用群方法求解幂律非牛顿导电流体的Rayleigh问题

M. B. 阿伯德-尔-马力克; N. A. 伯占; H. S. 豪赛恩

用群方法求解幂律非牛顿导电流体的Rayleigh问题

1.
亚历山大大学工程数学和物理系, 亚历山大, 21544, 埃及;
2.
阿拉伯科技和海运学院基础和应用科学系, 亚历山大, 埃及

详细信息

中图分类号: O361.4;O152.9
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出版历程
- 收稿日期: 2001-07-30
- 刊出日期: 2002-06-15

Solution of the Rayleigh Problem for a Power-Law Non-Newtonian Conducting Fluid via Group Method

1.
Department of Engineering Mathematics and Physics, Faculty of Engineering, Alexandria University, Alexandria 21544, Egypt;
2.
Department of Basic and Applied Science, Arab Academy for Science and Technology and Maritime Transport, P O Box 1029 Alexandria, Egypt

摘要

摘要: 研究了如下磁流体Rayleigh问题:一块半无限大平板受瞬态冲击后以恒定速度在无限大非牛顿幂律流体的区域内运动。讨论了在横向外在磁场作用下非牛顿导电流体在无限大区域内的非定常流动。用变换群理论得到了这个强非线性问题的解。通过单参数群变换减少了一个自变量,并使带边界条件的偏微分方程转化为带合适边界条件的常微分方程。同时研究了某些参数对流体速度的影响。
- Rayleigh问题 /
- 群方法 /
- 非线性 /
- 导电流体 /
- 非牛顿幂律流体
Abstract: An investigation is made of the magnetic Rayleigh problem where a semi-infinite plate is given an impulsive motion and thereafter moves with constant velocity in a non-Newtonian power law fluid of infinite extent.The solution of this highly non-linear problem is obtained by means of the transformation group theoretic approach.The one-parameter group transformation reduces the number of independent variables by one and the governing partial differential equation with the boundary conditions reduce to an ordinary differential equation with the appropriate boundary conditions.Effect of the some parameters on the velocity u(y,t) has been studied and the results are plotted.
- Rayleigh problem /
- group method /
- non-linearity /
- conducting fluid /
- non-Newtonian power law fluid

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参考文献(13)

[1]	Gerhart P M. Fundamentals of Fluid Mechanics[M]. Wesly Publishing Comp Inc,1993,11-20.
[2]	Vujanovic B, Stauss A M, Djukic Dj. A variational solution of the Rayleigh problem for a power law non-Newtonian conducting fluid[J]. Ingenieur-Archiv,1972,41:381-386.
[3]	Sapunkov Ya G. Rayleigh problem of non-Newtonian electroconductive fluids[J]. J Appl Math Tech Physics,1970,2:50-55.
[4]	Vujanovic B. An approach to linear and nonlinear heat transfer problem using a Lagrangian[J]. J AIAA,1971,9:327-330.
[5]	Birkhoff G. Mathematics for engineers[J]. Elect Eng,1948,67:1185-1192.
[6]	Morgan A J A. The reduction by one of the number of independent variables in some systems of nonlinear partial differential equations[J]. Quart J Math Oxford,1952,3(2):250-259.
[7]	Abd-el-Malek M B, Badran N A. Group method analysis of unsteady free-convective laminar boundary～layer flow on a nonisothermal vertical circular cylinder[J]. Acta Mechanica,1990,85:193-206.
[8]	Abd-el-Malek M B, Boutros Y Z, Badran N A. Group method analysis of unsteady free-convective boundary-layer flow on a nonisothermal vertical flat plate[J]. J Engineering Mathematics,1990,24:343-368.
[9]	Boutros Y Z, Abd-el-Malek M B, El-Awadi A, et al. Group method for temperature analysis of thermal stagnant lakes[J]. Acta Mechanica,1999,114:131-144.
[10]	Fayez H M, Abd-el-Malek M B. Symmetry reduction to higher order nonlinear diffusion equation[J]. Int J Appl Math,1999,1:537-548.
[11]	Ames W F. Similarity for the nonlinear diffusion equation[J]. I & EC Fundamentals,1965,4:72-76.
[12]	Moran M J, Gaggioli R A. Reduction of the number of variables in system of partial differential equations with auxiliary conditions[J]. SIAM J Applied Mathematics,1968,16:202-215.
[13]	Burden R, Faires D. Numerical Analysis[M]. Prindle: Weberand Scmidt,1985.