A Novel Nonlinear Calibration Method for Surface Heat Flux Prediction With Unknown Thermal Conductivity

Abstract Solving inverse heat conduction problems (IHCPs) is a critical challenge in many engineering applications. For typical engineering materials, the temperature dependence of thermophysical properties introduces nonlinearity, making IHCPs difficult to resolve. Moreover, measurement errors contained in thermophysical properties can further affect prediction accuracy. In this paper, linearization and Fourier's law are introduced to these equations to ensure the application of Laplace transform. Based on this calibration integral equation, the temperature-dependent volumetric heat capacity is required, while thermal conductivity measurement can be avoided. Numerical simulations demonstrate that, under 2% in-depth measurement noise, the relative root-mean-square errors (RRMSEs) of the predicted surface heat flux are approximately 8%. This level of accuracy is highly acceptable, especially considering that the thermal conductivity is unknown and not provided as a model input.