Coriolis effect on the stability of convection in mushy layers during the solidification of binary alloys.
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Date
2000
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Abstract
We consider the solidification of a binary alloy in a mushy layer subject to Coriolis
effects. A near-eutectic approximation and large far-field temperature is employed in
order to study the dynamics of the mushy layer in the form of small deviations from the
classical case of convection in a horizontal porous layer of homogenous permeability.
The linear stability theory is used to investigate analytically the Corio lis effect in a
rotating mushy layer for, a diffusion time scale used by Amberg & Homsey (1993) and
Anderson & Worster (1996), and for a new diffusion time scale proposed in the current
study. As such, it is found that in contrast to the problem of a stationary mushy layer,
rotating the mushy layer has a stabilising effect on convection. For the case of the new
diffusion time scale proposed by the author, it is established that the viscosity at high
rotation rates has a destabilising effect on the onset of stationary convection, ie. the
higher the viscosity, the less stable the liquid. Finite amplitude results obtained by using a
weak non-linear analysis provide differential equations for the amplitude, corresponding
to both stationary and overstable convection. These amplitude equations permit one to
identify from the post-transient conditions that the fluid is subject to a pitchfork
bifurcation in the stationary case and to a Hopf bifurcation associated with the overstable
convection. Heat transfer results were evaluated from the amplitude solution and are
presented in terms of the Nusselt number for both stationary and overstable convection.
They show that rotation enhances the convective heat transfer in the case of stationary
convection and retards convective heat transfer in the oscillatory case, but only for low
values of the parameter X I = 8 Pr ~ 0 So· The parameter 1/ X I represents the coefficient of
the time derivative term in the Darcy equation. For high X I values, the contribution from
the time derivative term is small (and may be neglected), whilst for small X I values the
time derivative term may be retained.
Description
Thesis (Ph.D.)-University of Durban-Westville, 2000.
Keywords
University of Durban-Westville--Dissertations., Binary alloys., Coriolis force., Theses--Mechanical engineering.