微分约束方法在求解二阶流体精确解上的应用

张道祥; 冯素晓; 卢志明; 刘宇陆

微分约束方法在求解二阶流体精确解上的应用

1.
上海大学上海市应用数学和力学研究所,上海 200072;2.安徽师范大学数学与计算机科学学院,安徽芜湖 241000

基金项目: 国家自然科学基金资助项目(10772110)

详细信息

作者简介:
张道祥(1979- ),男,安徽天长人,博士(E-mail:zdxiangp@yahoo.cn);卢志明,教授,博士(联系人.Tel:+86-21-56337398;E-mail:zmlu@shu.edu.cn).

中图分类号: O357；O302
计量
- 文章访问数: 3141
- HTML全文浏览量: 231
- PDF下载量: 671
- 被引次数: 0
出版历程
- 收稿日期: 2008-02-19
- 修回日期: 2009-02-13
- 刊出日期: 2009-04-15

Application of Differential Constraints Method on Solving Exact Solutions of a Second-Grade Fluid

1.
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China;

摘要

摘要: 利用微分约束方法研究了二阶流体的精确解．通过使用一阶微分约束条件,不仅获得了具有抽吸作用下的Couette和Poiseuille平行流、碰撞射流、平面拉伸流等具有明确物理意义的流动解,而且获得了两类新的精确解．所得精确解表明二阶流体的流动特性不仅依赖于物质粘性参数,而且依赖物质弹性参数A·D2此外讨论了部分边值问题．
- 非Newton流体 /
- 微分约束方法 /
- 二阶流体
Abstract: Differential constraints method is used to investigate analytical solutions for a second-grade fluid flow.By the first-order differential constraint condition,some exact solutions of Poiseuille flows,jet flows and Couette flows subjected to suction or blowing forces,planar elongational flows were derived.In addition,two new classes of exact solutions for a second-grade fluid flow were found.Exact solutions obtained show that the non-Newtonian second-grade flow behavior depends on not only the material viscosity but also the material elasticity.Finally some boundary value problems were discussed.
- non-Newtonian fluid /
- differential constraints method /
- second-grade fluid

HTML全文

参考文献(29)

