AC magnetohydrodynamic slip flow in microchannel with sinusoidal roughness

Perturbation solutions for the velocity and electric potential of a time periodic magnetohydrodynamic slip flow in a microchannel with sinusoidal wall corrugations are obtained using perturbation method. The effects of wall corrugations, slip length, Hartmann number and the frequency of the electric potential on the flow are analyzed theoretically and graphically. The results show that velocity and electric potential are significantly disturbed by wall roughness and that there exists a phase lag between the velocity and the electric potential. The velocity profile is characterized by the ratio of momentum diffusion time scale to the period of the applied electric field. The phase lag increases with frequency, slip length and decreases with Hartmann number, the wavenumber and phase difference of the wall corrugations. However, for a sufficiently small frequency, the phase lag is almost nonexistent. The effect of the phase difference of the wall corrugations on the phase lag becomes unimportant when the wavenumber is larger than 2. The velocity amplitude increases with slip length and decreases with frequency, wavenumber and phase difference. However, the phase difference becomes unimportant for sufficiently large wavenumber. When the frequency is large enough, the velocity amplitude is not influenced by slip length.