Oldroyd-B流体在拉伸板上的Boussinesq近似流动

Boussinesq Approximation Flow of Oldroyd-B Fluid on a Stretched Plate

摘要: 文章对变本构参数Oldroyd-B流体在非线性拉伸平板上的流动与传热进行了数值模拟。通过引入粘度系数随温度指数的变化，建立了改进的Oldroyd-B流体本构方程。在此基础上，建立了连续性方程、动量方程和能量方程。采用有限差分法对无量纲控制方程进行离散，验证了数值方法的收敛性和准确性。分析了不同雷诺数、普朗特数等关键参数对速度场、温度场和剪应力分布的影响。结果表明，随温度变化的变粘度模型能有效地降低流体中的粘性剪切应力损失。该研究为理解变物性非牛顿流体在拉伸平板条件下的流动与传热机理提供了理论依据，也为相关工业过程的优化设计提供了数值支持。

Abstract: In this paper, the flow and heat transfer of Oldroyd-B fluid with variable constitutive parameters on a nonlinear tensile plate are numerically simulated. The modified Oldroyd-B fluid constitutive equation was established by introducing the change of viscosity coefficient with temperature index. On this basis, the continuity equation, momentum equation, and energy equation are established. The finite difference method is used to discretize the dimensionless control equation, and the convergence and accuracy of the numerical method are verified. The effects of different Reynolds numbers, Prandtl numbers, and other key parameters on the velocity field, temperature field, and shear stress distribution are analyzed. The results show that the temperature-dependent variable viscosity model can effectively reduce the viscous shear stress loss in the fluid. This study provides a theoretical basis for understanding the flow and heat transfer mechanism of non-Newtonian fluid with variable physical properties under the condition of a stretched plate, and also provides numerical support for the optimization design of related industrial processes.