Electromagnetohydrodynamic (EMHD) Flow in a Microchannel with Random Surface Roughness

This study investigates the effect of small random transverse wall roughness on electromagnetohydrodynamic (EMHD) flow is in a microchannel, employing the perturbation method based upon stationary random function theory. An exact solution of a random corrugation function ξ, which is a measure of the flow rate deviated from the case without the roughness of two plates, is obtained by integrating the spectral density. After the sinusoidal, triangular, rectangular, and sawtooth functions that satisfy the Dirichlet condition are expanded into the Fourier sine series, the spectral density of the sine function is used to represent the corrugation function. Interestingly, for sinusoidal roughness, the final expression of the corrugation function is in good agreement with our previous work. Results show that no matter the shape of the wall roughness, the flow rate always decreases due to the existence of wall corrugation. Variations of the corrugation function and the flow rate strongly depend on fluid wavenumber λ and Hartmann number Ha. Finally, the flow resistance is found to become small, and the flow rate increases with roughness that is in phase (θ = 0) compared with the one that is out of phase (θ = π).