Application of homotopy perturbation method and inverse prediction of thermal parameters for an annular fin subjected to thermal load

Abstract

ABSTRACTIn this work, application of the homotopy perturbation method (HPM) and an inverse solution for estimating unknown thermal parameters such as the variable thermal conductivity parameter (β), the thermogeometric parameter (K), and the nondimensional coefficient of thermal expansion (χ) in an annular fin subjected to thermal stresses is presented. Initially, to obtain the nondimensional temperature distribution from the heat equation, the forward method is employed using an approximate analytical solution based on HPM. Thereafter, a closed form solution for the temperature-dependent thermal stresses is obtained using the classical theory of thermoelasticity coupled with HPM solution containing the temperature distribution. Next, for satisfying a particular stress criterion which makes relevance in selecting appropriate configurations for selecting the finned system, unknown thermal parameters are obtained using an inverse approach based on the Nelder–Mead simplex search minimization technique. The objective function is taken as the sum of square of the residuals between the measured stress field and an initially guessed value which is updated iteratively. It is found that more than one type of temperature distribution may yield a given stress distribution, thereby giving rise to different fin efficiencies. The agreement between the actual and the predicted results was found to be satisfactory.