The heat pulse (flash) experiment is a well-known and widely accepted method to measure the thermal diffusivity of a material. In recent years, it has been observed that the thermal behavior of heterogeneous materials can show deviation from the classical Fourier equation, resulting in a different thermal diffusivity and requiring further thermal parameters to identify. Such heterogeneity can be inclusions in metal foams, layered structure in composites, or even cracks and porous parts in rocks. Furthermore, the next candidate, the Guyer–Krumhansl equation is tested on these experiments with success. However, these recent evaluations required a computationally intensive fitting procedure using countless numerical solutions, even when a good initial guess for the parameters is found by hand. This paper presents a Galerkin-type discretization for the Guyer–Krumhansl equation, which helped us find a reasonably simple analytical solution for time-dependent boundary conditions. Utilizing this analytical solution, we developed a new evaluation technique to immediately estimate all the necessary thermal parameters using the measured temperature history.

热脉冲（闪光）实验是一种众所周知且被广泛接受的测量材料热扩散率的方法。近年来，已经观察到异质材料的热行为可能会偏离经典的傅立叶方程，导致不同的热扩散率，需要进一步的热参数来识别。这种异质性可以是金属泡沫中的夹杂物、复合材料中的层状结构，甚至是岩石中的裂缝和多孔部分。此外，下一个候选者 Guyer-Krumhansl 方程在这些实验中得到了成功测试。然而，这些最近的评估需要使用无数数值解的计算密集型拟合程序，即使手动找到参数的良好初始猜测也是如此。本文提出了 Guyer-Krumhansl 方程的 Galerkin 型离散化，它帮助我们找到了时间相关边界条件的合理简单的解析解。利用这种分析解决方案，我们开发了一种新的评估技术，可以使用测量的温度历史立即估计所有必要的热参数。