Journal of Advances in Mathematics and Computer Science

Magnetohydrodynamic (MHD) turbulent fluid flow plays a significant role in many engineering and industrial processes, including nuclear reactor cooling, metallurgical operations, electromagnetic pumps, petroleum transportation, liquid metal technology, geothermal energy extraction, thermal management systems, MHD power generation, biomedical fluid systems and other industrial heat transfer technologies where magnetic fields and Joule heating significantly influence fluid behaviour. Despite the extensive literature on MHD fluid flow, relatively limited attention has been given to the numerical analysis of turbulent MHD flow over a vertical semi-infinite plate under the combined influence of Joule heating and buoyancy effects. This study addresses this gap by developing and numerically analysing a mathematical model describing turbulent magnetohydrodynamic fluid flow over a vertical semi-infinite plate with Joule heating. The governing continuity, momentum, and energy equations were formulated based on the principles of fluid dynamics and electromagnetism. Reynolds time-Averaging (RANS) together with the Boussinesq approximation was employed to simplify the turbulence terms, while the resulting dimensionless governing equations were solved numerically using the finite difference method. Numerical simulations were conducted to investigate the influence of key dimensionless parameters, including the Grashof number, Joule heating parameter, magnetic parameter, and decay parameter, on the velocity and temperature distributions within the flow field. The numerical results demonstrate that increasing the Grashof number significantly enhances fluid velocity and heat transfer due to stronger buoyancy forces. The study further establishes that higher Joule heating intensities increase both fluid temperature and velocity by supplying additional thermal energy to the flow. Conversely, larger decay parameters reduce the influence of Joule heating, resulting in lower temperature and velocity profiles. The imposed magnetic field was observed to regulate fluid motion by introducing Lorentz forces that modify the velocity distribution, while turbulence effects were effectively represented through the Reynolds-Averaged Navier-Stokes formulation. Comparison of the numerical solutions with established results in the literature showed good agreement, confirming the accuracy and reliability of the developed numerical model. The findings contribute to the advancement of computational studies on turbulent magnetohydrodynamic flows and provide useful insights for the design and optimisation of engineering systems involving electrically conducting fluids.