Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 53, Issue 1, Pages 128-136Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2006.06.014
Keywords
MHD Jeffery-Hamel flow; small disturbances stability; spectral method; eigenvalue problem; Orr-Sommerfeld equation
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In this paper, the temporal development of small disturbances in magnetohydrodynamic (MHD) Jeffery-Hamel flows is investigated, in order to understand the stability of hydromagnetic steady flows in convergent/divergent channels at very small magnetic Reynolds number R-m. A modified form of normal modes that satisfy the linearized governing equations for small disturbance development asymptotically far downstream is employed [A. McAlpine, P.G. Drazin, On the spatio-development of small perturbations of Jeffery-Hamel flows, Fluid Dyn. Res. 22 (1998) 123-138]. The resulting fourth-order eigenvalue problem which reduces to the well known Orr-Sommerfeld equation in some limiting cases is solved numerically by a spectral collocation technique with expansions in Chebyshev polynomials. The results indicate that a small divergence of the walls is destabilizing for plane Poiseuille flow while a small convergence has a stabilizing effect. However, an increase in the magnetic field intensity has a strong stabilizing effect on both diverging and converging channel geometry. (c) 2007 Elsevier Ltd. All rights reserved.
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