In this short communication, exact solutions are obtained for a range of non-Newtonian flows between stationary parallel plates. The pressure-driven flow of fluids with a variational viscosity that adheres to the Carreau governing relationship are considered. Solutions are obtained for both shear-thinning (viscosity decreasing with increasing shear-rate) and shear-thickening (viscosity increasing with increasing shear-rate) flows. A discussion is presented regarding the requirements for such analytical solutions to exist. The dependence of the flow rate on the channel half width and the governing non-Newtonian parameters is also considered.

中文翻译：

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非牛顿通道流—精确的解决方案

在这种简短的交流中，对于固定平行板之间的一系列非牛顿流，可以获得精确的解决方案。考虑了粘度变化的流体的压力驱动流体，该流体遵循Carreau调节关系。获得了剪切稀化（粘度随剪切速率增加而降低）和剪切稠化（粘度随剪切速率增加而增加）的解决方案。提出了有关此类分析解决方案的要求的讨论。还考虑了流速对通道半宽度和控制非牛顿参数的依赖性。