A coupled velocity and temperature problem of the extruded spinning column in a micro-extrusion

In this paper, we investigate a coupled velocity and temperature phase changing problem for a spinning extruded micro-column. Molten polymer is squeezed out from a spinning container in the form of a symmetrical column. The extruded and spinning fluid is being solidified through the heat exchange between the polymer in the solid state and the ambient environment resulting in a two phases (solid and liquid) problem. Temperature profile has previously been determined analytically using the boundary layer and lubrication theory techniques. However, the study on the effect of the moving boundary on the fluid flow in the liquid phase and the induced stress on the condensed shell remains absent. In this paper, we analytically deduce the velocity and stress profiles for different stages during the micro-extrusion process. Several simulations have also been performed to validate the assumptions made in the current mathematical model. We find that the velocity profile alters from certain quadratic flows into linear flows when the moving boundary retreats, and the surface stress alters from shear stress into the principal stress on the outer-shell accordingly. In conjunction with the centrifugal force induced by the spinning fluid acting on the shell, these provide some crucial factors for ensuring extruded products in their highest quality.