Inverse Prediction and Application of Homotopy Perturbation Method for Efficient Design of an Annular Fin with Variable Thermal Conductivity and Heat Generation

Abstract

In the present work, various thermal parameters of an annular fin subjected to thermal loading are inversely estimated using differential evolution (DE) method. In order to obtain the temperature field, the second order nonlinear differential equation for heat transfer with variable thermal conductivity and internal heat generation is solved using Homotopy Perturbation Method (HPM). Classical thermoelasticity approach coupled with an HPM solution for temperature field is employed for the forward solution of thermal stresses. It is interesting that the internal heat generation does not affect the radial stresses, while the temperature field and the tangential stresses are influenced by the heat generation parameters. As the tangential stresses are mainly responsible for mechanical failure due to thermal loading in an annular fin, the unknown thermal parameters are inversely estimated from a prescribed tangential stress field. The reconstructed stress fields obtained from the inverse parameters are found to be in good agreement with the actual solution.

Keyword : heat conduction, inverse problem, nonlinear problem, perturbation method, mathematical model