Effects of small boundary perturbation on the MHD duct flow

In this paper, we investigate the effects of small boundary perturbation on the laminar motion of a conducting fluid in a rectangular duct under applied transverse magnetic field. A small boundary perturbation of magnitude $\epsilon$ is applied on cross-section of the duct. Using the asymptotic analysis with respect to $\epsilon$, we derive the effective model given by the explicit formulae for the velocity and induced magnetic field. Numerical results are provided confirming that the considered perturbation has nonlocal impact on the asymptotic solution.