Convective instabilities during the solidification of an ideal ternary alloy in a mushy layer
نویسندگان
چکیده
DANIEL M. ANDERSON†, GEOFFREY B. McFADDEN, SAM R. CORIELL AND BRUCE T. MURRAY Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030, USA Mathematical and Computational Sciences Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA Metallurgy Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA Department of Mechanical Engineering, State University of New York at Binghamton, Binghamton, NY 13902, USA
منابع مشابه
A model for diffusion - controlled solidification of ternary alloys in mushy layers †
We describe a model for non-convecting diffusion-controlled solidification of a ternary (three-component) alloy cooled from below at a planar boundary. The modelling extends previous theory for binary alloy solidification by including a conservation equation for the additional solute component and coupling the conservation equations for heat and species to equilibrium relations from the ternary...
متن کاملConvection in Mushy Layers
As a molten alloy or any multi-component liquid is cooled and solidified the growing solid phase usually forms a porous matrix through which the residual liquid can flow. The reactive two-phase medium comprising the solid matrix and residual liquid is called a mushy layer. Buoyancy forces, owing primarily to compositional depletion as one or more of the components of the alloy are extracted to ...
متن کاملShear flow, phase change and matched asymptotic expansions: Pattern formation in mushy layers
In many scientific and engineering problems the solidification of an alloy leads to a highly convoluted crystalline matrix modeled as a thermodynamically controlled reactive porous medium called a mushy layer. We analyze the interaction of an external shear flow with a solidifying mushy layer through a corrugated mush–liquid interface. We find that the external flow can drive forced convective ...
متن کاملAnalytical Solution for a Problem of Directional Solidification in a Ternary System
The seemingly trivial moving boundary problem of the crystallization of a solid phase from a cooled wall comes under the rubric of the so-called Stefan problems describing a wide range of physical processes. Their rich nonlinear behavior has attracted substantial scientific interest and their ubiquity in fields ranging from metallurgy to geophysics stimulates developing new mathematical approac...
متن کاملOptimal Control Solution to Nonlinear Causal Operator Systems with Target State
We will study the optimal control solution satisfying nonlinear causal operator differential equations. The transformation by these operators depends on the information about the trajectory as a function of past history which will not be affected by future events. These dynamical systems involve a large class of delay, integral, composition, or Cartesian products of operators. The optimal solut...
متن کامل