A thermomechanical model of pure metal solidification on a moving mold plat
e is considered. The goal of the model is to obtain a formula for the conta
ct pressure at the shell/mold interface as the mold moves into the molten l
iquid, From the contact pressure it is possible to infer the effects of the
mold velocity and the mold microgeometry on the time and location of gap n
ucleation which results from irregular distortion of the shell as it grows
from the melt. The mold, which moves at a constant velocity into the molten
liquid, has a sinusoidal surface with a lost, aspect ratio: this means tha
t its wavelength greatly exceeds its amplitude. The mold is of infinite are
a anti is assumed to be perfectly conducting and thermomechanically. rigid.
We therefore neglect the complexities associated with the physics of edge
constraints and/or free boundaries of the solidifying shell and the interac
ting distortions between deformable mold and shell materials along their in
terface, The ratio of the velocity of the solid/liquid interface to the mol
d velocity is identified as another dimensionless parameter in the analysis
. In order to arrive at an analytical solution for the contact pressure alo
ng the shell/mold interface, ive assume that this parameter is small. This
makes the velocity ratio a convenient perturbation parameter for the analys
is of thermomechanical distortion of the thin shell material as it grows fr
om the melt. This necessarily, limits the analysis to situations where the
mold moves at faster rather than slower speeds. It is assumed that there is
zero tangential shear stress between the fluid and the solidifying shell.
As the molten liquid flows over the mold, it perfectly wets the surface. Th
is precludes wetting effects due to surface tension, A hypoelastic constitu
tive law, which is a rate formulation of thermoelasticity. is assumed to go
vern deformation of the shell as it grows from the molten liquid. Latent he
at liberated at the freezing front is extracted across a constant contact r
esistance at the shell/mold interface. Peculiar fluid motion at the tip is
neglected. A solution for the contact pressure that is valid near the liqui
d surface (i.e.. the meniscus) is derived from the main theoretical develop
ments. Beyond the time of gap nucleation at the shell/mold interface. the m
odel is no longer valid since it cannot account for gross distortion of the
shell (i.e., distortions that greatly exceed the spatial perturbations con
sidered in the model).