Inverse Analysis of a Porous Fin to Estimate Time-Dependent Base Temperature

Abstract

This study deals with the application of the sequential function specification method for estimating the unknown time-dependent base temperature in a porous fin based on the temperature measurements at the fin tip. Subsequently, the distributions of temperature and rate of heat transfer of the fin can be obtained. Two examples are considered to illustrate the accuracy of the proposed method. The effects of measurement error, future time steps, initial guess, porous parameter, and nonlinearity on the inverse solution are studied. Results show that the unknown base temperature can be estimated in an inverse manner with any arbitrary initial guess. For correct reconstruction of the base temperature, a precise measurement of the temperature is necessary. In addition, it is shown that, for more reliable results in the presence of measurement error, the sensor should be put closer to the fin base. Results demonstrate that the porous parameter plays an important role in the estimation. The accuracy of the inverse solution decreases as the porous parameter increases. In addition, the inverse solution obtained with linear formulation is more accurate than the nonlinear one.