Flow distribution channels in extrusion dies are typically designed to assure uniform fluid velocity, pressure and temperature in the outlets. To ensure this uniformity, it is desirable to have the fluid melt to reach a steady state temperature in the entrance channel before entering the die body. This paper numerically investigates the temperature distribution of the fluid melt in the entrance channel. Analytical solutions of the velocity and finite element solutions of temperature distribution in Poiseuille flows of polypropylene melt with the Casson rheology model were derived and presented. In the velocity solution, the critical point that separates the core and the remaining parts in the flow was calculated by using the inlet flow rate and the yield stress in the Casson model. The velocity distribution was then substituted into the convective heat equation for temperature distribution simulations. A finite difference scheme was used to obtain the temperature distribution profiles along the flow direction in a parallel-plate, while the finite element model was used to model the flow temperature in circular tubes. The main outcome is the parametric analyses of the effect of various parameters such as radius, wall temperature, inlet temperature, and pressure drop to the optimal length of the channels required for the flow temperature to reach the steady state.

中文翻译：

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聚合物挤出进入通道内热流的数值模型：参数研究

挤出模头中的流量分配通道通常设计为确保出口处的流体速度，压力和温度均匀。为了确保这种均匀性，期望在进入模具主体之前使流体熔融以在进入通道中达到稳态温度。本文数值研究了入口通道内流体熔体的温度分布。利用Casson流变模型推导并给出了聚丙烯熔体Poiseuille流动中速度分布的速度解和有限元解。在速度解中，使用卡森模型中的入口流速和屈服应力，计算了将岩心与流中其余部分分开的临界点。然后将速度分布代入对流热方程，以进行温度分布模拟。有限差分方案用于获得平行板中沿流动方向的温度分布曲线，而有限元模型用于建模圆管中的流动温度。主要结果是对各种参数（例如半径，壁温，入口温度和压降）的影响进行参数分析，以达到流动温度达到稳态所需的最佳通道长度。而使用有限元模型来模拟圆管中的流动温度。主要结果是对各种参数（例如半径，壁温，入口温度和压降）的影响进行参数分析，以达到流动温度达到稳态所需的最佳通道长度。而使用有限元模型来模拟圆管中的流动温度。主要结果是对各种参数（例如半径，壁温，入口温度和压降）的影响进行参数分析，以达到流动温度达到稳态所需的最佳通道长度。