Coupling mechanism of seepage and heat transfer in rock fracture based on physics-informed neural networks

To investigate the coupling mechanism of seepage and heat transfer in rock fractures, a numerical model was developed based on the physics-informed neural networks method. The Navier-Stokes equations governing fluid seepage and the convection-diffusion equation describing heat transfer were embedded as physical constraints into the neural network training process. Additionally, a dynamic feedback mechanism for temperature-dependent kinematic viscosity was introduced to propose a numerical model simulating the coupled effects of fluid seepage and heat transfer. The accuracy of the proposed model was validated against the classical Poiseuille flow heat transfer problem. Furthermore, comparison with finite element method results demonstrated its superior stability in handling problems with irregular geometric boundaries. Finally, the effects of fluid kinematic viscosity, seepage velocity (hydraulic gradient, fracture aperture, wall roughness, etc.), and fracture wall temperature on the coupling mechanism of fluid seepage and heat transfer were investigated. The results indicate that if the effect of temperature on the fluid kinematic viscosity is considered, the maximum velocity in the fracture center increases from 0.53 mm/s to 1.92 mm/s, representing an increase of 262.3%. This velocity difference further alters the temperature distribution and reduces the central fracture temperature from 160.1 ℃ to 110.2 ℃(a 31.2% decrease). As the hydraulic gradient increases from 1 Pa/m to 4 Pa/m, the convective heat flux peak rises significantly, far exceeding the increase in diffusive heat flux, leading to a 42.3% decrease in the core fluid temperature. An increase in fracture aperture enhances fluid velocity, which effectively reduces boundary layer thickness and significantly improves heat transfer efficiency. An increase in the fractal dimension of the fracture wall leads to greater flow resistance, which enhances heat transfer through the fracture channel and results in a higher fluid temperature at the outlet. When the fracture wall temperature increases from 100 ℃ to 200 ℃, the peak fluid kinematic viscosity decreases by 55.7%, while the peak seepage velocity rises by 126.7%, and the core region temperature difference expands by 372.4%.