Transient Mold Cooling

The initial-boundary value problem represented by Eq. 7.1 can be transmuted into a boundary integral equation by several different methods. Brebbia and Walker (1980) and Curran et al. (1980) approximated the time derivative in the equation in a finite difference form, thus changing the original parabolic partial differential equation to an elliptical partial differential equation, for which the standard boundary integral equation may be established. 

Assuming that the mold temperamre field at time r i is known to be 7 i(r), where r is the position vector, then for a sufficiently small time increment Ar, Eq. 

The type of Eq. 8.75 is elliptical and the boundary integral equation for the formulation can be derived to give 

Starting from a given initial temperature field T at t i = to, one can solve Eq. 8.76 for the unknown temperature field at the next time step and advance the solution in time. The domain integral term has to be evaluated at each time level because changes at each time step. 

In the coupled BIE/FD formulation mentioned above, the requirement for the evaluation of the domain integral is certainly a costly feature. Zheng and Phan-Thien (1992), who considered a boundary integral equation for the following problem of heat conduction with a heat source, have employed an alternative approach that transforms the domain integral to a boundary integral. 

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D, fully transient. Mold Cooling, simulation, electrical... 

In Eq. 7.2, q is the heat flux across the melt and mold interface, which is not known beforehand. The mold cooling analysis is essentially coupled with the transient heat transfer in the polymer melt during filling, packing, and cooling stages. 

The mold cooling analysis and the flow analysis are essentially coupled since the transient cavity wall temperature and heat flux are unknown in both analysis, although in practice one may only need a couple of iterative loops, depending on the required accuracy and efficiency. 

As has been mentioned in Sect. 7.3, the continuous injection-molding operation results in a cyclic heat transfer behavior in the mold, after a short transient period. The cycle-averaged temperature can be represented by a steady state heat conduction equation, i.e., Eq. 7.10. The mold cooling analysis can be greatly simplihed by solving the steady state problem. The boundary integral equation of ( 7.10) is... 

During the molding cooling process, a three-dimensional, cyclic, transient heat conduction problem with convective boundary conditions on the cooling channel and mold base surfaces is involved. The overall heat transfer phenomena is governed by a three-dimensional Poisson equation. 

Slime masses or any biofilm may substantially reduce heat transfer and increase flow resistance. The thermal conductivity of a biofilm and water are identical (Table 6.1). For a 0.004-in. (lOO-pm)-thick biofilm, the thermal conductivity is only about one-fourth as great as for calcium carbonate and only about half that of analcite. In critical cooling applications such as continuous caster molds and blast furnace tuyeres, decreased thermal conductivity may lead to large transient thermal stresses. Such stresses can produce corrosion-fatigue cracking. Increased scaling and disastrous process failures may also occur if heat transfer is materially reduced. 

Figure 9.39 Trace of normal stress for a compression-molded 73/27 HBA/HNA copolyester specimen (a) during sample loading at 320 °C, (b) during squeezing and cooling to 290 °C, (c) during temperature equilibration at 290 °C for 4 h, (d) transient and steady-state shear flows at y = 0.5 for 200 s, and (e) during relaxation after cessation of shear flow. An unrelaxed normal stress of 195 Pa was present in the specimen before being subjected to shear flow. (Reprinted from Han et al., Molecular Crystals and Liquid Crystals 254 335. Copyright 1994, with permission from Taylor Francis Group.)...

Dimensionless analysis is a powerfiil tool in analyzing the transient heat transfer and flow processes accompanying melt flow in an injection mold or cooling in blown film,to quote a couple of examples. However, because of the nature of non-Newtonian polymer melt flow the dimensionless mmibers used to describe flow and heat transfer processes of Newtonian flnids have to be modified for polymer melts. This paper describes how an easily applicable equation for the cooling of melt in a spiral flow in injection molds has been derived on the basis of modified dimensionless numbers and verified by experiments. Analyzing the air gap dynamics in extrusion coating is another application of dimensional analysis. 

In the Rapid Heat Cycle Molding (RHCM) Process, the mold temperature is rapidly changed in each cycle to improve part quality and reduce cycle time. In this paper, an integrated fiilly transient true 3D simulation approach is proposed by considering the interplay between filling/pack and cooling stages to study and further optimize the RHCM process. 

During the startup of an injection mold, some injection cycles will be needed to obtain a constant steady state situation. Once a mold is at steady state, one can assume that the heat balance of the mold will be the same during every cycle time. During every cycle time, the mold will be at transient solution heat flow , as temperature will change due to the cooling down of the plastic within the mold. 

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