Three-Parameter Estimation Study in a Radial Fin Geometry Using FDM-Based Simplex Method

Abstract

Estimation of three parameters is done in a conductive-convective radial fin from the knowledge of steady-state temperature distribution. The three parameters are the thermal conductivity, the inner radius, and the thickness of the fin. In order to demonstrate the estimation methodology, using some known values of these three parameters, a forward problem using the finite-difference method (FDM) is solved to obtain the required temperature field. Using this temperature distribution, next an inverse method based on the Nelder-Mead simplex search optimization method is used for retrieving the unknown parameters. The relatively difficult among the estimated parameters are identified and the relative sensitiveness of the estimated parameters to the measurement errors is studied in detail. The results obtained from the inverse method are benchmarked with the forward method (FDM) and the analytical solution. Even for three-parameter retrievals, the study demonstrates that although a good reconstruction of the temperature field is possible, ill-posed behavior occurs for estimations with multiple parameters.