Abstract
This research analyzes the optimization of the thermal performance of the natural convective flow of Ag-MgO/H2O hybrid nanofluid within a quarter-circular cavity utilizing response surface methodology (RSM) and artificial neural network (ANN) techniques through a non-homogeneous dynamic mathematical model. The Galerkin-weighted residual finite element method numerically solves the governing dimensionless equations and boundary conditions. The numerical results are then used to train ANN and RSM models and evaluate their performance. The results indicated that both models are dependable for this investigation, exhibiting a notably high coefficient of determination for the performance control variable, the average Nusselt number. In addition, the error in response surface methodology was more than ANN at the optimum conditions. Therefore, ANN is more capable than RSM in predicting average Nusselt numbers in comparison with numerical data. The results further indicate that the presence of Brownian motion leads to a 108.83% increase in Nuave compared to its absence, 63.28%, at RaT = 106. The growth of the average Nusselt number is highly significant with the nanoparticle volume percentage, magnetic field period, and Rayleigh number. Increased nanoparticle size and Hartmann reduce the heat transfer rate.