Three-dimensional, time-dependent investigation of thermal enhancement in single rock fractures using magnetohydrodynamics and ternary hybrid nanofluids with predictive linear and nonlinear modeling

This study presents a detailed time-dependent analysis of thermal enhancement in fractured rock systems using ternary hybrid nanofluids under the influence of a magnetohydrodynamic field. The ternary hybrid nanofluids consisted of water-based solutions of nanoparticles consisting of ferric oxide (Fe 3 O 4 ), multi-walled carbon nanotubes and alumina (Al 2 O 3 ). To evaluate the performance of the hybrid nanofluids in the fractured rock systems, the finite element method will be employed by COMSOL Multiphysics to solve the coupled continuity, momentum and energy equations across a wide range of operating conditions: Reynolds numbers (10–50), volume fractions (1–10%), shape factors (3–8.9), Hartmann numbers (10–50), angles of inclination (0–90 ∘ ) to the direction of the magnetic field and aspect ratios of fracture (1–10%). Four key conclusions have been drawn from the analysis results. To begin with, increasing the Reynolds number from 10 to 50 decreased the peak mid-line temperature by as much as 28.2%, indicating that forced convection is more important than diffusion. Additionally, nanostructures can affect the thermal resistance of a fluid much more than volumetric or geometric characteristics; for example, blade-shaped structures at a concentration of 10% will increase the peak temperature by 3.16%, compared to their spherical counterparts, demonstrating how viscosity can dominate the thermal response to force. Third, magnetohydrodynamic effects created considerable flow resistance, resulting in a temperature increase of 4.05% at a magnetic field angle of 45 ∘ , which corresponds to the maximum Lorentz force. Finally, regression models based on supervised machine learning produced a high degree of accuracy ([Formula: see text]) for predicting maximum temperatures and mean Nusselt numbers, allowing for forecasting performance without performing extensive simulation studies. Importantly, this study is the first systematic 3D time-dependent investigation that combines ternary hybrid nanofluids ([Formula: see text]), variable nanoparticle shape factors and magnetohydrodynamic flow control in a fractured rock geometry, yielding new quantitative data and physically validated regression models for geothermal applications.