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# Chapter 3: Mathematical Models for the Filling And Packing Simulation

Huamin Zhou, Zixiang Hu, and Dequn Li

State Key Laboratory of Materials Processing and Die & Mould Technology, Huazhong University of Science and Technology, Wuhan, Hubei, China

In this chapter, material properties and governing equations for fluid flow in the filling and packing phases of injection molding process will be introduced first, and then boundary conditions and some mold simplifications will be presented.

At present, the mathematical description generally bases on the continuum assumption,1–3 on which the governing equations are premised, including mass conservation equation, momentum conservation equations, energy conservation equation, and constitutive equation reflecting the material properties. According to the characteristics of the problem, the governing equations can be simplified appropriately. Considering the appropriate initial conditions and boundary conditions, the above all create the mathematical model of fluid flow.

# 3.1 Material Constitutive Relationships and Viscosity Models

The relationship between the viscous stress tensor τ and the rate of strain tensor is called a constitutive equation. It is the property of material itself and is independent of the special conditions. For different polymers, different constitutive models are used to describe their material properties. Sometimes, ...

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