Abstract
This paper is concerned with the flow of a conducting fluid through a pipe with a square cross-section in the presence of a uniform magnetic field parallel to one pair of the sides and perpendicular to the axis of the pipe, when the Hartman number M is large. For the problem for the dimensionless induced magnetic field and the velocity (both parallel to the axis of the pipe) formal asymptotic approximations of the solution for ε=(2M)−1 ↓ 0 are constructed. This is done in two ways: (i) using the standard method of matched asymptotic expansions, (ii) using an ad hoc method, which yields "almost exact" results. For the difference between the constructed formal asymptotic approximations and the exact solution estimates are derived in various norms, but with the accent especially on estimates in the maximum norm. The method to derive these estimates is based on Sobolev-Hilbert space techniques.
Keywords
- Vertical Wall
- Uniform Magnetic Field
- Hartmann Number
- Formal Approximation
- Matched Asymptotic Expansion
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© 1979 Springer-Verlag
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van Harten, A. (1979). Asymptotic approximations in magneto-hydrcdynamic singular perturbation problems. In: Verhulst, F. (eds) Asymptotic Analysis. Lecture Notes in Mathematics, vol 711. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062949
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DOI: https://doi.org/10.1007/BFb0062949
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-09245-2
Online ISBN: 978-3-540-35332-4
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