Corner regions in the asymptotic solution of ε∇2u = ∂u/∂y with reference to MHD duct flow-Reference-Cited by-同舟云学术

Corner regions in the asymptotic solution of ε∇2u = ∂u/∂y with reference to MHD duct flow

Published:1972-07 Issue:1 Volume:72 Page:117-122
ISSN:0305-0041
Container-title:Mathematical Proceedings of the Cambridge Philosophical Society
language:en
Short-container-title:Math. Proc. Camb. Phil. Soc.

Author:

Cook L. Pamela,Ludford G. S. S.,Walker J. S.

Abstract

AbstractIn the asymptotic solution of the title equation for simple boundary data on the rectangle 0 ≤ x ≤ l, 0 ≤ y ≤ 1 the bottom corners are not passive, as has previously been supposed, but in fact generate the parabolic side layers at x = o, l. The top corners, though passive, lead to unconventional elliptic quarter-plane problems. Implications for the MHD duct problem are indicated.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference5 articles.

1. (5) Cook L. Pamela and Ludford G. S. S. The behaviour as ε → 0 + of solutions to ε∇2ω = ∂ω/∂y in |y| ≤ in the rectangle 0 ≤ x ≤ l, |y| 1. Submitted for publication.

2. The Behavior as $\varepsilon \to + 0$ of Solutions to $\varepsilon \nabla ^2 w = {{\partial w} / {\partial y}}$ in $| y | \leqq 1$ for Discontinuous Boundary Data

3. (3) Cook L. Pamela. The asymptotic solution of ε∇2ω = ∂ω/∂y on a rectangle. Ph.D. Thesis (Cornell University, 1971).

4. Three-dimensional MHD duct flows with strong transverse magnetic fields. Part 2. Variable-area rectangular ducts with conducting sides

5. The effects of wall conductivity in magnetohydrodynamic duct flow at high Hartmann numbers

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