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Title:Analytical investigations of convective effects on a solid-liquid interface
Author(s):Hadji, Layachi
Doctoral Committee Chair(s):Riahi, Daniel N.
Department / Program:Applied Mechanics
Engineering, Mechanical
Physics, Fluid and Plasma
Discipline:Applied Mechanics
Engineering, Mechanical
Physics, Fluid and Plasma
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):Applied Mechanics
Engineering, Mechanical
Physics, Fluid and Plasma
Abstract:A thin layer of a single-component Boussinesq fluid, contained between two rigid horizontal plates of low thermal conductivity, is cooled from above and heated from below. In the steady-static state, a heat flux traverses the system so that the temperature attained at the upper boundary of the layer is in the solid phase. An interface is planar in the conductive state, and corrugated in the convective regime. A small amplitude expansion study reveals that the critical Rayleigh number and the critical wavenumber for the onset of the interface deformation increase with the solid layer thickness. A weakly nonlinear stability analysis reveals that there is subcritical instability irrespective of the interface shape. The stable forms of the solidified front are then found. In the case of hexagonal pattern, the fluid motion is shown to be upward at the cells centers. Hexagons are also found to exhibit a higher heat flux than either rolls or squares. The non-planar interface is shown to have a cellular structure identical to the convection patterns which arise in this situation.
A long wavelength approximation is used to derive a non-linear evolution equation for the leading order interface pertubation. This evolution equation is found to be ill-posed when the dimensionless thickness of the solid layer A exceeds 0.256. The equation is then solved numerically for A between 0 and 0.256. The curve shifts to the right as A approaches the value 0.256.
The linear stability analysis for the binary alloy case is performed. This part complements the work done by Caroli et al. (1985). The critical value for the pulling velocity V at which both the morphological and convective instabilities are excited at the same concentration level is determined numerically.
Issue Date:1989
Rights Information:Copyright 1989 Hadji, Layachi
Date Available in IDEALS:2011-05-07
Identifier in Online Catalog:AAI9010871
OCLC Identifier:(UMI)AAI9010871

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