Numerical Simulation of Unsteady Hydromagnetic Flow in Channel Flows with Variable Conductivity

Abstract

The study of magnetohydrodynamic (MHD) flows has gained considerable importance due to its wide range of applications in engineering, industrial processing, and geophysical fluid dynamics. The present research investigates the numerical simulation of unsteady hydromagnetic flow in channel flows with variable electrical conductivity. The primary objective of this work is to analyze how variations in electrical conductivity influence the velocity distribution, magnetic field interaction, and overall flow characteristics within a channel subjected to an external magnetic field. Understanding these effects is essential in applications such as cooling systems of nuclear reactors, MHD power generators, metallurgical processes, and plasma flow control. A mathematical model describing the unsteady incompressible flow of an electrically conducting fluid between two parallel plates is formulated using the governing equations of momentum and continuity. The presence of a transverse magnetic field introduces Lorentz forces, which significantly affect the velocity profile and fluid motion. The model also incorporates spatial variations in electrical conductivity to represent realistic physical conditions. To solve the resulting nonlinear partial differential equations, suitable numerical techniques are applied, enabling the computation of velocity distributions and flow behavior under different parameter conditions. The numerical results reveal that the magnetic field strength and conductivity variation play a crucial role in controlling the flow structure. An increase in the magnetic parameter tends to reduce the fluid velocity due to the resistive Lorentz force acting against the flow direction. Additionally, variations in electrical conductivity alter the distribution of magnetic forces within the channel, leading to noticeable changes in flow stability and velocity gradients. The unsteady nature of the flow further highlights the time-dependent development of the velocity field before reaching a steady state. Overall, the study provides valuable insights into the complex interaction between magnetic fields and conductive fluids in channel flows. The findings contribute to a better understanding of hydromagnetic transport phenomena and may assist in optimizing engineering systems where magnetic field control of fluid motion is required.