Numerical Study on Shear Effects on Heat Transfer Characteristics Considering Nonlinear Water Flow through 3D Rough-Walled Fractures

Efficient heat exchange in fractured geothermal reservoirs is crucial for improving geothermal energy extraction and optimizing operational costs. However, the impact of shear-induced permeability changes on heat transfer remains poorly understood. This study aims to systematically investigate the effect of shear displacement (us) on nonlinear flow properties and convective heat transfer characteristics in three-dimensional (3D) rough-walled fractures. Four fracture models were constructed based on Brazilian splitting test data, with shear displacements of 4.44, 8.88, 13.32, and 17.76 mm applied under constant normal stiffness boundary conditions. Four assumptions are made. First, the rock matrix is impermeable and homogeneous. Second, the solids and fluids are undeformable. Third, no-slip and no-flow conditions are assigned at the fracture walls. Fourth, the constant-temperature boundaries are maintained at 300 °C. Numerical simulations were performed using COMSOL Multiphysics, coupling “Heat Transfer in Solids and Fluids” and “Turbulent Flow (SST)” physics to solve Navier–Stokes and energy equations. Fluid flow velocities ranging from 0.001 to 1 m/s were applied at the inlet. The results show that as us increases from 4.44 to 17.76 mm, the nonlinear coefficient (β) in Forchheimer’s law decreases from 2.29×1012 to 3.5×10 Pa·s2·m−6. The β characterizes the degree of deviations from linear (Darcy) flow, and its increase indicates earlier onset of nonlinear fluid flow induced by inertial and turbulent effects. The increase in us from 4.44 to 17.76 mm reduces the maximum convective heat transfer coefficient (hmax) from 3795.4 W·m−2·K−1 (Re=1423.5) to 1243.5 W·m−2·K−1 (Re=342.33) due to reduced turbulence and insufficient fluid–solid contact time. An optimal flow rate (Qbest) that balances heat extraction efficiency and outlet temperature was proposed. These findings can provide critical insights for optimizing thermo–hydro–mechanical processes in enhanced geothermal systems.