Nonlinear Convective Hybrid Nanofluid Flow in a Porous Square Cavity: Numerical Simulation and ANN Prediction

Nonlinear buoyancy effects can significantly influence heat transfer in systems involving large temperature differences, such as electronic cooling and solar thermal applications. This study investigates quadratic Darcy convection of an Ag–Al 2 O 3 /water hybrid nanofluid (HNF) in a porous square cavity, with particular emphasis on the combined effects of nonlinear buoyancy and nanoparticle concentration. The cavity has a heated bottom wall, cooled vertical walls, and an insulated top wall. The governing equations are formulated using the Darcy–Boussinesq approximation and solved using the finite difference method(FDM) with a damped Newton iterative scheme. The effects of the Rayleigh number (Ra), quadratic convection parameter (Qc), and nanoparticle volume fraction ([Formula: see text]) are examined through streamlines, isotherms, and the average Nusselt number (Nu). The results show that increasing Ra strengthens buoyancy-driven circulation and enhances heat transfer, while positive and negative values of Qc respectively intensify and suppress convective transport. Increasing Ra from 100 to 10 4 enhances the average Nu by 352.03% at Qc = 0.1 and [Formula: see text] = 0.01. At Ra = 10 3 and [Formula: see text] = 0.01, increasing Qc from 0 to 1.5 enhances Nu by 23.68%, whereas decreasing Qc from 0 to –1.3 reduces it by 54.64%. Increasing [Formula: see text] from 0.01 to 0.03 improves Nu by approximately 2.39% at Ra = 10 3 and Qc = 0.1. Furthermore, a Bayesian-regularized artificial neural network (ANN) is developed to predict the average Nu from the governing parameters. The ANN achieves a mean testing R 2 of approximately 0.99998, demonstrating good agreement with the FDM results.