Magnetohydrodynamics slip flow in a microchannel with moving walls

Magnetohydrodynamics (MHD) flows in microchannels play a critical role in the design of microfluidic and biomedical devices, where precise control of fluid motion is essential. This study presents a theoretical model for MHD flow in a microchannel with a dynamically squeezing upper wall, incorporating lubrication theory and Maxwell's equations. Analytical solutions are derived for velocity components, pressure distribution, and shear stress under the influence of a transverse magnetic field and slip boundary conditions. The results show that increasing magnetic forces significantly modify the axial velocity profile, flattening its classical parabolic shape and reducing its peak magnitude. Electromagnetic effects also influence wall shear stress, while having little impact on vertical velocity. Additionally, the magnetic field increases both the pressure and the axial pressure gradient along the channel. Slip boundary conditions further reduce axial velocity and wall shear stress by weakening near-wall velocity gradients. The proposed model offers a simplified yet insightful framework for analyzing MHD-driven flows in microchannels with moving boundaries, with potential applications in lab-on-a-chip technologies, targeted drug delivery, and microscale flow pumping.