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多孔介质期刊
影响因子: 1.061 5年影响因子: 1.151 SJR: 0.504 SNIP: 0.671 CiteScore™: 1.58

ISSN 打印: 1091-028X
ISSN 在线: 1934-0508

多孔介质期刊

DOI: 10.1615/JPorMedia.v9.i2.40
pages 135-153

Effect of Permeability on Steady Flow in a Dendrite Layer

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 convective flow in a horizontal dendrite layer during alloy directional solidification. We analyze the effect of the permeability of the layer on the stationary modes of convection in the form of two-dimensional rolls and three-dimensional patterns. Under a near-eutectic approximation and in the limit of large far-field temperature, we determine the two- and three-dimensional solutions to the weakly nonlinear problem by using a perturbation technique, and the stability of these solutions is investigated with respect to arbitrary three-dimensional disturbances. An inverse form of the permeability function introduces two nonnegative nondimensional parameters K1 and K2 that are significant in the present problem. The results of the analyses in some particular range of values of the magnitude |ε| of the amplitude of convection indicate, in particular, that the effects of K1 and K2 on the flow features can be significant, and different types of flow pattern can become stable for particular values of these two parameters. For sufficiently small and nonzero values of |ε| and K1, the steady flow pattern in the form of subcritical hexagons can be stable. For |ε| beyond some value, and depending on the values of the parameters of the problem, supercritical rolls, squares, or rectangles can be stable. For K1 = 0.0, the only stable flow pattern is that due to steady rolls.


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