Application of differential constraint method to exact solution of second-grade fluid

doi:10.1007/S10483-009-0401-x

Applied Mathematics and Mechanics (English Edition) ›› 2009, Vol. 30 ›› Issue (4): 403-412.doi: https://doi.org/10.1007/S10483-009-0401-x

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Application of differential constraint method to exact solution of second-grade fluid

张道祥^1,2冯素晓¹卢志明¹刘宇陆¹

1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University
2. College of Mathematics and Computer Science,Anhui Normal University,

收稿日期:2008-02-19 修回日期:2009-02-13 出版日期:2009-04-16 发布日期:2009-04-01

Application of differential constraint method to exact solution of second-grade fluid

Dao-xiang ZHANG ^1,2 Su-xiao FENG ¹ Zhi-ming¹ LUYu-lu LIU¹

1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University
2. College of Mathematics and Computer Science,Anhui Normal University,

Received:2008-02-19 Revised:2009-02-13 Online:2009-04-16 Published:2009-04-01

摘要/Abstract

摘要： A differential constraint method is used to obtain analytical solutions of a second-grade fluid flow. By using the first-order differential constraint condition, exact solutions of Poiseuille flows, jet flows and Couette flows subjected to suction or blowing forces, and planar elongational flows are derived. In addition, two new classes of exact solutions for a second-grade fluid flow are found. The obtained exact solutions show that the non-Newtonian second-grade flow behavior depends not only on the material viscosity but also on the material elasticity. Finally, some boundary value problems are discussed.

关键词: non-Newtonian fluid;differential constraint method; second-grade fluid

Abstract: A differential constraint method is used to obtain analytical solutions of a second-grade fluid flow. By using the first-order differential constraint condition, exact solutions of Poiseuille flows, jet flows and Couette flows subjected to suction or blowing forces, and planar elongational flows are derived. In addition, two new classes of exact solutions for a second-grade fluid flow are found. The obtained exact solutions show that the non-Newtonian second-grade flow behavior depends not only on the material viscosity but also on the material elasticity. Finally, some boundary value problems are discussed.

Key words: non-Newtonian fluid;differential constraint method; second-grade fluid

中图分类号:

O357
O302

张道祥冯素晓卢志明刘宇陆. Application of differential constraint method to exact solution of second-grade fluid[J]. Applied Mathematics and Mechanics (English Edition), 2009, 30(4): 403-412.

Dao-Xiang ZHANG;Su-Xiao FENG;Zhi-Ming LU;Yu-Liu LIU. Application of differential constraint method to exact solution of second-grade fluid[J]. Applied Mathematics and Mechanics (English Edition), 2009, 30(4): 403-412.

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Application of differential constraint method to exact solution of second-grade fluid

Application of differential constraint method to exact solution of second-grade fluid

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