Taking the near field of nuclear waste repositories in fractured rocks as the subject of study

a simplified conceptual model for three-dimensional water flow and heat transfer in single-fracture rock is proposed. The mathematical model

taking into account of distributed heat source and saturated single-fracture rock of infinite extent

is formulated and solved by using a Green function approach

in which a fundamental solution of the governing differential equations after Laplace transform is employed. The fracture surface is discretized by rectangular elements. The singularities in the integral equation are handled through analytical integration in polar coordinates; and a numerical procedure is developed to solve the transient temperature distributions in fracture water and rock matrix. Two numerical examples with special flow field are provided for illustration of the proposed method with comparison of an analytical solution based on 1D rock thermal conduction; and other numerical examples with distributed heat sources are extended for characteristics of flow and heat transfer in single-fracture rock and the sensitivities to flow velocity

rock thermal conductivity and heat source intensity. The calculations show the following observations: Comparing with the direct Gaussian method

the proposed analytical approach to handling the singular integrals is more accurate. The temperature of water in the fracture calculated by using the semi-analytical method is lower in upstream and higher in downstream than the analytical solution

due to the fact that the former method takes into account 3D thermal conduction in the rock matrix

whereas the latter assumes 1D conduction. Without interior heat source

the greater the rock thermal conductivity

the lower the temperature of facture water

due to more heat exchange between fracture water and rock matrix. The larger the fracture water velocity

the more significant of the influence of the inlet fracture water temperature on the temperatures of fracture water and rock matrix. The effects of the distributed heat source on the temperatures of fracture water and rock are more sensitive in downstream as a result of the heat advection of fracture fluid flow.