Stokes'first problem for a viscoelastic fluid with the generalized Oldroyd-B model  

作　　者：Haitao Qi Mingyu Xu 

机构地区：[1]Department of Applied Mathematics and Statistics, Shandong University at Weihai, Weihai 264209, China [2]School of Mathematics and System Science Shandong University, Jinan 250100, China

出　　处：《Acta Mechanica Sinica》2007年第5期463-469,共7页力学学报（英文版）

基　　金：The project supported by the National Natural Science Foundation of China(10272067);the Doctoral Program Foundation of the Education Ministry of China(20030422046);the Natural Science Foundation of Shandong Province,China(Y2006A 14);the Research Foundation of Shandong University at Weihai.

摘　　要：The flow near a wall suddenly set in motion for a viscoelastic fluid with the generalized Oldroyd-B model is studied. The fractional calculus approach is used in the constitutive relationship of fluid model. Exact analytical solutions of velocity and stress are obtained by using the discrete Laplace transform of the sequential fractional derivative and the Fox H-function. The obtained results indicate that some well known solutions for the Newtonian fluid, the generalized second grade fluid as well as the ordinary Oldroyd-B fluid, as limiting cases, are included in our solutions.The flow near a wall suddenly set in motion for a viscoelastic fluid with the generalized Oldroyd-B model is studied. The fractional calculus approach is used in the constitutive relationship of fluid model. Exact analytical solutions of velocity and stress are obtained by using the discrete Laplace transform of the sequential fractional derivative and the Fox H-function. The obtained results indicate that some well known solutions for the Newtonian fluid, the generalized second grade fluid as well as the ordinary Oldroyd-B fluid, as limiting cases, are included in our solutions.

关 键 词：Generalized Oldroyd-B fluid Stokes＇ first problem Fractional calculus Exact solution Fox H-function 

分 类 号：O357[理学—流体力学]