Optimization of magnetohydrodynamic flow in a sudden expansion channel: Effects of Hartmann and Reynolds number on pressure and velocity dynamics

Abstract

This research investigates the optimization of magnetohydrodynamic (MHD) flow in a sudden expansion channel using response surface methodology. The study focuses on the effects of Hartmann number (Ha) and Reynolds number (Re) on pressure drop and velocity dynamics. The numerical investigation was conducted using a robust 3D MHD solver called ANUPRAVAHA, developed by researchers at IIT Guwahati and IIT Kanpur, across a range of Hartmann numbers (10−100) and Reynolds numbers (100–500), and results were optimized using response surface methodology. Key findings include the development of mathematical models that effectively captures the nonlinear relationships between Hartmann number, Reynolds number and critical flow parameters: pressure drop, maximum velocity, and outlet velocity. Mathematical models were created to predict these flow parameters, showing high accuracy when validated against numerical results. The effectiveness of the model is further validated by prediction errors of less than 1.899 % for all response variables. Response surface methodology (RSM) optimization identified the optimal conditions for balancing pressure drop, maximum velocity, and outlet velocity at Ha = 76.83 and Re = 500, with a desirability score of 0.963. The analysis reveals that while Reynolds number has a stronger impact on pressure drop, Hartmann number's quadratic and cubic terms significantly impact the maximum velocity within the channel. The results also show that increasing Hartmann number leads to a higher pressure drop and nonlinear changes in velocity distribution, whereas higher Reynolds number generally increases maximum and outlet velocities.