Heat transfer coefficient (HTC) is a useful concept to characterize the heat exchange performance of rock fracture. However, existing study has preliminarily found that some HTC formulas would lead to abnormal values, which claims a systematical evaluation of existing formulas. In this paper, 214 test records are employed to evaluate 8 existing formulas from literature. It is found that, for all these experimental data, Bai’s formula (Formula D) developed in 2017 shows fairly good numerical stability, while the rest show numerical oscillations and anomalies in different degrees. Moreover, the numerical oscillations and anomalies would be exacerbated with the increase of flow rates, which leads to poor applicability. Error propagation theory in numerical analysis is used to analyze the mechanism of the numerical oscillations and anomalies which can be effectively explained with the condition number and the relative error of the corresponding formula.

中文翻译：

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岩石裂缝传热系数公式的评价分析

传热系数 (HTC) 是表征岩石断裂热交换性能的有用概念。但现有研究初步发现，部分HTC公式会导致数值异常，这要求对现有公式进行系统评估。在本文中，使用 214 条测试记录来评估文献中的 8 个现有公式。发现，对于所有这些实验数据，2017年开发的白氏公式（Formula D）表现出较好的数值稳定性，而其余的数值均出现不同程度的振荡和异常。此外，随着流量的增加，数值振荡和异常会加剧，导致适用性差。