标题： 基于蒸发冷冻冷却激励的热扩散率测量：理论与实验 显示英文标题

标题： Thermal diffusivity measurement based on evaporative cryocooling excitation: Theory and experiments

摘要： 光热方法测量热扩散率本质上是一个不适定的逆问题，受样品厚度、加热或冷却时间以及激发能量等因素的影响。 在非脉冲脉冲激发下，当观测时间尺度与脉冲持续时间相当，测量精度变得尤为具有挑战性。 这通常是由于脉冲形状定义不明确、热响应展宽以及缺乏清晰的边界条件造成的，尤其是在显著的界面温度梯度下，自然对流占主导地位时。 经典的Parker解虽然被广泛使用，但其物理上并不现实，因为它假设了绝热热通量和浅层区域的热吸收。 在本研究中，我们证明Parker的假设在数学上等价于狄拉克脉冲边界条件。 然后，我们给出了在狄拉克脉冲和矩形脉冲激发下的热/冷却响应的全面解析解。 通过与具有良好设定边界条件的特征函数解进行比较，我们表明 Parker解仅在热峰之前有效。 通过无量纲处理，我们进一步证明Parker解可以视为加热持续时间趋近于零时矩形脉冲解的一个极限情况。 此外，我们提出了一种新颖的激发方法——蒸发冷冻冷却法，用于热扩散率的测量。 这种方法提供了一种紧凑、低成本且易于实现的传统激发方案的替代方法。 理论模型通过与实验结果的比较得到了进一步验证。 显示英文摘要

摘要： Photo-thermal methods for measuring thermal diffusivity inherently pose an ill-posed inverse problem, affected by factors such as sample thickness, heating or cooling time, and excitation energy. Measurement accuracy becomes particularly challenging under non-impulsive pulsed excitation when the observation timescale is comparable to the pulse duration. This is often due to poorly defined pulse shapes, broadened thermal responses, and the absence of clear boundary conditions, especially under significant interfacial temperature gradients where natural convection dominates. The classic Parker solution, while widely used, is physically unrealistic as it assumes adiabatic heat flux and shallow-region heat absorption. In this study, we prove that Parker's assumption is equivalent to the Dirac pulse boundary condition in mathematics. Then, we present comprehensive analytical solutions for thermal/cooling responses under Dirac and rectangular pulse excitations. By comparing with eigenfunction-based solutions for well-posed boundary conditions, we show that Parker's solution is only valid before the thermal peak. Through dimensionless processing, we further demonstrate that Parker's solution can be regarded as a limiting case of the rectangular pulse solution as the heating duration approaches zero. Furthermore, we propose a novel excitation approach, evaporative cryocooling, for thermal diffusivity measurement. This method offers a compact, low-cost, and easy-to-implement alternative to conventional excitation schemes. The theoretical model was further validated through comparison with experimental results.