Variational method for solving non-linear problems of unsteady-state heat conduction

J of Applied Polymer Sci

Miao

Min

et al. 2012

It was widely established that many end-use properties of the final parts are considerably affected by the macromolecular hierarchical structures formed during the cooling stage of injection molding, especially for crystalline polymers which undergo both solidification and crystallization processes simultaneously. Enthalpy transformation method (ETM) has been demonstrated to give the reasonable descriptions of the temperature profiles for real processing operations (e.g., injection molding, gas-assisted injection molding, and compression molding, etc.) in our previous work. However, to observe the phase-change plateau, where rapid cooling rate is imposed, is not easy in traditional treatments using the enthalpy approach. In this work, ''modified cooling curves'' (i.e., temperature versus time, plotted in logarithmic scale) at various locations in the mold cavity were found to show similar trend with an obvious turning point indicating the occurrence of phase transition. Mold temperature is more effective in controlling the cooling rate than melt temperature. Turing point of the cooling curves in the plot of ln y vs. ln t can be used to estimate the minimum cooling time of the injection molding of crystalline polymers.

Section: Introductionmentioning

confidence: 99%

Solidification behavior of high‐density polyethylene during injection molding process: Enthalpy transformation method

J of Applied Polymer Sci

Miao

Min

et al. 2012

“…However, due to the very nature of the nonlinearity which is caused by the fact that the interface between the liquid and the solid is always moving with the absorption or liberation of the latent heat at the interface, only limited exact closed-form solutions are available for some simplified or idealized systems within one-dimensional infinite or semi-infinite domains [2]. With the fundamental assumption that the solidification occurs at a discrete temperature, which gains wide applications in the solidification of pure small molecule substances, various methods were developed to settle these problems, such as the variational method [3,4], the moving heat source method [5,6], the perturbation method [7,8] as well as the numerical methods [9][10][11]. The numerical methods have been widely used in the solution of multidimensional phasechange heat transfer issues.…”

Section: Introductionmentioning

confidence: 99%

Numerical prediction of phase‐change heat conduction of injection‐molded high density polyethylene thick‐walled parts via the enthalpy transforming model with mushy zone

Polymer Engineering & Sci

et al. 2008

Transient heat transfer problems with phase-changes, also known as the ''Stefan problems'' or ''movingboundary problems,'' are practically significant in many engineering and technological fields. Injection molding, one of the most widely used plastics processing techniques, mainly consists of filling, packing, and cooling, and the cooling stage is crucial since it considerably affects the productivity and quality of the molded parts. Thus, solutions for transient phase-change heat conduction problems during injection molding will be instructive. In this article, the enthalpy transforming scheme proposed by Cao and Faghri, which could handle the Stefan problems for generalized multidimensional phase-change structures, is applied coupled with the control-volume/finite-difference techniques. Considering the polydispersity and hierarchical structures, the polymer extended phase change temperature range or mushy zone was included in the two-dimensional enthalpy formulation to forecast the transient phase-change heat conduction during the cooling stage for injection-molded high density polyethylene (HDPE) parts. Experiments were performed and good agreement has been achieved, which reveals that the enthalpy transforming model gives good prediction, especially for the cooling analysis for the injection molding of thick-walled parts of crystalline polymers. The understanding of the phase-change heat conduction characteristics may facilitate the optimal designs of polymer injection molding process for industrial applications.

“…The transient thermal conduction problems were originally proposed by Stefan in 1981, 1 which was also referred to as ‘ Stefan problems ’ or ‘ moving boundary problems ‘. For a long time, many methods had been put forward to numerically solving the multi-dimensional phase-change heat conduction problems, for instance, the variational method, 2, 3 the moving heat source method, 4 the finite element method, 5 the enthalpy method, 6 variable space-grid method, 7, 8 node integral method 9 etc. As a matter of fact, this kind of problem still widely exists in the fields of engineering and modern industries.…”

Section: Introductionmentioning

confidence: 99%

Investigation on solidification behaviour of high-density polyethylene during thin-walled injection moulding: correlation between crystallisation kinetics and thermal gradient field

Plastics, Rubber and Composites

Shi

et al. 2016

The influence of temperature fields on the crystallisation kinetics of high-density polyethylene during injection moulding was disclosed in this work. The dimensionless X = 0.4 along the part thickness was a critical location, within which the heat transfer of polymer was primarily affected by thermal conduction. When X > 0.4, the decay in temperature tended to become stable with limited variation in t 1/2 −1 value (an indicator of average crystallisation rate). The experimental results indicated that the crystallisation rate was proportional to the cooling speed, regardless of the cooling conditions utilised. The sequence of relative crystallinity was in consistence with that of secondary temperature difference. The present study will be of practical significance to further investigation on the 'processing-structure-property' relationship for polymeric materials.