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
