Effects of wall roughness on coupled flow and heat transport in fractured media

Heat transfer in fractured media results from the interplay between advective transport within the fracture and conductive heat exchange with the surrounding rock matrix. Aperture heterogeneity structures this interplay by generating preferential flow channels and quasi-stagnant zones, leading to early-time anomalous transport dominated by advective channelling and to late-time non-Fickian dynamics controlled by matrix conduction. This study develops a physics-based stochastic framework that couples a time-domain random walk (TDRW) representation of in-fracture advection and conduction with a semi-analytical description of matrix–fracture heat exchange, enabling a unified characterisation of both short- and long-time anomalous heat-transport regimes. Matrix trapping times follow a Lévy–Smirnov distribution derived from first-passage theory, and the interfacial heat flux is evaluated through a non-local Duhamel kernel that rigorously captures the temporal non-locality imposed by heat-conduction theory. Monte Carlo simulations over stochastic aperture fields elucidate the roles of fracture closure, correlation length and Péclet number in shaping heat transport. Increasing fracture closure enhances channelisation and accelerates early-time heat transport, whereas larger correlation lengths amplify anomalous spreading. Higher Péclet numbers strengthen advective dominance, but do not suppress the long-time subdiffusive tail induced by matrix conduction. Breakthrough curves exhibit heavy-tailed decay consistent with Lévy–Smirnov trapping induced by semi-infinite matrix diffusion. Results reveal a transition from superdiffusive to subdiffusive transport governed by advective channelling, aperture-induced dispersion and matrix conduction. The framework provides a predictive and computationally efficient route for modelling heat transport in heterogeneous fractures, with relevance to geothermal energy extraction, subsurface thermal storage and engineered thermal systems.