’s ratio. The Fourier’s law and Darcy model are used to model the ordinary differential equation (ODE) that governs the fin problem. The equation’s components have been arranged into dimensionless parameters, and their effects on fin efficiency, thermal stresses, and heat transfer rate are discussed and illustrated visually. The analysis comprehensively addresses the radial and tangential stresses and their thermal effects on the fin. It shows that near the base region of the fin, the tangential stress demonstrates less compression, and near the tip radius, there is smaller tensile stress. It has been found that for heat generation coefficient G=0.1 and εG=0.1 the percentage increase in efficiency is 28.1927%.