Permeability impact on electromagnetohydrodynamic flow through corrugated walls of microchannel with variable viscosity

This investigation based on electromagnetohydrodynamic flow in microchannels through lightly corrugated walls effects is reported in the presence of variable liquid properties. In microparallel plates, we consider incompressible and electrically conducting viscous fluid. With small amplitudes, the wall corrugations are described by periodic sin waves. The governing equations are rendered dimensionless and solved with the help of the perturbation technique. The analytical solutions for velocity are obtained and analyzed graphically. A connection between flow rate and roughness is acquired by perturbation solutions of the stream function. By utilizing numerical computations, we analyzed the corrugation consequences on the velocity for electromagnetohydrodynamic flow. We graphically clarified the velocity and temperature profiles and their dependencies on all parameters. The three-dimensional velocity and contour distributions shown that the wall roughness can cause changes in the velocity distribution. For in phase the phase difference among the two corrugated walls is equals to 0°, and for out of phase the phase difference is equal to 180° between the two walls. The wave phenomenon of the flow shape becomes obvious with the expansion of the corrugation. The electromagnetohydrodynamic velocities first grow and then reduce. The electromagnetohydrodynamic velocity increases for Reynolds number, Hartmann number, and Darcy parameter. Velocity profile decreases for variable viscosity, velocity slip parameter.