Analytical investigations of convective effects on a solid-liquid interface

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Applied Mechanics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Hadji, Layachi

Contributors dc:contributor

• Riahi, Daniel N.

• Applied Mechanics
• Engineering, Mechanical
• Physics, Fluid and Plasma

Statement dc:rights

• Copyright 1989 Hadji, Layachi

Language dc:language

eng

Identifier

AAI9010871
(UMI)AAI9010871

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/23424