Theoretical Model of Contiguous Solids Melting

The melt flows from the melt film towards the active flight flank. Only a small fraction of the material can flow through the clearance. As a result, the majority of the melt will flow into the melt pool. A circulating flow will be set up in the melt pool as a result of the barrel velocity. Since most of the viscous heat generation occurs in the upper melt film, it is generally assumed that all melting takes place at the upper solid bed-melt film interface. As melting proceeds, the cross-sectional area of the solid bed will reduce and the cross-sectional area of the melt pool will tend to increase. The melt pool, therefore, will exert considerable pressure on the solid bed. This reduces the width of the solid bed, while the melt film between the solid bed 

The heat supplied by the barrel heaters has to be conducted through the entire thickness of the barrel and through the entire thickness of the melt film before it can reach the solid bed. Problems with this energy transport are considerable heat losses by conduction, convection, and radiation. Another, probably more severe, problem is the low thermal conductivity of the polymer. The heat has to be transferred across the entire melt film thickness. Therefore, the conductive heat flux will be small, particularly when the melt film thickness is large. Increasing the barrel temperature can accelerate the heating process however, this temperature is limited by the possibility of degradation of the polymer. 

In order to be able to predict the melting rate, the amount of heat flowing towards the solid-melt interface has to be known. This can be determined if the temperature profiles in the melt film and in the solid bed are known. The temperature profile in the melt film can be determined from the velocity profile in the melt fdm. In order to derive an expression for the temperature profile in the melt film, the following assumptions are made  

The polymer melt density and thermal conductivity are constant. 

Conductive heat transfer occurs only in a direction normal to interface. 

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