Effects of three-dimensional surface corrugations on electromagnetohydrodynamic flow through microchannel

This article deals with the electromagnetohydrodynamic (EMHD) flow through a microchannel with three-dimensional corrugated walls where the fluid is driven by non-uniform electric field and uniform magnetic field. The three-dimensional corrugations are depicted by the product of two sinusoid functions with small amplitude epsilon and wave numbers alpha and beta in two horizontal directions. The analytic expressions of the electric potentials, velocities and volume flow rates are deduced by utilizing the perturbation method. The impacts of the corrugations on the electric potentials, the EMHD velocities and volume flow rates are discussed. Moreover, the influences of relevant parameters, including Hartmann number Ha, aspect ratio chi (chi= beta/alpha) of the corrugations and the parameter R (R = beta-alpha) on the flow are analyzed. Furthermore, the comparisons of the flow rates with experimental data are performed. The results show that the maximum flow rate can be obtained by increasing magnetic field strength parameter Ha or adjusting the phases of the wavy walls.