Magnetohydrodynamic flow and heat transfer of a ternary hybrid nanofluid over an expanding porous sheet: Numerical, entropy, and ANN analysis

This study investigates magnetohydrodynamic (MHD) boundary-layer flow, heat transfer, and entropy generation in a ternary hybrid nanofluid composed of $Cu–Mo{S}_2-GO$ nanoparticles dispersed in an ethylene glycol-water mixture flowing over an expanding porous sheet. Using similarity transformations, the governing partial differential equations are reduced to a coupled system of nonlinear ordinary differential equations and solved numerically. The effects of key physical parameters-including magnetic field strength, nanoparticle volume fraction, particle shape, porous expansion rate, and unsteadiness-on velocity, temperature, skin friction, Nusselt number, and entropy generation are examined in detail. In addition, an artificial neural network (ANN) model is developed to accurately predict the flow and thermal characteristics, demonstrating excellent agreement with numerical results. The findings reveal that nanoparticle shape and concentration significantly influence heat transfer and entropy production, while magnetic and slip effects suppress momentum transport. The combined numerical and ANN-based framework provides an efficient and reliable tool for analyzing complex MHD nanofluid systems.