Stokes' first problem for a viscoelastic fluid with the generalized Oldroyd-B model |
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摘 要: |
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关 键 词: | 流体力学 粘弹性流体 数学模型 分形微积分 |
收稿时间: | 23 October 2006 |
修稿时间: | 8 May 2007 |
Stokes’ first problem for a viscoelastic fluid with the generalized Oldroyd-B model |
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Authors: | Haitao Qi Mingyu Xu |
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Institution: | (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 |
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Abstract: | 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 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 (Y2006A14) and the Research
Foundation of Shandong University at Weihai.
The English text was polished by Keren Wang. |
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Keywords: | Generalized Oldroyd-B fluid Stokes’ first problem Fractional calculus Exact solution Fox H-function |
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