A thermomechanical model of solidification on a mold moving with constant velocity

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 the m odel is no longer valid since it cannot account for gross distortion of the shell (i.e., distortions that greatly exceed the spatial perturbations con sidered in the model).