Inverse estimation of surface heating condition in a three-dimensional object using conjugate gradient method

Abstract

Temperature and heat flux on inaccessible surfaces can be estimated by solving an inverse heat conduction problem (IHCP) based on the measured temperature and/or heat flux on accessible surfaces. In this study, the heat flux and temperature on the front (heated) surface of a three-dimensional (3D) object is recovered using the conjugate gradient method (CGM) with temperature and heat flux measured on back surface (opposite to the heated surface). The thermal properties of the 3D object are considered to be temperature-dependent. The simulated measurement data, i.e., the temperature and heat flux on the back surface, are obtained by numerically solving a direct problem where the front surface of the object is subjected to high intensity periodic laser heat flux with a Gaussian profile. The robustness of the formulated 3D IHCP algorithm is tested for two materials. The effects of the uncertainties in thermophysical properties on the inverse solutions are also examined. Efforts are made to reduce the total number of heat flux sensors on the back surface required to recover the front-surface heating condition.