Application of simplex search method for predicting unknown parameters in an annular fin subjected to thermal stresses

Abstract

This article presents an inverse approach aimed at estimating the unknown parameters such as the coefficient of thermal expansion and the Biot number for satisfying a prescribed thermal stresses field in radial fin geometry. The variation of temperature with the radius of fin is obtained by solving the heat conduction-convection equation using regular perturbation method and applying proper boundary conditions. A closed form solution for the temperature dependent stress field has been derived by employing the classical elasticity theory coupled with semi-analytical solution for the temperature field. Using the data obtained from a forward method based on the analytical solution, two unknown parameters such as the coefficient of thermal expansion and the Biot number of the fin are simultaneously estimated by an inverse technique using the Nelder-Mead simplex search method. Effects of measurement errors and number of measurement points have been analyzed in detail. It is found that even with 10 measurement points a fairly good reconstruction of the stress field can be achieved