## 6 Conclusions  
In this study, a hydro-thermal coupling model was developed to investigate the influence of fluid flow direction on the heat transfer characteristics of fractures. The accuracy of the proposed numerical model was verified by laminar convection heat transfer tests of smooth-plate fractured rock samples. A detailed analysis of the temperature field distribution, total heat transfer coefficient, and local heat transfer coefficient of the model were provided based on the numerical simulations. The main conclusions are as follows:  
(1) At \(\alpha=30^{\circ}\) and \(\alpha=60^{\circ}\), the temperature of the fracture surface in the negative direction of the \(x\)-axis is higher than that in the positive direction. This is because the flow direction of the fluid is not parallel to the orientation of the microfracture surface that prevents the fluid from flowing forward, resulting in fluid deflection.  
(2) When the initial temperature is raised from 70 to 90 \({}^{\circ}\)C, the cumulative heat extraction rate \(Q_{sum}\) increases the yield by 45%. Although the cumulative heat extraction increases with the injection flow rate, the rate of increase gradually decreases. An increase in the injection flow rate from 10 to 40 mL/min enhances the peak heat extraction rate. However, the increase in flow rate speeds up the rate of reduction of the heat extraction rate.  
(3) Variations in the total heat transfer coefficient with time can be divided into increasing and decreasing stages. The total heat transfer coefficients decrease with \(\alpha\). This  
Figure 20: Local heat transfer coefficient, wall temperature, and average velocity distributed along the \(x\)-direction at \(z=0.05\) m (\(V_{0}=20\) mL/min, \(T_{0}=90\)\({}^{\circ}\)C).  
indicates that the presence of rough fractured surfaces in the forward direction of the fluid does not necessarily increase the convection heat transfer intensity between the fluid and the fractured surfaces. Increasing the flow rate and temperature can enhance the total heat transfer coefficient. However, a higher flow rate will shorten the time required by the total heat transfer coefficient to reach its peak value, while also increasing the rate of reduction of the total heat transfer coefficient in the decreasing stage.  
(4) The local heat transfer coefficient gradually decreases along the direction of the water flow, which is consistent with the conclusions drawn by [PERSON] [46]. An increasing flow rate not only increases the local heat transfer coefficient, but also has an enhancing effect that highlights the influence of the fracture profile on the local heat transfer coefficient distribution.  
(5) There is a consistently strong correlation between the local heat transfer coefficient and the fracture profile, independent of the axis. In particular, although a change in the angle between the flow direction and the fracture profile can affect the local heat transfer coefficient, it does not affect the distribution characteristics of the local heat transfer coefficient.  
Conceptualization, writing--original draft preparation, X.G.; supervision and review, Y.Z.; formal analysis, data curation, Z.H.; software, Y.H. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the National Natural Science Foundation of China (Nos. 41772238), by the New Energy Program of Jilin Province (Nos. SXGJSF2017-5), and the Interdisciplinary Fund of Jilin University (Nos. 101832020 DJX072).  
Not applicable.  
The data used to support the findings of this study are available from the first author or the corresponding author upon request.  
The authors declare no conflict of interest.  
References