Stagnation-Flow Models
Multiphase Heat Transfer and Fluid Flow
Professor Roger H. Rangel
Graduate Student: Ruth A. Lambert
Solidification of a Supercooled Liquid: Interface Stability and
Stagnation-Point Flow
Analytical analyses of the solidification process of a supercooled liquid in a
half-space provide further insight into classical solidification problems and
crystal growth theory. Under consideration are the cases pertaining to
stagnation-point flow in the liquid phase and instability at the solid-liquid
interface, with and without convective effects. The posed problems involve a
phase change with a moving boundary at the solid-liquid interface. A classical
solution exists for the case of solidification of a supercooled liquid in the
absence of convection. Previous research shows that the onset of crystal growth
can be predicted by the growth of a disturbance introduced at the solid-liquid
interface. The solution of the unsteady temperature profile and the development
of the solid region is found using numerical methods to solve the energy
transport equation. The position of the solid-liquid interface is found using
the heat-balance equation. The results show that after a long time the velocity
of the solid-liquid interface approaches a constant value and the temperature
field reaches a quasi-steady state. The quasi-steady temperature field is used
to develop the governing equations of a linear perturbation analysis in the
presence of stagnation-point flow. A linear perturbation analysis, including a
complete dispersion analysis, is conducted for the case of solidification in the
absence of convection, including the effects of surface curvature. The results
show that the capillary effect increases interface stability, within the limits
of large surface curvature, while thermal gradients have a destabilizing effect.
References
-
R.A. Lambert and R.H. Rangel, “Linear
stability analysis of the solidification of a supercooled liquid in a
half-space”, International Journal of
Heat and Mass Transfer,
No. 45, 4577-4587,
2002.
-
R.A. Lambert and R.H. Rangel, “Solidification of a
supercooled liquid in stagnation-point flow”, International
Journal of Heat and
Mass Transfer, No. 46,
4013-4021, 2003.
Figures
Fig. 1
Stagnation-point flow solidification.
Fig. 2
Stagnation-point flow solidification: numerical calculation of the interface
velocity versus time for values of the Stefan number.
Fig. 3 Dispersion analysis
at interface: effect of the capillary number,
B, on
the disturbance growth rate.
Fig. 4
Dispersion analysis at interface: effect of thermal supercooling,
l,
on the disturbance growth rate.
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This page has been last updated by JMS 2/11/2004
