Temporal stability of small disturbances in MHD Jeffery–Hamel flows
✍ Scribed by O.D. Makinde; P.Y. Mhone
- Publisher
- Elsevier Science
- Year
- 2007
- Tongue
- English
- Weight
- 438 KB
- Volume
- 53
- Category
- Article
- ISSN
- 0898-1221
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✦ Synopsis
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.