Geodesic
Effects of small boundary perturbation on the MHD duct flow
Theoretical and applied mechanics, Tome 44 (2017) no. 1.

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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.
Keywords: MHD flow, boundary perturbation, asymptotic analysis, nonlocal effects 
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     author = {Ulavathi Shettar Mahabaleshwar and Igor Pa\v{z}anin and Marko Radulovi\'c and Francisco Javier Su\'arez-Grau},
     title = {Effects of small boundary perturbation on the {MHD} duct flow},
     journal = {Theoretical and applied mechanics},
     pages = {83 - 101},
     publisher = {mathdoc},
     volume = {44},
     number = {1},
     year = {2017},
     url = {http://geodesic.mathdoc.fr/item/TAM_2017_44_1_a6/}
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Ulavathi Shettar Mahabaleshwar; Igor Pažanin; Marko Radulović; Francisco Javier Suárez-Grau. Effects of small boundary perturbation on the MHD duct flow. Theoretical and applied mechanics, Tome 44 (2017) no. 1. http://geodesic.mathdoc.fr/item/TAM_2017_44_1_a6/