Discrete fracture network models routinely rely on analytical solutions to estimate heat transfer in fractured rocks. We develop analytical models for advective and conductive heat transfer in a fracture surrounded by an infinite matrix. These models account for longitudinal and transverse diffusion in the matrix, a two-way coupling between heat transfer in the fracture and matrix, and an arbitrary configuration of heat sources. This is in contrast to the existing analytical solutions that restrict matrix conduction to the direction perpendicular to the fracture. We demonstrate that longitudinal thermal diffusivity in the matrix is a critical parameter that determines the impact of local heat sources on fluid temperature in the fracture. By neglecting longitudinal conduction in the matrix, the classical models significantly overestimate both fracture temperature and time-to-equilibrium. We also identify the fracture-matrix Péclet number, defined as the ratio of advection timescale in the fracture to diffusion timescale in the matrix, as a key parameter that determines the efficiency of geothermal systems. Our analytical models provide an easy-to-use tool for parametric sensitivity analysis, benchmark studies, geothermal site evaluation, and parameter identification.
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