Electromagnetohydrodynamic (EMHD) micropumps under a spatially non-uniform magnetic field

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Abstract
As an effective driven mechanism proved experimentally, magnetohydrodynamic (MHD) micropump has attracted the attentions of many researchers in recent years. In this article, an analytical solution of EMHD velocity of an electrically conducting, incompressible and viscous fluid through a slit microchannel in presence of a lateral uniform electrical field and a spatially non-uniform vertical magnetic field is obtained by using the variation of parameter approach and Gauss numerical integration. In order to verify the validity of the exact solution, Chebyshev spectral collocation method is employed to give the numerical solutions. A very well agreement is reached when the analytical solutions are compared to those obtained by numerical simulation. The dependence of velocity profiles on Hartmann number Ha, electrical field strength parameter S and decay factor A of the magnetic field is interpreted graphically in detail. In addition, the comparison of our analytical results with available experimental data is presented.

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