Abstract
The magnetohydrodynamic (MHD) flow of an electrically conducting fluid is considered in a long channel of rectangular cross-section along with the z-axis. The fluid is driven by a pressure gradient along the z-axis. The flow is steady, laminar, fully-developed and is influenced by an external magnetic field applied perpendicular to the channel axis. So, the velocity field V = (0, 0, V ) and the magnetic field B = (0, B 0, B) have only channel-axis components V and B depending only on the plane coordinates x and y on the cross-section of the channel which is a rectangular duct. The finite difference method (FDM) is devised to solve the problem tackling mixed type of boundary conditions such as no-slip and insulated walls and both slipping and variably conducting walls. Thus, the numerical results show the effects of the Hartmann number Ha, the conductivity parameter c and the slipping length α on both of the velocity and the induced magnetic field, especially near the walls. It is observed that the well-known characteristics of the MHD flow are also caught.
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The support of The Scientific and Technological Research Council of Turkey (TUBITAK) is acknowledged.
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Arslan, S., Tezer-Sezgin, M. (2021). Finite Difference Solutions of 2D Magnetohydrodynamic Channel Flow in a Rectangular Duct. In: Vermolen, F.J., Vuik, C. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2019. Lecture Notes in Computational Science and Engineering, vol 139. Springer, Cham. https://doi.org/10.1007/978-3-030-55874-1_5
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DOI: https://doi.org/10.1007/978-3-030-55874-1_5
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