A Calibration Integral Equation Method for Inverse Heat Conduction Problems With Nonlinear Back Surface Boundary Condition

The radiative heat transfer boundary condition typically occurs in high-temperature environments and is highly nonlinear. In these cases, noncontact measurements are usually utilized to substitute contact-based measurements that often interfere with the structure. This article proposes a linearization approach to derive a calibration integral equation for predicting surface heat flux based on temperature measurement on the back surface, where noncontact temperature measurement techniques can be effectively utilized. Our numerical simulations demonstrate that the relative root mean square errors of the predictions are only 2% when the linearization assumption is valid, making the approach highly suitable for certain engineering applications. Additionally, through an analysis of boundary conditions involving both heat convection and radiation, a criterion is proposed to ensure the feasibility of the linearization assumption.