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Please use this identifier to cite this item:
http://hdl.handle.net/2142/987
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| Title: |
On nonlinear convection in mushy layers. Part 1: Oscillatory modes of convection. With Corrigendums |
| Authors: |
Riahi, Daniel N. |
| Keywords: |
Nonlinear convection |
| Issue Date: |
2002 |
| Publisher: |
Cambridge University Press |
| Citation Information: |
D.N. Riahi (2002) On nonlinear convection in mushy layers. Part 1. Oscillatory modes of convection. Journal of Fluid Mechanics 467, 331–359. |
| Abstract / Summary: |
We consider the problem of nonlinear convection in horizontal mushy layers during
the solidification of binary alloys. We analyse the oscillatory modes of convection
in the form of two- and three-dimensional travelling and standing waves. Under a
near-eutectic approximation and the limit of large far-field temperature, we determine
the solutions to the nonlinear problem by using a perturbation technique, and the
stability of two- and three-dimensional solutions in the form of simple travelling
waves, general travelling waves and standing waves is investigated. The results of the
stability and the nonlinear analyses indicate that supercritical simple travelling rolls
are stable over most of the studied range of parameter values, while supercritical
standing rolls can be stable only over some small range of parameter values, where
the simple travelling rolls are unstable. The results of the investigation of the onset
of plume convection and chimney formation leading to the occurrence of freckles in
the alloy crystal indicate that the chimney of the plume can be generated internally
or near the lower boundary of the mushy layer. The roles of a Stefan number, a
permeability parameter and a concentration ratio on the flow instability in both linear
and nonlinear regimes are also determined. |
| URI: |
http://hdl.handle.net/2142/987 |
| DOI: |
10.1017/S0022112002001465 |
| Type of Resource: |
text |
| Genre of Resource: |
article |
| Publication Status: |
published or submitted for publication |
| Peer-Reviewed: |
is peer reviewed |
| Appears in Collections: |
Theoretical and Applied Mechanics (TAM) Published Papers
|
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