Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 191
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Kawczynski, Charlie Smolentsev, Sergey and Abdou, Mohamed 2016. An induction-based magnetohydrodynamic 3D code for finite magnetic Reynolds number liquid-metal flows in fusion blankets. Fusion Engineering and Design,

    Rashidi, M.M. Nasiri, Mohammad Khezerloo, Marzieh and Laraqi, Najib 2016. Numerical investigation of magnetic field effect on mixed convection heat transfer of nanofluid in a channel with sinusoidal walls. Journal of Magnetism and Magnetic Materials, Vol. 401, p. 159.

    Tatari, Mehdi Shahriari, Mostafa and Raoofi, Mohammadreza 2016. Numerical modeling of magneto-hydrodynamics flows using reproducing kernel particle method. International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, Vol. 29, Issue. 4, p. 548.

    Yang, Jong Hoon Yan, Yue and Kim, Chang Nyung 2016. Numerical investigation of the LM MHD flows in a curved duct with an FCI with varying slot locations. Fusion Engineering and Design, Vol. 105, p. 86.

    Bluck, Michael J. Wolfendale, Michael J. and Marquis, Andrew J. 2015. An analytical solution to the heat transfer problem in Shercliff flow. International Journal of Heat and Mass Transfer, Vol. 86, p. 542.

    Dehghan, Mehdi and Mohammadi, Vahid 2015. The method of variably scaled radial kernels for solving two-dimensional magnetohydrodynamic (MHD) equations using two discretizations: The Crank–Nicolson scheme and the method of lines (MOL). Computers & Mathematics with Applications, Vol. 70, Issue. 10, p. 2292.

    Delacroix, Jules and Davoust, Laurent 2015. On the role of surface rheology in a magnetohydrodynamic swirling flow. Physics of Fluids, Vol. 27, Issue. 6, p. 062104.

    Kumar, J. Prathap Umavathi, J.C. Chamkha, Ali J. and Ramarao, Y. 2015. Mixed convection of electrically conducting and viscous fluid in a vertical channel using Robin boundary conditions. Canadian Journal of Physics, Vol. 93, Issue. 6, p. 698.

    Mistrangelo, C. and Bühler, L. 2015. Magnetohydrodynamic flow in ducts with discontinuous electrical insulation. Fusion Engineering and Design, Vol. 98-99, p. 1833.

    Morovati, Vahid and Malek, Alaeddin 2015. Solving inhomogeneous magnetohydrodynamic flow equations in an infinite region using boundary element method. Engineering Analysis with Boundary Elements, Vol. 58, p. 202.

    Pan, Jun-Hua Ni, Ming-Jiu and Zhang, Nian-Mei 2015. A Velocity-pressure Coupling Based Consistent and Conservative Method for MHD Flow. Procedia Engineering, Vol. 126, p. 686.

    Rashidi, S. Dehghan, M. Ellahi, R. Riaz, M. and Jamal-Abad, M.T. 2015. Study of stream wise transverse magnetic fluid flow with heat transfer around an obstacle embedded in a porous medium. Journal of Magnetism and Magnetic Materials, Vol. 378, p. 128.

    Smolentsev, S. Badia, S. Bhattacharyay, R. Bühler, L. Chen, L. Huang, Q. Jin, H.-G. Krasnov, D. Lee, D.-W. de les Valls, E. Mas Mistrangelo, C. Munipalli, R. Ni, M.-J. Pashkevich, D. Patel, A. Pulugundla, G. Satyamurthy, P. Snegirev, A. Sviridov, V. Swain, P. Zhou, T. and Zikanov, O. 2015. An approach to verification and validation of MHD codes for fusion applications. Fusion Engineering and Design, Vol. 100, p. 65.

    Stelzer, Zacharias Cébron, David Miralles, Sophie Vantieghem, Stijn Noir, Jérôme Scarfe, Peter and Jackson, Andrew 2015. Experimental and numerical study of electrically driven magnetohydrodynamic flow in a modified cylindrical annulus. I. Base flow. Physics of Fluids, Vol. 27, Issue. 7, p. 077101.

    Tao, Zhen and Ni, MingJiu 2015. Analytical solutions for MHD flow at a rectangular duct with unsymmetrical walls of arbitrary conductivity. Science China Physics, Mechanics & Astronomy, Vol. 58, Issue. 2, p. 1.

    Xinghui, Cai Hongfu, Qiang Sanqiang, Dong Guoliang, Wang Jiangren, Lu Guo, Z. and Chang, G. 2015. Numerical simulations of a fully developed liquid-metal magnetohydrodynamic flow in a circular duct. MATEC Web of Conferences, Vol. 35, p. 07001.

    Zhou, K. Ni, S.H. and Tian, Z.F. 2015. Exponential high-order compact scheme on nonuniform grids for the steady MHD duct flow problems with high Hartmann numbers. Computer Physics Communications, Vol. 196, p. 194.

    Aoyagi, Mitsuhiro Ito, Satoshi and Hashizume, Hidetoshi 2014. Numerical study of the MHD flow characteristics in a three-surface-multi-layered channel with different inlet conditions. Fusion Engineering and Design, Vol. 89, Issue. 7-8, p. 1227.

    Asghar, Saleem Minhas, Tayyaba and Ali, Aamir 2014. Existence of a Hartmann layer in the peristalsis of Sisko fluid. Chinese Physics B, Vol. 23, Issue. 5, p. 054702.

    Badia, Santiago Martín, Alberto F. and Planas, Ramon 2014. Block recursive LU preconditioners for the thermally coupled incompressible inductionless MHD problem. Journal of Computational Physics, Vol. 274, p. 562.

  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 49, Issue 1
  • January 1953, pp. 136-144

Steady motion of conducting fluids in pipes under transverse magnetic fields

  • J. A. Shercliff (a1)
  • DOI:
  • Published online: 24 October 2008

This paper studies the steady motion of an electrically conducting, viscous fluid along channels in the presence of an imposed transverse magnetic field when the walls do not conduct currents. The equations which determine the velocity profile, induced currents and field are derived and solved exactly in the case of a rectangular channel. When the imposed field is sufficiently strong the velocity profile is found to degenerate into a core of uniform flow surrounded by boundary layers on each wall. The layers on the walls parallel to the imposed field are of a novel character. An analogous degenerate solution for channels of any symmetrical shape is developed. The predicted pressure gradients for given volumes of flow at various field strengths are finally compared with experimental results for square and circular pipes.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

(1)G. K. Batchelor Proc. roy. Soc. A, 201 (1950), 405.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *