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Journal of Porous Media
IF: 1.49 5-Year IF: 1.159 SJR: 0.504 SNIP: 0.671 CiteScore™: 1.58

ISSN Print: 1091-028X
ISSN Online: 1934-0508

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Journal of Porous Media

DOI: 10.1615/JPorMedia.v11.i3.60
pages 291-303

Nonlinear Buoyant Convection in Mushy Layers during Alloy Solidification

B. S. Okhuysen
Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Daniel N. Riahi
School of Mathematical and Statistical Sciences, One West University Boulevard, University of Texas Rio Grande Valley, Brownsville, Texas 78520 USA

ABSTRACT

We consider the problem of nonlinear steady buoyant convection in horizontal mushy layers during alloy solidification. We analyze the effects of several parameters on the stationary modes of convection in the form of either hexagons or nonhexagons such as rolls, rectangles, and squares. No assumption is made on the thickness of the mushy layer, and a number of simplifying assumptions made in previous nonlinear analyses are relaxed here to study a richer set of phenomena. Using both analytical and numerical methods, we determine the steady solutions to the weakly nonlinear problem. The results of the analyses and computations indicate, in particular, that depending on the range of values of the parameters, bifurcation to nonhexagonal convection can be either supercritical or subcritical, while bifurcation to hexagon pattern convection, corresponding to the smallest value of the Rayleigh number, is subcritical. For variable permeability, subcritical down-hexagons with down-flow at the cell centers and up-flow at the cell boundaries, which have been observed in related experiments, and supercritical nonhexagons were predicted in a particular range of values of the parameters.


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