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Natural convection in steady solidification - Finite element analysis of a two-phase Rayleigh-Benard problemGalerkin finite-element approximations and Newton's method for solving free boundary problems are combined with computer-implemented techniques from nonlinear perturbation analysis to study solidification problems with natural convection in the melt. The Newton method gives rapid convergence to steady state velocity, temperature and pressure fields and melt-solid interface shapes, and forms the basis for algebraic methods for detecting multiple steady flows and assessing their stability. The power of this combination is demonstrated for a two-phase Rayleigh-Benard problem composed of melt and solid in a veritical cylinder with the thermal boundary conditions arranged so that a static melt with a flat melt-solid interface is always a solution. Multiple cellular flows bifurcating from the static state are detected and followed as Rayleigh number is varied. Changing the boundary conditions to approach those appropriate for the vertical Bridgman solidification system causes imperfections that eliminate the static state. The flow structure in the Bridgman system is related to those for the Rayleigh-Benard system by a continuous evolution of the boundary conditions.
Document ID
19840039974
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
Authors
Chang, C. J.
(Massachusetts Inst. of Tech. Cambridge, MA, United States)
Brown, R. A.
(MIT Cambridge, MA, United States)
Date Acquired
August 12, 2013
Publication Date
January 1, 1984
Publication Information
Publication: Journal of Computational Physics
Volume: 53
ISSN: 0021-9991
Subject Category
Fluid Mechanics And Heat Transfer
Accession Number
84A22761
Distribution Limits
Public
Copyright
Other

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