DECAY OF VORTEX VELOCITY AND DIFFUSION OF TEMPERATURE IN A GENERALIZED SECOND GRADE FLUID

Applied Mathematics and Mechanics (English Edition) ›› 2004, Vol. 25 ›› Issue (10): 1151-1159.

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DECAY OF VORTEX VELOCITY AND DIFFUSION OF TEMPERATURE IN A GENERALIZED SECOND GRADE FLUID

SHEN Fang^1,2, TAN Wen-chang^1,3, ZHAO Yao-hua⁴, T. Masuoka³

1. Department of Mechanics and Engineering Science, State Key Laboratory for Turbulence and Complex System Research, Peking University, Beijing 100871, P.R.China;
2. Key Laboratory for Space Weather, Center for Space Sciecne and Applied Research, Chinese Academy of Science, Beijing 100080, P.R.China;
3. Department of Mechanical Engineering Science, Kyushu University, Fukuoka, 812-8581, Japan;
4. Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing 100080, P.R.China

Received:2002-12-29 Revised:2004-03-12 Online:2004-10-18 Published:2004-10-18
Supported by:
the Society Promotion Science Foundation of Japan(P02325),the National Natural Science Foundation of China(10372007)

Abstract

Abstract: The fractional calculus approach in the constitutive relationship model of viscoelastic fluid was introduced. The velocity and temperature fields of the vortex flow of a generalized second fluid with fractional derivative model were described by fractional partial differential equations. Exact analytical solutions of these differential equations were obtained by using the discrete Laplace transform of the sequential fractional derivatives and generalized Mittag-Leffler function. The influence of fractional coefficient on the decay of vortex velocity and diffusion of temperature was also analyzed.

Key words: generalized second grade fluid, fractional calculus, unsteady flow, temperature field, generalized Mittag-Leffler function

2010 MSC Number:

O357.1

SHEN Fang;TAN Wen-chang;ZHAO Yao-hua;T. Masuoka. DECAY OF VORTEX VELOCITY AND DIFFUSION OF TEMPERATURE IN A GENERALIZED SECOND GRADE FLUID. Applied Mathematics and Mechanics (English Edition), 2004, 25(10): 1151-1159.

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References

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DECAY OF VORTEX VELOCITY AND DIFFUSION OF TEMPERATURE IN A GENERALIZED SECOND GRADE FLUID

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