[1]	Яненко Н Н.Избранные Труды[M].Москва:Наука,1991.
[2]	Сидоров А Ф,Шапеев В П,Яненко Н Н.Метод Дифференциальных Связей и Его Приложения в Газовой Динамике[M].Новосибирск: Наука,1984.
[3]	Andreev V K,Kaptsov O V,Pukhnachev V V,et al.Applications of Group-Theoretic Methods in Hydrodynamics[M]. Dordrecht: Kluwer,1998.
[4]	Olver P,Rosenau P. The construction of special solutions to partial differential equations[J].SIAM J Appl Math,1987,47(2):263-278. doi: 10.1137/0147018
[5]	Olver P. Direct reduction and differential constraints[J].Proceedings of the Society of London,Series A,1994,444(1922):509-523. doi: 10.1098/rspa.1994.0035
[6]	Levi D,Winternitz P. Nonclassical symmetry reduction:example of the Boussinesq equation[J]. J Phys A:Math Gen, 1989,22(15):2915-2924. doi: 10.1088/0305-4470/22/15/010
[7]	Polyanin A D,Zaitsev V F. Handbook of Nonlinear Partial Differential Equations[M]. Florida:A CRC Press Company,2004.
[8]	Nemenyi P F. Recent developments in inverse and semi-inverse methods in the mechanics of continua[J]. Advances in Applied Mechanics,1951,2(11):123-151. doi: 10.1016/S0065-2156(08)70300-4
[9]	Hayat T,Mohyuddin M R,Asghar S. Some inverse solutions for unsteanian fluid[J]. Tamsui Oxford Journal of Mathematical Sciences, 2005,21(1):1-20.
[10]	Asghar S,Mohyuddin M R,Hayat T,et al. On inverse solutions of unsteady Riabouchinsky flows of second grade fluid[J]. Tamsui Oxford Journal of Mathematical Sciences, 2006,22(2):221-229.
[11]	Labropulu F. A few more exact solutions of a second grade fluid via inverse method[J]. Mech Res Communications,2000,27(6):713-720. doi: 10.1016/S0093-6413(00)00145-2
[12]	Mohyuddin M R,Ahmad A. Corrigendum to:inverse solutions for a second-grade fluid for porous medium channel and Hall current effects by Muhammad R Mohyuddin and Ehsan Ellahi Ashraf[J]. Proc Indian Acad Sci (Math Sci),2007,117(2):283-285. doi: 10.1007/s12044-007-0022-0
[13]	Siddiqui A M,Mohyuddin M R,Hayat T,et al. Some more inverse solutions for steady flows of a second-grade fluid[J]. Arch Mech,2003,55(4):373-387.
[14]	Siddiqui A M,Islam S,Ghori Q K. Two dimensional viscous incompressible flows in a porous medium[J]. Journal of Porous Media,2006,9(6):591-596. doi: 10.1615/JPorMedia.v9.i6.70
[15]	谢松柏. 非牛顿流体的某些反解[J]. 北京师范大学学报（自然科学版）,2001,37(1):19-21.
[16]	刘慈群,黄军旗. 非牛顿流体管内不定常流的解析解[J]. 应用数学和力学,1989, 10(11):939-946.
[17]	朱文辉,刘慈群. 二阶非Newton流体环管流动解析解[J]. 应用数学和力学,1993,14(3):195-201.
[18]	黄军旗,刘慈群. 环空管内粘弹性流体不定常旋转流的解及流动特性分析[J]. 应用数学和力学,1997,18(6):499-506.
[19]	M·禹儒索一. 第二梯度流体的蠕变流和热传导相似解[J]. 应用数学和力学,2004,25(4):425-432.
[20]	沈芳,谭文长,赵耀华,等. 广义二阶流体涡流速度的衰减和温度扩散[J]. 应用数学和力学,2004,25(10):1053-1060.
[21]	Tan W C,Xian F,Wei L. An exact solution of unsteady Couette flow of generalized second grade fluid[J]. Chinese Science Bulletin,2002,47(21):1783-1785. doi: 10.1360/02tb9389
[22]	Xu M Y,Tan W C. Theoretical analysis of the velocity field,stress field and vortex sheet of generalized second order fluid with fractional anomalous diffusion[J]. Science in China ,Ser A,2001,44(11):1387-1399. doi: 10.1007/BF02877067
[23]	Coleman B D,Noll W. An approximation theorem for functionals with applications in continuum mechanics[J]. Arch Rat Mech Anal, 1960,6: 355-370. doi: 10.1007/BF00276168
[24]	Kaloni P N,Siddqui A M. The flow of a second grade fluid[J].Int J Engng Sci,1983,21(10):1157-1169. doi: 10.1016/0020-7225(83)90080-0
[25]	Rivlin R S,Ericksen J L. Stress deformation relations for isotropic materials[J]. J Rat Mech Anal, 1955,4(4):323-425.
[26]	王竹溪,郭敦仁.特殊函数概论[M].北京:北京大学出版社,2000.
[27]	Thomas A H,Todd B D. On the Arnold cat map and periodic boundary conditions for planar elongational flow[J].Molecular Physics,2003,101(23):3445-3454. doi: 10.1080/00268970310001648726
[28]	d’Avino G,Maffettone P L,Hulsen M A,et al. Numerical simulation of planar elongational flow of concentrated rigid particle suspensions in a viscoelastic fluid[J]. J Non-Newtonian Fluid Mech,2008,150(2/3):65-79. doi: 10.1016/j.jnnfm.2007.10.001
[29]	陈文芳. 非Newton流体力学[M]. 北京:科学出版社,1984.

施引文献

资源附件(0)

访问统计

计量

文章访问数: 3141
HTML全文浏览量: 231
PDF下载量: 671
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

留言板

微分约束方法在求解二阶流体精确解上的应用

作者简介:
张道祥(1979- ),男,安徽天长人,博士(E-mail:zdxiangp@yahoo.cn);卢志明,教授,博士(联系人.Tel:+86-21-56337398;E-mail:zmlu@shu.edu.cn).

计量

Application of Differential Constraints Method on Solving Exact Solutions of a Second-Grade Fluid

计量

目录

留言板

微分约束方法在求解二阶流体精确解上的应用

作者简介: 张道祥(1979- ),男,安徽天长人,博士(E-mail:zdxiangp@yahoo.cn);卢志明,教授,博士(联系人.Tel:+86-21-56337398;E-mail:zmlu@shu.edu.cn).

计量

出版历程

Application of Differential Constraints Method on Solving Exact Solutions of a Second-Grade Fluid

计量

出版历程

目录

作者简介:
张道祥(1979- ),男,安徽天长人,博士(E-mail:zdxiangp@yahoo.cn);卢志明,教授,博士(联系人.Tel:+86-21-56337398;E-mail:zmlu@shu.edu.cn).