Thermal stresses and efficiency analysis of a radial porous fin with radiation and variable thermal conductivity and internal heat generation

The porous fin of radial profile is considered in the current analysis along with the radiation and thermal-dependent internal heat generation condition. In addition, two different cases have been examined based on the linear dependency and exponential dependency of thermal conductivity on temperature. The Darcy’s law is used to study the porous nature of fin. The modeled governing equation is a second-order nonlinear ordinary differential equation and is solved via Runge–Kutta–Fehlberg fourth–fifth-order method. The important terms are grouped as dimensionless parameters and discussed their influence on the heat transfer rate and thermal stresses of the fin. The thermal stresses like radial stress and tangential stress are addressed comprehensively and interpreted graphically. Also, the fin efficiency is defined and discussed graphically. It is found that the tangential stress shows higher compression near fin base region and larger tensile stress near tip radius.