### Abstract

We present numerical simulations without modeling of an incompressible, laminar, unidirectional circular pipe flow of an electrically conducting fluid under the influence of a uniform transverse magnetic field. Our computations are performed using a finite-volume code that uses a charge-conserving formulation [called current-conservative formulation in references (Ni et al J Comput Phys 221(1):174-204, 2007, Ni et al J Comput Phys 227(1):205-228, 2007)]. Using high resolution unstructured meshes, we consider Hartmann numbers up to 3000 and various values of the wall conductance ratio c. In the limit $${c{\ll}{\rm Ha}^{-1}}$$ (insulating wall), our results are in excellent agreement with the so-called asymptotic solution (Shercliff J Fluid Mech 1:644-666, 1956). For higher values of the wall conductance ratio, a discrepancy with the asymptotic solution is observed and we exhibit regions of velocity overspeed in the Roberts layers. We characterise these overspeed regions as a function of the wall conductance ratio and the Hartmann number; a set of scaling laws is derived that is coherent with existing asymptotic analysis.

Original language | English |
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Pages (from-to) | 525-533 |

Number of pages | 9 |

Journal | Theoretical and Computational Fluid Dynamics |

Volume | 23 |

Issue number | 6 |

DOIs | |

Publication status | Published - Nov 2009 |

Externally published | Yes |

### Keywords

- Circular pipe
- MHD
- Numerics
- Wall conductivity

### ASJC Scopus subject areas

- Condensed Matter Physics
- Fluid Flow and Transfer Processes
- Engineering(all)
- Computational Mechanics

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## Cite this

*Theoretical and Computational Fluid Dynamics*,

*23*(6), 525-533. https://doi.org/10.1007/s00162-009-0163-0