Finite Element Analysis of Transient Thermal Behaviour of a Radiative-Convective Fin with Functionally Graded Material under the Influence of Magnetic Field

Finite Element Analysis of Transient Thermal Behaviour of a Radiative-Convective Fin

Abstract

In this work, finite element analysis of transient thermal response of a convective-radiative fin with functionally graded material under the influence of temperature-variant magnetic field is presented. The thermal conductivity of the fin with functional graded fin is considered to be linear, quadratic and exponential variation of space. The comparisons of exact analytical solution with the numerical solution show good agreement between the two results. The parametric studies reveal that the temperature of the extended surface increases as the in-homogeneity index. The impact of the in-homogeneity index reduces as the value of the thermo-geometric parameter increases. The change in the fin temperature becomes very insignificant for higher values of the thermo-geometric parameter. This same trend is also noticed under increasing values of the magnetic field and radiative parameters. The augmentations of the radiation and magnetic field parameters leads to decrease in the thermal distribution of the extended surface which in consequent increases the rate of heat transfer through the passive device. The thermal distribution increases as time progresses and later converge to a steady state heat as time evolves. The material under exponential law function needs smaller time to reach steady state than when the material operates under the linear and quadratic law. The results depict that the application of the passive device with functional graded material reduces the thermal resistance along the length of the fin. Therefore,  there is a significant higher rate of energy saving in an extended surface with functional graded material than the heat sink with homogenous material.