Artificial Neural Network-Based Parameter Estimation in Lattice Boltzmann Simulations of MHD Nanofluid Natural Convection with Oscillating Wall Temperature

Abstract

This study investigates magnetohydrodynamic natural convection of nanofluids in a square cavity subjected to sinusoidally varying thermal boundary conditions along the bottom wall. Understanding such flows is important for applications in thermal management, energy systems, and materials processing. The problem is solved using the lattice Boltzmann method coupled with an artificial neural network model to accelerate prediction of heat transfer responses. A comprehensive parametric analysis is performed for Rayleigh numbers up to 106, Hartmann numbers up to 40, nanoparticle concentrations up to 4%, and a range of thermal wavelength parameters. The results show that the oscillatory thermal boundary significantly modifies flow structures and heat transfer characteristics: for example, at Ra = 106 and tau=0.5, the average Nusselt number is enhanced by nearly 28% compared with uniform heating, while strong magnetic damping (Ha=40) reduces it by about 35%. The neural network model reproduces LBM results with prediction errors below 2%, offering rapid estimation of Nusselt numbers across the studied parameter space. The novelty of this work lies in combining a high-fidelity lattice Boltzmann solver with data-driven prediction to study magnetically controlled nanofluid convection under oscillatory heating, an area not previously addressed in the literature. These findings provide new insights into the manipulation of convective transport in multiphysics thermal systems.