Inverse Estimation of Surface Heating Condition in a Finite Slab With Temperature-Dependent Thermophysical Properties

Abstract

Temperature and heat flux at the heated surface can be estimated by solving an inverse heat conduction problem (IHCP) based on measured temperature and/or heat flux at the accessible locations (e.g., back surface). Most of the previous studies used temperature measurement data in the objective function, and little work has been done for the inverse numerical algorithm based on heat flux measurement data. In this study, a one-dimensional IHCP in a finite slab is solved by using the conjugate gradient method. The heat flux measurement data are, for the first time, incorporated into the objective function for a nonlinear heat conduction problem with temperature-dependent thermophysical properties. The results clearly show that the inverse approach of using heat flux measurement data in the objective function can provide much better predictions than the traditional approaches in which the temperature measurements are employed in the objective function. Parametric studies are performed to demonstrate the robustness of the formulated IHCP algorithm by testing it for two different materials under different frequencies of the imposed heat flux along with random errors of the measured heat flux at the back surface.