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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. [ABSTRACT FROM AUTHOR]

An amendment to this paper has been published and can be accessed via the original article. [ABSTRACT FROM AUTHOR]

Understanding working fluids flow and heat transfer in Enhanced Geothermal System (EGS) is critically important for assessing production capabilities and heat extraction rates from hot dry rock (HDR) effectively. Water is a conventional working fluid of EGS; therefore, it is necessary to study water–rock coupling heat transfer within HDR fractures. A single fracture is a basic element of complex fracture systems of EGS, so there has been many researches investigating water flow and heat transfer through a single fracture within a cylindrical HDR specimen for preliminary study, and heat transfer coefficient (HTC) is often adopted to evaluate heat transfer performance between water and rock, but there is a lack of knowledge about the inner surface temperature (Ti), which is a key parameter to calculate HTCs, due to limitations of current experimental methods and analytical solutions. Numerical modeling can be an alternative way to help us have a more comprehensive understanding of the distributions of Ti, but the 2D numerical models only reveal the distribution of Ti along the flow direction without its distribution perpendicular to the flow direction, namely, the distribution along radius. Therefore, it is essential to conduct the corresponding 3D numerical modeling to obtain the radial distribution of Ti. In this paper, a 3D numerical model accounting for surface morphology is proposed to simulate water flow and heat transfer through a single fracture within a cylindrical HDR specimen and verified by experimental data. The results reveal that the radial distribution of Ti can be described by a quadratic function mostly, and neither the surface morphology nor the phase state has influence on the tendency of Ti. Finally, four relatively stable formulas to calculate HTCs so far are compared and discussed. [ABSTRACT FROM AUTHOR]