Electromagnetohydrodynamic (EMHD) Micropump Of Jeffrey Fluids Through Two Parallel Microchannels With Corrugated Walls

The approximate analytical solutions of velocity, volume flow rate and mean velocity are presented for electronmagnetohydrodynamic (EMHD) flow of an electrically conducting and incompressible Jeffrey fluid between two slit microparallel plates with corrugated walls, by employing perturbation method. The corrugations of the two walls are described as periodic sinusoidal waves with small amplitude either in phase or half-period out of phase. The effects of the corrugations on the EMHD flow velocity are analyzed by using numerical computation. The variations of velocity profiles and mean velocity parameter and their dependences on the Reynolds number Re, Hartmann number Ha, dimensionless pressure gradient parameter A, dimensionless wave number k of the wall perturbation, the dimensionless relaxation time λ1ω and retardation time λ2ω are explained graphically. The profiles of EMHD velocity in phase and out of phase are dependent on the boundary conditions. With the increasing of dimensionless relaxation time λ1ω, the EMHD velocity increases, while with the increasing of retardation time λ2ω, the EMHD velocity decreases. At the end of the article, setting the perturbation parameter ε=0 in the approximate analytical solution, we verify the correction of the analytical solution by utilizing the test results presented by Lemoff and Lee.