MHD flow in a rectangular duct with a perturbed boundary

Date

2018-06-28

Author

Fendoğlu, Hande
Bozkaya, Canan
Tezer, Münevver

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In this paper, a numerical study is carried for solving the unsteady magnetohydrodynamic (MHD) flow of a viscous, incompressible and electrically conducting fluid in a rectangular duct with a perturbed boundary subjected to an external magnetic field applied in y-direction. A small boundary perturbation of magnitude ε is applied on the upper wall of the duct which is encountered in the visualization of the vein anatomy and blood flow in constricted arteries. The governing MHD flow convection-diffusion type equations are coupled in the velocity and the induced magnetic field. No-slip conditions are assumed on the boundary of the duct in which the vertical walls are insulated and the horizontal walls are perfectly conducting. The numerical method is based on the use of the domain boundary element method (DBEM) in spatial discretization and a backward finite difference scheme is employed in time integration. These MHD equations are decoupled first into two transient convection-diffusion equations, and then into two modified Helmholtz equations by using suitable transformations. Then, DBEM is used to transform these equations into equivalent integral equations by employing the fundamental solution of either steady-state convection-diffusion or modified Helmholtz equations. Thus, the resulting BEM integral equations contain a domain integral whose kernel involves the multiplication of the fundamental solution with the first order time derivative of the unknown, and it is treated by numerical integration. The velocity and the induced magnetic fields are visualized in terms of equi-velocity and current lines at transient and steady-state levels for several values of Hartmann number and the boundary perturbation parameter. The validity of the code is ascertained by comparing the obtained results with the ones given in literature [2]. The results reveal that the well-known characteristics of MHD flow are captured, that is, as M increases the velocity decreases and becomes stagnant at the center of the duct and a boundary layer formation is observed for both the velocity and the induced magnetic field. The perturbation parameter and the shape of the curved boundary significantly affect the behavior of the flow and cause an increase in the magnitude of induced magnetic field. DBEM with the fundamental solution of convection-diffusion equation gives better results compared to the ones obtained with the fundamental solution of modified Helmholtz equation in the sense of increasing M.

URI

https://hdl.handle.net/11511/85810

Conference Name

Symposiom of the International Association for Boundary Element Methods- IABEM 2018, (26 - 28 Haziran 2018)

Collections

Department of Mathematics, Conference / Seminar

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Citation Formats

H. Fendoğlu, C. Bozkaya, and M. Tezer, “MHD flow in a rectangular duct with a perturbed boundary,” presented at the Symposiom of the International Association for Boundary Element Methods- IABEM 2018, (26 - 28 Haziran 2018), Paris, Fransa, 2018, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/85810.