Computational modeling of turbulent nanofluid heat transfer over a heated moving surface with local thermal non-equilibrium and machine-learned eddy viscosity

Abstract

This study presents an adaptive modified Runge-Kutta compact scheme for the numerical simulation of unsteady k − ω turbulent nanofluid flow over a heated moving surface under local thermal non-equilibrium conditions. The surface-interfacial model incorporates mixed convection, viscous dissipation, turbulence transport, and separate energy equations for the base fluid and nanoparticle phases, with the effective thermal conductivity described by Xue’s formulation. The proposed time-integration method is explicit and combined with a compact finite-difference discretization that provides fourth-order spatial accuracy. The temporal coefficients are selected to achieve second-order accuracy, and the method is further enhanced through adaptive time stepping based on local error control. Stability analysis for the scalar convection–diffusion problem and conditional convergence analysis for the corresponding system formulation are also established. Numerical comparisons show that the proposed adaptive scheme yields lower error than existing adaptive Euler- and Runge-Kutta-based schemes. The computed results further demonstrate that thermal buoyancy increases the mean velocity, whereas larger Prandtl numbers reduce the thermal boundary-layer thickness of the fluid and nanoparticle phases. In addition, stronger interphase coupling modifies the two-temperature fields in a manner consistent with local thermal nonequilibrium. A machine-learning model is also employed to predict eddy viscosity, and its reliability is confirmed through profile comparisons, contour analyses, sensitivity assessments, and Taylor diagram evaluations. Overall, the proposed framework provides an accurate and efficient computational tool for surface-associated turbulent nanofluid transport with interfacial thermal nonequilibrium.