Friday, January 20, 2006
1:00pm – 2:00pm
Dr. Steven Roper *
Department of Engineering Sciences and Applied Mathematics
Northwestern University
“Convection In Mushy Layers With Sidewall Heat Fluxes”
Abstract:
During the directional solidification of a binary alloy a morphological instability can lead
to the development of a mushy layer. The complicated structure of the mushy layer can
be modeled as a reactive porous medium in which the solid fraction and permeability are
functions of the local liquid solute concentration and temperature. In the basic state the
density of the fluid in the melt and the mushy layer is unstably stratified and convection
occurs if the mush Rayleigh number exceeds a critical. The convective motions lead to
the development of chimneys which solidify as imperfections or freckles in the final cast
solid.
We examine the role of sidewall heat fluxes in modifying the onset of convection and
altering the convective patterns. An overview of modeling the mushy layer will be given
and a discussion of our research so far.
* Published with Stephen Davis and Peter Voorhees