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2021 | OriginalPaper | Buchkapitel

Finite Difference Solutions of 2D Magnetohydrodynamic Channel Flow in a Rectangular Duct

verfasst von : Sinem Arslan, Münevver Tezer-Sezgin

Erschienen in: Numerical Mathematics and Advanced Applications ENUMATH 2019

Verlag: Springer International Publishing

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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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Literatur
1.
Zurück zum Zitat Arslan, S., Tezer, M.: Finite difference method solution of magnetohydrodynamic flow in channels with electrically conducting and slipping walls. [Electronic resource]. METU (2018) Arslan, S., Tezer, M.: Finite difference method solution of magnetohydrodynamic flow in channels with electrically conducting and slipping walls. [Electronic resource]. METU (2018)
2.
Zurück zum Zitat Arslan, S., Tezer-Sezgin, M.: Exact and FDM solutions of 1D MHD flow between parallel electrically conducting and slipping plates. Advances in Computational Mathematics 45, 1923–1938 (2019)MathSciNetCrossRef Arslan, S., Tezer-Sezgin, M.: Exact and FDM solutions of 1D MHD flow between parallel electrically conducting and slipping plates. Advances in Computational Mathematics 45, 1923–1938 (2019)MathSciNetCrossRef
3.
Zurück zum Zitat Carabineanu, A., Dinu, A., Oprea, I.: The application of the boundary element method to the magnetohydrodynamic duct flow. Zeitschrift für angewandte Mathematik und Physik ZAMP 46(6), 971–981 (1995)MathSciNetCrossRef Carabineanu, A., Dinu, A., Oprea, I.: The application of the boundary element method to the magnetohydrodynamic duct flow. Zeitschrift für angewandte Mathematik und Physik ZAMP 46(6), 971–981 (1995)MathSciNetCrossRef
4.
Zurück zum Zitat Dragos, L.: Magnetofluid dynamics. Abacus Press (1975) Dragos, L.: Magnetofluid dynamics. Abacus Press (1975)
5.
Zurück zum Zitat Hartmann, J., Lazarus, F.: Hg-dynamics. Levin & Munksgaard Copenhagen (1937) Hartmann, J., Lazarus, F.: Hg-dynamics. Levin & Munksgaard Copenhagen (1937)
6.
Zurück zum Zitat Müller, U., Bühler, L.: Magnetofluiddynamics in Channels and Containers. Springer, New York (2001)CrossRef Müller, U., Bühler, L.: Magnetofluiddynamics in Channels and Containers. Springer, New York (2001)CrossRef
7.
Zurück zum Zitat Singh, B., Lal, J.: MHD axial-flow in a triangular pipe under transverse magnetic-field parallel to a side of the triangle. Indian Journal of Technology 17(5), 184–189 (1979)MATH Singh, B., Lal, J.: MHD axial-flow in a triangular pipe under transverse magnetic-field parallel to a side of the triangle. Indian Journal of Technology 17(5), 184–189 (1979)MATH
8.
Zurück zum Zitat Singh, B., Lal, J.: Finite element method in magnetohydrodynamic channel flow problems. International Journal for Numerical Methods in Engineering 18(7), 1104–1111 (1982)CrossRef Singh, B., Lal, J.: Finite element method in magnetohydrodynamic channel flow problems. International Journal for Numerical Methods in Engineering 18(7), 1104–1111 (1982)CrossRef
9.
Zurück zum Zitat Smolentsev, S.: MHD duct flows under hydrodynamic “slip” condition. Theoretical and Computational Fluid Dynamics 23(6), 557 (2009)CrossRef Smolentsev, S.: MHD duct flows under hydrodynamic “slip” condition. Theoretical and Computational Fluid Dynamics 23(6), 557 (2009)CrossRef
10.
Zurück zum Zitat Tezer-Sezgin, M.: Boundary element method solution of MHD flow in a rectangular duct. International journal for numerical methods in fluids 18(10), 937–952 (1994)CrossRef Tezer-Sezgin, M.: Boundary element method solution of MHD flow in a rectangular duct. International journal for numerical methods in fluids 18(10), 937–952 (1994)CrossRef
11.
Zurück zum Zitat Tezer-Sezgin, M., Köksal, S.: Finite element method for solving MHD flow in a rectangular duct. International journal for numerical methods in engineering 28(2), 445–45 (1989)CrossRef Tezer-Sezgin, M., Köksal, S.: Finite element method for solving MHD flow in a rectangular duct. International journal for numerical methods in engineering 28(2), 445–45 (1989)CrossRef
Metadaten
Titel
Finite Difference Solutions of 2D Magnetohydrodynamic Channel Flow in a Rectangular Duct
verfasst von
Sinem Arslan
Münevver Tezer-Sezgin
Copyright-Jahr
2021
DOI
https://doi.org/10.1007/978-3-030-55874-1_5