Unsteady flows of a generalized second grade fluid with the fractional derivative model between two parallel plates |
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| Authors: | Tan Wenchang Xu Mingyu |
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| Institution: | (1) Department of Mechanics and Engineering Science & State Key Laboratory for Turbulence and Complex System Research, Peking University, 100871 Beijing, China;(2) Institute of Mathematics and Systematical Science, Shandong University, 250100 Jinan, China |
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| Abstract: | The fractional calculus approach in the constitutive relationship model of a generalized second grade fluid is introduced.
Exact analytical solutions are obtained for a class of unsteady flows for the generalized second grade fluid with the fractional
derivative model between two parallel plates by using the Laplace transform and Fourier transform for fractional calculus.
The unsteady flows are generated by the impulsive motion or periodic oscillation of one of the plates. In addition, the solutions
of the shear stresses at the plates are also determined.
The project supported by the National Natural Science Foundation of China (10372007, 10002003) and CNPC Innovation Fund |
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| Keywords: | fractional derivative unsteady flows generalized second grade fluid parallel plates |
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