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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
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-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)
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)
Dragos, L.: Magnetofluid dynamics. Abacus Press (1975)
Hartmann, J., Lazarus, F.: Hg-dynamics. Levin & Munksgaard Copenhagen (1937)
Müller, U., Bühler, L.: Magnetofluiddynamics in Channels and Containers. Springer, New York (2001)
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)
Singh, B., Lal, J.: Finite element method in magnetohydrodynamic channel flow problems. International Journal for Numerical Methods in Engineering 18(7), 1104–1111 (1982)
Smolentsev, S.: MHD duct flows under hydrodynamic “slip” condition. Theoretical and Computational Fluid Dynamics 23(6), 557 (2009)
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)
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)
Acknowledgement
The support of The Scientific and Technological Research Council of Turkey (TUBITAK) is acknowledged.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-3-030-55874-1_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-55873-4
Online ISBN: 978-3-030-55874-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)