A Weakly Parameter-Dependent Approach for Resolving Non-Fourier Inverse Heat Conduction Problems Based on Calibration Integral Equation Method

Abstract

Abstract. With the development of technology, phenomena with ultrahigh heat flux, small space, short time span heat conduction becomes more common. In these cases, the traditional Fourier's law is not applicable. Accurately predicting heat flux or temperature at special locations is prerequisite of thermal design in electronic cooling, laser engineering and so on. However, the existence of non-Fourier heat conduction makes it difficult to obtain demanding data. Numerous physical parameters also increase difficulties in estimating the heat flux and temperature at special locations by resolving inverse problems. In this paper, Laplace transform treats the heat equation and boundary conditions to exclude the necessity of system parameters. Furthermore, we derive a calibration integral equation based on dual-phase-lag model to resolve surface heat flux in non-Fourier heat conduction process, and prove the correctness of the algorithm by designing calibration tests with different heat fluxes. Under 2% and 10% noise factor, the relative root-mean-square errors of prediction results are less than 3% by selecting optimum regularization parameters, which verify the robustness of the algorithm.