The flash method is a commonly used technique for estimating the thermal diffusivity of solid materials. In this work, we develop a new efficient formula for the thermal diffusivity calculation to process the flash method data in the case of heat losses at the rear and front faces. First, the transient heat equation is analytically solved using the Green functions under time-dependent convection boundary conditions. The property of the descending part of the analytical solution, containing series which converges very quickly for long times, allows to express the thermal diffusivity as a function of the slope of the natural logarithm of the temperature rise and the Biot numbers related to heat losses at the rear and front faces. These Biot numbers are calculated from the ratio between the integrals of the complete temperature trends of the two faces. For this purpose, we developed a novel way to evaluate these integrals using the analytical solutions in Laplace domain. To verify the accuracy of these formulas, we simulated experimental data adding a Gaussian noise to the theoretical temperature results of the flash method data.

中文翻译：

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考虑到前后表面热损失的闪光法热扩散率估计的新有效公式

闪蒸法是一种常用的估算固体材料热扩散系数的技术。在这项工作中，我们为热扩散率计算开发了一个新的有效公式，以处理背面和正面热损失情况下的闪光方法数据。首先，瞬态热方程在瞬态对流边界条件下使用格林函数进行解析求解。解析解的下降部分的性质，包含长时间收敛非常快的级数，允许将热扩散率表示为温度升高的自然对数斜率的函数和与热损失相关的比奥数背面和正面。这些比奥数是根据两个面的完整温度趋势积分之间的比率计算得出的。为此，我们开发了一种使用拉普拉斯域中的解析解来评估这些积分的新方法。为了验证这些公式的准确性，我们模拟了实验数据，在闪光法数据的理论温度结果中添加了高斯噪声。