A Uniformly Valid Series Solution to Sakiadis Flow
-
摘要: 通过引入一个变换式,克服了Sakiadis流动中半无限大流动区域以及无穷远处渐近边界条件所带来的数学处理上的困难.基于泛函分析中的不动点理论,采用不动点方法求解了变换后的非线性微分方程,获得了Sakiadis流动的近似解析解.该近似解析解用级数的形式来表达并在整个半无限大流动区域内一致有效.
-
关键词:
- Sakiadis流动 /
- 不动点方法 /
- 边界层 /
- 一致有效
Abstract: In order to overcome the major mathematical difficulties in Sakiadis flow due to the semi-infinite flow domain and the asymptotic far field boundary condition, transformations were introduced for both the related independent variables and functions simultaneously, to convert the semi-infinite domain to a finite one and the asymptotic boundary condition to a convenient form. Then, based on the fixed point theory in functional analysis, the deduced nonlinear differential equation was solved, and an approximate semi-analytical series solution to Sakiadis flow was obtained. The calculation results show that the solution is uniformly valid in the semi-infinite domain, and the fixed point method makes an effective way to achieve approximate analytical solutions to differential equations.-
Key words:
- Sakiadis flow /
- fixed point method /
- boundary layer /
- uniformly valid
-
[1] Sakiadis B C. Boundary-layer behavior on continuous solid surfaces—II: the boundary layer on a continuous flat surface[J]. AIChE Journal,1961,7(2): 221-225. [2] Schlichting H, Gersten K. Boundary-Layer Theory [M]. Springer Verlag, 2000. [3] Tsou F K, Sparrow E M, Goldstein R J. Flow and heat transfer in the boundary layer on a continuous moving surface[J]. International Journal of Heat and Mass Transfer, 1967,10(2): 219-235. [4] Takhar H S, Nitu S, Pop I. Boundary layer flow due to a moving plate: variable fluid properties[J]. Acta Mechanica,1991,90(1/4): 37-42. [5] Pop I, Gorla R S R, Rashidi M. The effect of variable viscosity on flow and heat transfer to a continuous moving flat plate[J]. International Journal of Engineering Science,1992,30(1): 1-6. [6] Pantokratoras A. Further results on the variable viscosity on flow and heat transfer to a continuous moving flat plate[J]. International Journal of Engineering Science,2004,42(17/18): 1891-1896. [7] Andersson H I, Aarseth J B. Sakiadis flow with variable fluid properties revisited[J]. International Journal of Engineering Science,2007,45(2/8): 554-561. [8] Cortell R. A numerical tackling on Sakiadis flow with thermal radiation[J]. Chinese Phys Lett,2008,25(4): 1340-1342. [9] Pantokratoras A. The Blasius and Sakiadis flow with variable fluid properties[J]. Heat Mass Transfer,2008,44(10): 1187-1198. [10] Pantokratoras A. Asymptotic suction profiles for the Blasius and Sakiadis flow with constant and variable fluid properties[J]. Arch Appl Mech,2009,79(5): 469-478. [11] Ahmad S, Rohni A, Pop I. Blasius and Sakiadis problems in nanofluids[J]. Acta Mechanica,2011,218(3/4): 195-204. [12] Bataller R C. Radiation effects for the Blasius and Sakiadis flows with a convective surface boundary condition[J]. Appl Math Comput,2008,206(2): 832-840. [13] 梅金德 O D. 纳米流体在粘性耗散和Newton传热组合影响下的Sakiadis流动分析[J]. 应用数学和力学, 2012,33(12): 1442-1450.(Makinde O D. Analysis of Sakiadis flow of nanofluids with viscous dissipation and Newtonian heating[J]. Applied Mathematics and Mechchanics,2012,33(12): 1442-1450.(in Chinese)) [14] Salama A A, Mansour A A. Fourth-order finite-difference method for third-order boundary-value problems[J]. Numerical Heat Transfer, Part B: Fundamentals: An International Journal of Computation and Methodology,2005,47(4): 383-401. [15] Salama A A. Higher-order method for solving free boundary-value problems[J]. Numerical Heat Transfer, Part B: Fundamentals: An International Journal of Computation and Methodology, 2004,45(4): 385-394. [16] Xu D, Guo X. Fixed point analytical method for nonlinear differential equations[J]. Journal of Computational and Nonlinear Dynamics,2013,8(1): 011005. [17] Zeidler E. Nonlinear Functional Analysis and Its Applications I(Fixed-Point Theorems)[M]. New York: Springer-Verlag, 1986.
点击查看大图
计量
- 文章访问数: 884
- HTML全文浏览量: 105
- PDF下载量: 919
- 被引次数: 0