Sui Jize, Zhao Peng, Cheng Zhengdong, Zheng Liancun, Zhang Xinxin
School of Energy and Environmental Engineering, University of Science and Technology Beijing , Beijing 100083, China.
School of Chemistry, Beijing Normal University , Beijing 100875, China.
Phys Fluids (1994). 2017 Feb;29(2):023105. doi: 10.1063/1.4976642. Epub 2017 Feb 24.
The rheological and heat-conduction constitutive models of micropolar fluids (MFs), which are important non-Newtonian fluids, have been, until now, characterized by simple linear expressions, and as a consequence, the non-Newtonian performance of such fluids could not be effectively captured. Here, we establish the novel nonlinear constitutive models of a micropolar fluid and apply them to boundary layer flow and heat transfer problems. The nonlinear power law function of angular velocity is represented in the new models by employing generalized "-diffusion theory," which has successfully described the characteristics of non-Newtonian fluids, such as shear-thinning and shear-thickening fluids. These novel models may offer a new approach to the theoretical understanding of shear-thinning behavior and anomalous heat transfer caused by the collective micro-rotation effects in a MF with shear flow according to recent experiments. The nonlinear similarity equations with a power law form are derived and the approximate analytical solutions are obtained by the homotopy analysis method, which is in good agreement with the numerical solutions. The results indicate that non-Newtonian behaviors involving a MF depend substantially on the power exponent and the modified material parameter [Formula: see text] introduced by us. Furthermore, the relations of the engineering interest parameters, including local boundary layer thickness, local skin friction, and Nusselt number are found to be fitted by a quadratic polynomial to with high precision, which enables the extraction of the rapid predictions from a complex nonlinear boundary-layer transport system.
微极流体（MFs）作为重要的非牛顿流体，其流变学和热传导本构模型至今仍以简单的线性表达式为特征，因此，这类流体的非牛顿性能无法得到有效体现。在此，我们建立了微极流体的新型非线性本构模型，并将其应用于边界层流动和传热问题。新模型通过采用广义“-扩散理论”来表示角速度的非线性幂律函数，该理论已成功描述了非牛顿流体的特性，如剪切变稀和剪切增稠流体。根据最近的实验，这些新型模型可能为从理论上理解具有剪切流的微极流体中集体微旋转效应引起的剪切变稀行为和反常传热提供一种新方法。推导了幂律形式的非线性相似方程，并通过同伦分析方法得到了近似解析解，该解与数值解吻合良好。结果表明，涉及微极流体的非牛顿行为在很大程度上取决于幂指数以及我们引入的修正材料参数[公式：见正文]。此外，发现包括局部边界层厚度、局部表面摩擦和努塞尔数在内的工程关注参数之间的关系可以用二次多项式高精度地拟合到，这使得能够从复杂的非线性边界层传输系统中快速提取预测结果。
