discuss the fluid mechanics during the quieting time. Dissipation problems
during solidification, Residual flow in the sleeve and effects on the critical
plunger velocity. What is optimum quieting minimum heat transfer and maximum
removal of residual flow. open problem!
In this section we examine the solidification effects.
One of the assumptions in the analysis of the critical slow plunger velocity
was that the solidification process does not play important role
(see Figure ).
The typical time for heat to penetrate a typical layer in air/gas phase is
in order of minutes.
Moreover, the density of the air/gas is 3 order magnitude smaller than the
Hence, most of the resistance to heat transfer is in the gas phase.
Therefore, if we look at the heat transfer from the liquid metal surface to the air as shown in Figure (mark as process 1) the air acts as insulator to the liquid metal. to show the calculations of natural convection between hot surface and air above The solidified layer thickness can be approximated by looking at the case of a plate with temperature below melting point of the liquid metal when the liquid metal initial temperature is constant and above the freezing point (above the mushy zone and ). = 0.5
The governing equation in the sleeve is
Boundary condition between the sleeve and the air/gas is
The governing equation for the liquid metal (solid phase)
Boundary condition between the phases of the liquid metal is given by
the heat of solidification
liquid metal density at the solid phase
velocity of the liquid/solid interface
The governing equation in the liquid phase with neglecting of the natural
convection and density change is
There are three different periods in the heat transfer 1) filling the shot sleeve 2)during the quieting time, and 3)during the plunger movement. In the first period heat transfer is relatively very large (major solidification). At present we don't know much about the fluid mechanics not to say much about the solidification process/heat transfer. The second period can be simplified and analyzed as if we know more the initial velocity profile. A simplified assumption can be made considering the fact that number is very small (large thermal boundary layer compared to fluid mechanics boundary layer). Additionally, it can be assumed that the natural convection effects are marginal. Perhaps modified Goodman's method (the integral method) can be applied. In the last period, the heat transfer is composed from two zones: one) behind the jump and two) ahead of the jump. The heat transfer head of the jump is the same as in the second period while the heat transfer behind the jump is like heat transfer in to a plug flow for low number. The heat transfer in such cases have been studied in the past. The reader can refer to, for example, the book ``Heat and Mass Transfer'' by Eckert and Drake. to check what it is in the new version and put the exact ref put the typical solution, or just the ref