Analytical solution for temperature equation of a fin problem with variable temperature-dependent thermal properties: Application of LSM and DTM-Pade approximant

Abstract

Temperature variation through a longitudinal fin with linear and nonlinear temperature-dependent thermal conductivities and heat transfer coefficient, subject to radiative heat flux and convective heat transport is explained in the present examination. For the radiative heat flux, the Rosseland approximation is incorporated and convection mode of energy transmission is accounted on the fin's surface. The associated physical problem is developed in such a manner that the steady-state heat transmission problem is governed with the help of dimensionless variables signified by a second order differential equation (ODE). To solve this equation, an analytical approach, DTM-Pade, and the LSM are implemented. Moreover, the consequence of a few non-dimensional factors on the temperature field are depicted graphically. The investigation's main findings illustrate that a significant decline in the thermal field is caused by an increment in the convection and the radiation mechanism. The internal development of heat affects the thermal distribution in the fin.