不同流条件下随温度变化的流体黏性和热泳微粒沉积对自由传热传质作用的Lie群分析

Lie Group Analysis for the Effect of Temperature-Dependent Fluid Viscosity and Thermophoresis Particle Deposition on Free Convective Heat and Mass Transfer in the Presence of Variable Stream Conditions

研究二维稳定不可压缩流体在竖向延伸平面上的流动.流体黏性假设为与温度相关的线性函数.对控制方程进行伸缩群变换,由于变换参数之间的关系让方程解保持不变.在找到3个绝对不变量后,推导对应动量方程的一个三阶一般微分方程和两个对应能量方程和扩散方程的二阶一般微分方程.求出具有边界条件方程的数值解,发现随着平面延伸距离增加,随温度变化的流体黏性降低让流速变慢.在平面的某个特定点处,随着黏性减少流速变慢但温度增加.热泳微粒沉积在浓度边界层起着关键作用.最后对计算结果进行讨论并给出图例.

A steady two-dimensional flow of incompressible fluid over a vertical stretching sheet was studied. The fluid viscosity was assumed to vary as a linear function of temperature. A scaling group of transformations was applied to the governing equations. The system re- mained invariant due to some relations among the parameters of the transformations. After finding three absolute invariants, a third-order ordinary differential equation corresponding to the momentum equation and two second-order ordinary differential equations corresponding to energy and diffusion equations were derived. The equations along with the boundary conditions were solved numerically. It is found that the decrease in the temperature-dependent fluid vis- cosity makes the velocity decrease with the increasing distance of the stretching sheet. At a par- ticular point of the sheet, the fluid velocity decreases with the decreasing viscosity while the temperature increases in this case. The impact of thermophoresis particle deposition plays an important role on the concentration boundary layer. The results thus obtained are presented graphically and discussed.