Hongchu Chen

This paper investigates the reconstruction of surface heat fluxes with discontinuity, which is of significant importance in engineering applications. Based on the underlying mechanism of heat conduction, a calibration integral equation is proposed, which formulates the inverse problem into a Volterra integral equation. Combined with Bayesian regularization, this approach can effectively predict surface heat flux with sudden changes or discontinuities in the thermal data. Results demonstrate that Bayesian regularization outperforms traditional methods, such as Tikhonov regularization, in reconstructing both smooth and abrupt heat flux variations. It accurately captures sudden changes, even in the presence of noise and rapid thermal fluctuations. In contrast, classical regularization methods are only effective for smooth heat flux predictions. The contributions of this study include: (1) demonstrating the effectiveness of CIEM for dynamic and abrupt boundary conditions, (2) introducing Bayesian regularization to mitigate over-smoothing. These advancements provide critical insights for optimizing thermal protection systems and improving safety in high-speed flight applications.

Slug calorimeters are commonly used for surface heat flux measurements in hypersonic flight and ground tests. Based on the measurement principle of slug calorimeters, an analytical solution for one-dimensional heat conduction is applied to obtain surface heat fluxes. However, due to the differences in thermophysical properties among substrate, slug, and insulation sleeve, the occurrence of lateral heat conduction leads to measurement errors of surface heat flux in calorimeter. Therefore, a quantitative analysis of lateral heat transfer should be performed in the slug calorimeter and at the interface between the insulation sleeve and the model wall. In this paper, the multidimensional heat conduction between six materials of the model wall and four materials of the insulation sleeve under long-term heating was investigated using numerical simulations. The structural designs were then implemented for slug calorimeter and model wall considering the lateral heat transfer characteristics. The derivation of the axisymmetric finite difference equation is obtained by improved Crank–Nicolson discrete scheme. We found that the best model wall material for thermal matching with slug calorimeters is aluminum. Some structural optimizations can maintain a stable inverted heat flux curve. This study’s conclusions offer practical guidance for the selection of model wall materials and the design optimization of slug calorimeters.

In this review, we have endeavored to summarize and describe the research conducted to date on coaxial thermocouples for transient heat flux testing as well as the manufacturing processes. The review paper not only summarized important advances in coaxial thermocouple research along the time, but also suggested future directions and trends in coaxial thermocouple development. Main sections of presentation include major calibration techniques for coaxial thermocouples, experimental evaluation of coaxial thermocouple performance, and the influence of lateral heat transfer benefits on thermal measurements. In addition, the design of new type coaxial thermocouples, heat flux inversion methods and applications of coaxial thermocouples in other fields were also introduced. Finally, the direction of coaxial thermocouple development was discussed based on the needs of hypersonic thermal testing.

In this paper, a parameter estimation approach, based on a least-square method and a quantified heat flux source, is proposed for estimating the effective thermal effusivity of a co-axial thermocou...

A calibration integral equation method is proposed for estimating the surface temperature in the context of a nonlinear inverse heat conduction problem. The temperature-dependent thermophysical properties and probe positioning are implicitly accounted in the integral equation formulation through calibration tests. A first kind Chebyshev expansion is applied to represent the temperature-dependent property transform function. The undetermined expansion coefficients associated with the Chebyshev expansion are then estimated through two calibration tests. Regularization of the ill-posed problem is achieved by the future-time method. The optimal regularization parameter is estimated using a phase plane and cross-correlation phase plane analyses. Numerical simulation for stainless steel yields highly favorable surface temperature prediction.