Deep learning-based physics-informed neural network analysis of magnetohydrodynamics mixed convection flow

This study develops a deep learning-based Physics-Informed Neural Network (PINN) to investigate magnetohydrodynamic (MHD) mixed convection flow over a fixed vertical permeable plate. The model incorporates nonlinear density-temperature (NDT) variations, nonlinear thermal radiation, wall suction/injection, and convective boundary conditions. Governing equations are transformed into nonlinear ordinary differential equations and embedded into the PINN loss function. Results demonstrate that transitioning from linear to nonlinear density variation enhances the heat transfer rate and wall shear stress by 13.38% and 1.68%, respectively. While magnetic fields suppress velocity and increase temperature, higher Grashof numbers accelerate fluid motion via buoyancy. For air and mercury, the heat transfer rate is boosted by wall suction, higher convective parameters, and Grashof numbers (by 7.45% & 3.57%, 1.61% & 22.71%, and 9.61% & 10.60%), but it decreases with wall injection and stronger radiation (by 21.81% & 4.57% and 12.98% & 44.65%). Furthermore, wall suction and increased nonlinear radiation or convective heat transfer improve fluid transport, though suction induces free-stream decay. The PINN predictions show excellent agreement with established literature. These findings are critical for optimising high-temperature systems, such as nuclear cooling and aerospace thermal protection, where precise control of MHD thermal-fluid dynamics is essential.