Inverse Estimation of Surface Temperature Induced by a Moving Heat Source in a 3-D Object Based on Back Surface Temperature with Random Measurement Errors

Abstract

Temperatures on inaccessible surfaces can be estimated by solving an inverse heat conduction problem (IHCP) based on the measured temperature on accessible surfaces. In this article, the transient temperatures on the front (heated) surface of a three-dimensional (3-D) object is recovered using the conjugate gradient method (CGM) based on temperatures measured on the back surface (opposite to the heated surface). The simulated measurement data are generated from the exact solution obtained by solving the direct problem, in which the front surface of the object is subjected to a moving heat source having an elliptic spot with a Gaussian profile. Random errors are artificially imposed on the back surface data. It is shown that the front-surface temperatures of the 3-D object can be well recovered using the algorithm presented here. Studies are also carried out to test the effect of large measurement errors on the accuracy of the inverse solution.