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A mathematical model is proposed for the quantitative treatment of the injection molding of thermoplastics as it relates to the behavior of polymer in the cavity. The model is based on setting up the equations of continuity, motion, and energy for the s stem during each of the stages of the injection molding cycle klling, packing and cooling) and the coupling of these equations with practical boundary conditions. The treatment takes into consideration the non-Newtonian behavior of the melt, the effect of temperature on density and viscosity, the latent heat of solidification, and the differences in thermal properties between the solid and the melt. In employing the model, it is necessary to know the pressure-time variation at the cavity entrance. Numerical solutions have been obtained for the case of spreading radial flow in a semi-circular cavity. The numerical results yield significant data on the progression of the melt front, the flow rate, and the velocity profiles at different times and positions in the cavity. They also yield temperature and pressure profiles throughout the packing and cooling stages.

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