## 1 Introduction
Confining pressure has a significant impact on the fracture aperture. [PERSON] [23] employed a novel experimental device to simulate the evolution of the hydraulic and heat transfer characteristics of fractures under a confining pressure. Results show that both the heat transfer rate and total heat transfer coefficient decrease with an increasing confining pressure. [PERSON] [24] established a three-dimensional numerical model based on three-dimensional laser scanning to evaluate the effects of rock temperature, water flow velocity, roughness, and fracture aperture on the heat transfer coefficient. Simulation tests reveal the dominant influence of the flow rate on the rock roughness, followed by the aperture size. [PERSON] et al. [25] simulated the flow and heat transfer between two-dimensional parallel rough surfaces, demonstrating the minimal effect of wall roughness on the heat transfer for the characteristic parameter \(Pe=u(d/2)2/L<200\). [PERSON] [26] performed convection heat transfer tests of carbon dioxide in a single fracture to establish a numerical model and proposed the rough fracture channel effect. Experimental and numerical simulations can increase our understanding of the geothermal field model. [PERSON] et al. [27] established a discrete fracture network and investigated the relationship between hydraulic aperture and fluid runoff, concluding that variations in the fracture aperture can cause flow channeling and reduce the heat transfer area. Furthermore, several studies [28; 29] have employed Monte-Carlo [30; 31] stochastic simulations to build fracture network models with different geometric parameters, and in particular, the EGS site model to predict the heat recovery performance. [PERSON] [32] integrated experimental data into a single model used to generate an estimation model of the main hydraulic parameters. [PERSON] [33] established a geothermal reservoir model with a rough fracture surface based on small-scale research results, revealing the constant heat transfer coefficient (HTC) recommended in previous studies to underestimate the final outlet fluid temperature in the case of rough fractures. These studies demonstrate that research on the influence of fracture morphology on the fluid flow and heat transfer process at the experimental scale can be applied to the actual site model [28; 34]. In summary, previous studies have shown that the geometry of the fracture surface has a profound influence on the fluid flow and heat transfer process in the fracture [35; 36]. According to the different influencing factors, many scholars [23; 37; 38] have designed experiments and carried out corresponding numerical simulations to determine how these influence factors affect the heat transfer process in fractures. The results of such studies are very important for the development of EGS stimulation technology. The aforementioned research generally focuses on the influence of fracture morphology on fluid heat transfer, while studies on the effect of the angle between the direction of the fluid flow and the morphology of the fracture wall on the heat transfer performance are limited. In addition, because of the geological history, the fracture aperture of EGS reservoirs range from the micron to centimeter scale [39]. This makes it difficult to obtain the temperature distribution of rock fractures and thermal mediums under laboratory conditions. Hence, in the current study, we established a single fracture heat transfer model with a random geometry profile that was subsequently verified by experiments. Four cases with fracture profiles and varying angles between flow direction were set up to simulate and explore the heat transfer performance of distilled water through fractures. The influence of the fluid flow direction on the fracture heat transfer characteristics was then discussed.