Thermal analysis of van der Waals magnetohydrodynamic flow behind a normal shock wave via numerical and neural network techniques

This study analyzes gas dynamics and heat transfer behind shock waves, incorporating complex parameters, making it essential for improving the performance and stability of systems requiring precise control over shock waves, thermal management, and non-ideal gas behavior. This explores the impact of shock wave intensity, slippage, dissipation, van der Waals constants, the Prandtl number, the Knudsen number, the Brinkman number, and the magnetic field on the flow's dynamic and thermal behavior, including frictional forces and heat transfer characteristics, while considering the temperature ratio between the flow and the wall. Self-similar transformation variables were employed to transform the governing equations into ordinary differential equations, which were subsequently solved using MATLAB's boundary value problem (BVP4c) solver and cross-verified through artificial neural networks (ANN). The study revealed that increasing the Knudsen number enhances the velocity gradient and broadens the boundary layer, while a stronger magnetic field suppresses flow velocity and increases temperature uniformity. Higher Eckert numbers result in greater viscous dissipation and temperature rise near the wall, while van der Waals forces significantly reduce skin friction and heat transfer. The ANN model achieved over 95% prediction accuracy, and sensitivity analysis indicated that a 10% increase in the Knudsen number led to a 15% rise in the velocity gradient, with variations in the magnetic field causing a 20% change in temperature profiles. This model is applicable in microfluidics, magnetohydrodynamics, thermal management, and high-speed fluid dynamics, where precise control of friction and heat transfer is crucial.