The Quasi-Newtonian Approach has been developed for the closed-form analytical solution of isothermic, inelastic, and steady-state fully developed axial power law fluid flow in a concentric annuli. This approach is developed to eliminate the need to solve the two flow regions separately in the rheological flow problems. Using the approximate definition shear deformation distribution of power law rheological model, an analytical expression, which permits direct evaluation of the velocity distribution profiles, volumetric flow rate, and pressure drop in concentric annuli is derived. It is shown that all developed equations are applicable for both Newtonian and non-Newtonian flows in concentric annuli, and these can be applied for a wider range of rheological parameters of the power law rheological model. Final analytical equations can easily be used in all theoretical and practical applications of the power law flow problems in annuli that are encountered in several interdisciplinary fields without using tables, graphs, and tedious numerical calculations. Theoretically obtained, fully developed velocity profiles are compared with the experimental results taken from the relevant literature.

中文翻译：

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准牛顿法确定同心环中完全发展的轴向幂律流体流动的速度剖面

拟牛顿法已开发用于同心环中等温、非弹性和稳态完全发展的轴向幂律流体流动的封闭形式解析解。开发这种方法是为了消除在流变流动问题中分别求解两个流动区域的需要。使用幂律流变模型的近似定义剪切变形分布，可以导出允许直接评估同心环中的速度分布剖面、体积流量和压降的解析表达式。结果表明，所有发展的方程都适用于同心环中的牛顿和非牛顿流动，并且这些方程可以适用于幂律流变模型的更广泛的流变参数。最终解析方程可以很容易地用于在多个跨学科领域中遇到的环中幂律流问题的所有理论和实际应用，而无需使用表格、图形和繁琐的数值计算。将理论上获得的、完全发展的速度剖面与从相关文献中获取的实验结果进行比较。