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Year 2006, Volume 9 / Issue 2

DOI: 10.1615/JPorMedia.v9.i2

Pages: 102

DOI: 10.1615/JPorMedia.v9.i2.40

Article price - $35.00

Effect of Permeability on Steady Flow in a Dendrite Layer

Daniel Riahi
University of Texas-Pan American

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.

pages 135-153

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