A reliable and efficient numerical model is required for predictions of convection-conduction behavior in fractured rock mass to obtain a better understanding of heat transfer processes within it. This study presents a composite element formulation that addresses the problem of heat transfer via fluid flow in fractured rock mass. The three-dimensional convection-conduction equation is converted to an equivalent variational principle, and the governing equations of the rock sub-elements and fracture segments are subsequently deduced based on the composite element method (CEM). The developed CEM algorithm takes into account the heat transfer inside the fracture fluid and inside the rock matrix, respectively, as well as the heat exchange between the fracture fluid and the adjacent rock blocks. The CEM model allows for the simulation of the discontinuous characteristics of temperature across the fractures via a simplified computational mesh that is generated without restrictions, and the fractures are explicitly and automatically embedded into the mapped composite element via the CEM pre-process program. The composite element contains fracture segments exhibiting arbitrary shapes, the temperatures of fractures are interpolated from their corresponding mapped nodal temperatures of rock sub-elements delimited by the fractures, and, therefore, the temperature of the fracture is not necessarily continuous. The performance of the developed CEM algorithm is verified by comparisons with analytical solutions, a case study of lab experiments and numerical results, which demonstrate the validity and advantages of the composite element solution.

需要一个可靠而有效的数值模型来预测裂隙岩体中的对流传导行为，以便更好地了解其中的传热过程。这项研究提出了一种复合元素配方，该配方解决了裂隙岩体中通过流体流动传热的问题。将三维对流传导方程转化为等效的变分原理，然后基于复合单元法（CEM）推导岩石子单元和裂缝段的控制方程。所开发的CEM算法分别考虑了压裂液内部和岩石基质内部的传热，以及压裂液与相邻岩石块之间的热交换。CEM模型允许通过不受限制地生成的简化计算网格来模拟裂缝两端温度的不连续特性，并且可以通过CEM预处理程序将裂缝明确自动地嵌入到映射的复合元素中。复合单元包含显示任意形状的裂缝段，裂缝温度是从裂缝所界定的岩石子元素的对应映射节点温度中插入的，因此，裂缝温度不一定是连续的。通过与分析解决方案的比较，实验室实验的案例研究和数值结果，验证了所开发的CEM算法的性能，证明了复合单元解决方案的有效性和优势。