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J. Fluid Mech. (2005), vol. 545, pp. 213243. c 2005 Cambridge University Press doi:10.1017/S0022112005006439 Printed in the United Kingdom
 

Summary: J. Fluid Mech. (2005), vol. 545, pp. 213243. c 2005 Cambridge University Press
doi:10.1017/S0022112005006439 Printed in the United Kingdom
213
Linear and nonlinear convection in solidifying
ternary alloys
By D. M. ANDERSON1
AND T. P. SCHULZE2
1
Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030, USA
2
Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300, USA
(Received 3 June 2004 and in revised form 9 May 2005)
In this paper we consider buoyancy-driven flow and directional solidification of a
ternary alloy in two dimensions. A steady flow can be established by forcing liquid
downward at an average rate V through a temperature gradient that is fixed in the
laboratory frame of reference and spans both the eutectic and liquidus temperature
of the material being solidified. Our results include both a linear stability analysis
and numerical solution of the governing equations for finite-amplitude steady states.
The ternary system is characterized by two distinct mushy zones a primary layer
with dendrites composed of a single species and, beneath the primary layer, a

  

Source: Anderson, Daniel M. - Department of Mathematical Sciences, George Mason University
Schulze, Tim - Department of Mathematics, University of Tennessee at Knoxville

 

Collections: Mathematics