TY - JOUR
T1 - Effect of axial magnetic field on three-dimensional instability of natural convection in a vertical Bridgman growth configuration
AU - Gelfgat, A. Yu
AU - Bar-Yoseph, P. Z.
AU - Solan, A.
N1 - Funding Information:
This work was supported by the Israel Ministry of Science (Grant 8575-1-98), the Israel Ministry of Immigrant Absorption (to A. Gelfgat), the Israel High Performance Computer Unit, the Fund for Promotion of Research and the Y. Winograd Chair of Fluid Dynamics and Heat Transfer at Technion.
Copyright:
Copyright 2007 Elsevier B.V., All rights reserved.
PY - 2001/8
Y1 - 2001/8
N2 - A study of the effect of an externally imposed magnetic field on the axisymmetry-breaking instability of an axisymmetric convective flow, associated with crystal growth from bulk of melt, is presented. Convection in a vertical cylinder with a parabolic temperature profile on the sidewall is considered as a representative model. A parametric study of the dependence of the critical Grashof number Grcr on the Hartmann number Ha for fixed values of the Prandtl number (Pr = 0.015) and the aspect ratio of the cylinder (A = height/radius = 1,2 and 3) is carried out. The stability diagram Grcr(Ha) corresponding to the axisymmetric - three-dimensional transition for increasing values of the axial magnetic field is obtained. The calculations are done using the spectral Galerkin method allowing an effective and accurate three-dimensional stability analysis. It is shown that at relatively small values of Ha the axisymmetric flow tends to be oscillatory unstable. After the magnitude of the magnetic field (Ha) exceeds a certain value the instability switches to a steady bifurcation caused by the Rayleigh-Bénard mechanism.
AB - A study of the effect of an externally imposed magnetic field on the axisymmetry-breaking instability of an axisymmetric convective flow, associated with crystal growth from bulk of melt, is presented. Convection in a vertical cylinder with a parabolic temperature profile on the sidewall is considered as a representative model. A parametric study of the dependence of the critical Grashof number Grcr on the Hartmann number Ha for fixed values of the Prandtl number (Pr = 0.015) and the aspect ratio of the cylinder (A = height/radius = 1,2 and 3) is carried out. The stability diagram Grcr(Ha) corresponding to the axisymmetric - three-dimensional transition for increasing values of the axial magnetic field is obtained. The calculations are done using the spectral Galerkin method allowing an effective and accurate three-dimensional stability analysis. It is shown that at relatively small values of Ha the axisymmetric flow tends to be oscillatory unstable. After the magnitude of the magnetic field (Ha) exceeds a certain value the instability switches to a steady bifurcation caused by the Rayleigh-Bénard mechanism.
KW - A1. Computer simulation
KW - A1. Convection
KW - A1. Heat transfer
KW - A1. Magnetic fields
KW - A2. Bridgman technique
UR - http://www.scopus.com/inward/record.url?scp=0035426354&partnerID=8YFLogxK
U2 - 10.1016/S0022-0248(01)01335-5
DO - 10.1016/S0022-0248(01)01335-5
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AN - SCOPUS:0035426354
SN - 0022-0248
VL - 230
SP - 63
EP - 72
JO - Journal of Crystal Growth
JF - Journal of Crystal Growth
IS - 1-2
ER -