StagnationFlow Models
Multiphase Heat Transfer and Fluid Flow
Professor Roger H. Rangel
Assistant Specialist: Xiaoli Bian
StagnationFlow Solidification Models
Transient heat transfer problems involving melting or solidification are
important in many engineering applications involving processes such as
casting, welding and spray forming. The problem of solidliquid phase change
belongs to the class of moving boundary problems because of the existence of
a moving interface. The rate of propagation of this boundary into the
liquid region (solidification) or into the solid region (melting) depends
on the
thermal properties of the solid and liquid regions, and in addition, in the
cases where there exists motion in the liquid phase, such as metal
droplet
solidification in spray processes, it also depends on the fluid and flow
properties of the liquid region. In our study, the effect of the liquid motion
on its solidification behavior has been investigated by considering the
twodimensional stagnation flow onto a cold substrate. By coupling
liquidphase momentum equation and
the conductiveconvective liquid energy equation with the heat conduction
equation in the solid region as well as the energy balance equation at the
interface, we set up the mathematical model of the half space convective
Stefan solidification problem. An instantaneoussimilarity method and a
quasisteady method,
as well as the finitedifference method have been applied to solve the
timedependent system of equations. Parametric studies such as
the effect of Prandtl number, Stefan number, the stagnationflow
flow strain rate, and the ratio of the liquid and solid
phase thermal diffusivity, as well as the initial substrate and liquid phase
temperatures on the solidification behavior have been conducted.
The solution provides a more reasonable model
for the solidification behavior of the liquid in motion, and provides better
insight into situations such as those encountered during the deformation
and solidification of a droplet impinging on a cold substrate.
References

Rangel, R.H. and Bian, X.,
"The Inviscid StagnationFlow Solidification Problem"
,
Int. J. Heat Mass Transfer,
39, No. 8, 15911602, 1996.

Rangel, R.H. and Bian, X.,
"Numerical Solution of the
Inviscid StagnationFlow Solidification Problem"
,
Numerical Heat TransferPart A: Applications,
28, No. 5, 589603, 1995.

Bian, X. and Rangel, R.H.,
"The Viscous StagnationFlow
Solidification Problem"
,
Int. J. Heat Mass Transfer,
, No. 17, 35813594, 1996.

Bian, X. and Rangel, R.H.,
"
StagnationFLow Solidification on
a Finite Thickness Substrate
"
,
Int. J. Heat Mass Transfer,
(1997) in press.
Figures
(1) Schematic of the StagnationFlow Solidification Problem.
(2) Evolution of the Solid Front (Comparison of
Three Methods of Solution).
(3) Evolution of the Solid and Liquid Temperature Profiles
(Comparison of Three Methods of Solution).
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This page has been last updated by XB 9/15/97