Analysis of MHD Flow With Convective Boundary Conditions Over a Permeable Stretching Surface Using a Physics-Informed Neural Network

Abstract

In this study, we examine the impact of heat and mass transfer of magnetohydrodynamic (MHD) flow through a stretching permeable surface while considering a chemical reaction and convective boundary conditions. A physics-informed neural network (PINN) approach is employed to obtain precise solutions, representing a key novelty of this work. The governing partial differential equations were transformed into nonlinear ordinary differential equations by applying similarity transformations. These equations are integrated into the PINN's loss function to enforce initial and boundary conditions, enabling the model to learn effectively during training. We analyze various parameters related to velocity, thermal, and concentration distributions and present the results graphically. The findings indicate that injecting fluid leads to a reduction in the velocity gradient as the fluid moves away from the surface, whereas suction has the opposite effect, increasing the velocity gradient. The velocity parameter significantly reduces the velocity boundary layer thickness, an effect further enhanced by the magnetic parameter. The thermal and concentration boundary layers are primarily affected by the Schmidt and Prandtl numbers. Additionally, the reaction parameter slows the concentration boundary layer near the sheet, while the convective parameter increases the temperature at the plate's surface. Our proposed method shows significant agreement with previous studies, validating its effectiveness in solving complex MHD flow problems. These findings provide deeper insights into fluid dynamics in MHD flows and have implications for applications involving heat and mass transfer, such as in chemical reactors, cooling systems, material processing, and environmental management.