Magnetohydrodynamic flow through a wavy curved channel

The flow of an electrically conducting fluid through a curved channel with wavy boundaries is studied. The waviness of the curved boundaries is sinusoidal and periodic. The analytical results for the velocity field and the volumetric flow rate are obtained using the boundary perturbation method. The effects of the wavy boundaries, the channel radius of curvature, and the applied magnetic field on the flow field are analyzed. The study shows that the impact of the wavy boundaries on the flow decreases with the increase in the flow Hartmann number. However, the flow rate increases for any alignment of the wavy curved boundaries and for the wave numbers less than a threshold wavenumber (depending on the radius of curvature and the Hartmann number), and a further increase in the flow rate occurs with the increase in the phase difference between the wavy curved boundaries. On the other hand, the flow rate decreases with the increasing wavenumber, and for a sufficiently large wavenumber and Hartmann number, the phase difference between the wavy curved boundaries becomes irrelevant to the flow.