特殊坐标系中特殊非牛顿流边界层方程的相似解

M.禹儒索一

特殊坐标系中特殊非牛顿流边界层方程的相似解

M.禹儒索一

阿夫坚考卡特裴大学技术教育学院力学教育系,TR_03200,阿夫坚,土耳其

详细信息

中图分类号: O357.4
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出版历程
- 收稿日期: 2002-10-31
- 刊出日期: 2004-05-15

Similarity Solutions of Boundary Layer Equations for a Special Non-Newtonian Fluid in a Special Coordinate System

Muhammet Yürüsoy

Department of Mechanical Education, Faculty of Technical Education, Ahmet Necdet Sezer Camputs, Afyon Kocatepe University, TR-03200, Afyon, Turkey

摘要

摘要: 给出了在一个特殊坐标系中三阶流体的二维定常运动方程组．该坐标系中由无粘流体的势流确定，即以环绕任意物体的非粘性流动的流线为 -坐标，速度势线为ψ -坐标，构成正交曲线坐标系．结果表明，边界层方程与浸没在流体中的物体的形状无关．第一次近似假定第二梯度项与粘性项和第三梯度项相比，可以忽略不计．第二梯度项的存在，将防碍第三梯度流相似解的比例变换的导出．利用李群方法计算了边界层方程的无穷小生成元．将边界层方程组变换为常微分方程组．利用Runge-Kutta法结合打靶技术求解了该非线性微分方程组的数值解．
- 边界层方程 /
- 李群 /
- 第三梯度流体
Abstract: Two dimensional equations of steade motion for third order fluids are expressed in a special coordinate system generated by the potential flow corresponding to an inviscid fluid. For the inviscid flow around an arbitrary object, the streamlines are the phi-coordinates and velocity potential lines are psi-coordinates which form an orthogonal curvilinear set of coordinates. The out come, boundary layer equations, is then shown to be independent of the body shape immersed into the flow. As a first approximation, assumption that second grade terms are negligible compared to viscous and third grade terms. Second grade terms spoil scaling transformation which is only transformation leading to similarity solutions for third grade fluid. By using Lie group methods, infinitesimal generators of boundary layer equations are calculated. The equations are transformed into an ordinary differential system. Numerical solutions of outcoming nonlinear differential equations are found by using combination of a Runge-Kutta algorithm and shooting technique.
- boundary layer equation /
- Lie group /
- third grade fluid

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参考文献(14)

[1]	Acrivos A,Shah M J,Petersen E E.Momentum and heat transfer in laminar boundary layer flows of non-Newtonian fluids past external surface[J].A I Ch E Jl,1960,6:312—317. doi: 10.1002/aic.690060227
[2]	Pakdemirli M.Boundary layer flow of power-law past arbitrary profile[J].IMA Journal of Applied Mathematics,1993,50:133—148. doi: 10.1093/imamat/50.2.133
[3]	Beard D W,Walters K.Elastico-viscous boundary layer flows[J].Proc Camb Phil,1964,60:667—674. doi: 10.1017/S0305004100038147
[4]	Astin J,Jones R S,Lockyer P.Boundary layer in non-Newtonian fluids[J].J Mec,1973,12:527—539.
[5]	Pakdemirli M.Conventional and multiple deck boundary layer approach to second and third grade fluids[J].Internat J Engng Sci,1994,32(1):141—154. doi: 10.1016/0020-7225(94)90156-2
[6]	Yürüsoy M,Pakdemirli M.Exact solutions of boundary layer equations of a special non-Newtonian fluid over a stretching sheet[J].Mechanics Research Communications,1999,26(2):171—175. doi: 10.1016/S0093-6413(99)00009-9
[7]	Kaplun S.The role of coordinate systems in boundary layer theory[J].ZAMP,1954,5:111—135. doi: 10.1007/BF01600771
[8]	Kevorkian J,Cole J D.Perturbation Method in Applied Mathematics[M].New York:Springer,1981.
[9]	Pakdemirli M,Suhubi E S.Boundary layer theory second order fluids[J].Int J Engng Sci,1992,30(4):523—532. doi: 10.1016/0020-7225(92)90042-F
[10]	Pakdemirli M,Suhubi E S.Similarity solutions of boundary layer equations for second order fluids[J].Int J Engng Sci,1992,30(5):611—629. doi: 10.1016/0020-7225(92)90006-3
[11]	Pakdemirli M.The boundary layer equations of third-grade fluids[J].Int J Non-Linear Mech,1992,27(5):785—793. doi: 10.1016/0020-7462(92)90034-5
[12]	Fosdick R L,Rajagopal K R.Thermodynamics and stability of fluids of third grade[J].Proc R Soc,1980,339:351.
[13]	Bluman G W,Kumei S.Symmetries and Differential Equations[M].New York:Springer,1989.
[14]	Stephani H.Differential Equations:Their Solution Using Symmetries[M].England:Cambrideg Univeristy Press,1989.