旋转圆盘上非牛顿纳米流体Marangoni边界层数值解研究

In this project, based on the background of nonlinear differential equation, non-Newtonian fluid mechanics, nanofluid and nanotechnology, we investigate the complex transfer process behavior of non-Newtonian nanofluid by the modern mathematical similarity theory and the numerical calculation method. Under the cylindrical polar coordinate system, Marangoni boundary layer flow heat and mass transfer of non-Newtonian nanofluid over a rotating disk is considered. Two popular types of heat and mass transfer models for non-Newtonian nanofluid are presented. The strong nonlinear governing partial differential equations will be converted into a set of ordinary differential equations or feasible partial differential equations boundary value problems by using suitable similarity transformations. The simplified ordinary differential equations boundary value problem will be solved by the shooting method coupled with Runge-Kutta method and Newton scheme. The feasible partial differential equations boundary value problem will be solved by the continuous finite element method coupled with the Freefem++ program. The effects of the non-Fourier heat transfer and anomalous diffusion process on the behavior of non-Newtonian nanofluid will be analyzed and discussed in detail. The study of this project will be reveal some essences of the nonlinear behavior and provide a new idea or method for basic research and engineering practice.

本项目以非线性微分方程、非牛顿流体力学、纳米流体与纳米科技为背景，基于近代数学相似理论与数值计算方法研究非牛顿纳米流体复杂的传输过程。本项目将建立旋转圆盘上柱坐标下非牛顿纳米流体Marangoni边界层流动传热传质的数理模型。非牛顿纳米流体的传热传质本构方程考虑国际上主流的两类模型。寻找合适的相似变换方法，将强非线性偏微分控制方程组转化成常微分方程组或可行的偏微分方程组边值问题。利用打靶法结合龙格库塔法与牛顿迭代格式，或者成熟的连续有限元方法结合Freefem++程序，求解化简后的非线性微分方程组。分析并探讨非牛顿纳米流体非傅立叶导热与反常扩散过程，深刻理解输运的本质，揭示其内在规律，为相关科学研究和工程应用提供依据、思路和方法。