Transient rotating electromagnetohydrodynamic micropumps between two infinite microparallel plates

Abstract By using the method of separation of variables, analytical investigations are performed for combined transient rotating electromagnetohydrodynamic (EMHD) flow of an electrically conducting, incompressible and viscous fluid between two slit microparallel plates. The flow relies on the rotating effect and the Lorentz force produced by the interaction between an externally imposed electrical current and a transverse magnetic field. Three different cases associated with electric and magnetic fields are discussed respectively, i.e., uniform electric and magnetic fields (case I); AC electric field and uniform magnetic field (case II); AC electric and magnetic fields (case III). The variations of velocity profiles and volume flow rates with time and their dependence on the rotating Reynolds number Re Ω and the Hartmann number Ha are explained graphically. The results show that the magnitude of rotating EMHD velocity increases with Ha within a range when Ha Ω , an interesting phenomenon for case I is that the maximum is not shifted and the maximum of the velocity in axial direction is the minimum of the velocity in lateral direction, and vice versa. However, there is a shift of the maximum for large rotating Reynolds number Re Ω . Under the case II and the case III, the periodic oscillating phenomenon of the rotating EMHD velocity occurs. In addition, for three cases, the flow rate in y ⁎ direction increases with Hartmann number and decreases with rotating Reynolds number. The amplitude of EMHD velocity is larger under the case II than that of steady solution under case I, but smaller than that under case III for prescribed Hartmann number Ha and rotating Reynolds number Re Ω . Interestingly, there is a giant augmentation of the flow rates both in axial and in lateral directions for case III due to the aiding part of Lorentz force being greatly larger than retarding one in certain parameter ranges of phase of the magnetic field relative to the electrical field. By comparing our theoretical results in the limit case without rotation effect with related experimental data, the analytical results coincide qualitatively with the fitted curve obtained in experiments.