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Decay of vortex velocity and diffusion of temperature in a generalized second grade fluid

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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.

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Authors and Affiliations

  1. Department of Mechanics and Engineering Science, State Key Laboratory for Turbulence and Complex System Research, Peking University, 100871, Beijing, P. R. China

    Shen Fang Doctor & Tan Wen-chang

  2. Key Laboratory for Space Weather, Center for Space Sciecne and Applied Research, Chinese Academy of Science, 100080, Beijing, P. R. China

    Shen Fang Doctor

  3. Department of Mechanical Engineering Science, Kyushu University, 812-8581, Fukuoka, Japan

    Tan Wen-chang & T. Masuoka

  4. Institute of Engineering Thermophysics, Chinese Academy of Sciences, 100080, Beijing, P. R. China

    Zhao Yao-hua

Authors
  1. Shen Fang Doctor
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  2. Tan Wen-chang
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  3. Zhao Yao-hua
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  4. T. Masuoka
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Corresponding author

Correspondence to Tan Wen-chang.

Additional information

Communicated by Wu Wang-yi, Original Member of Editorial Committee, AMM

Foundation items: the Society Promotion Science Foundation of Japan (P02325); the National Natural Science Foundation of China (10372007)

Biographies: Shen Fang (1977∼)

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Fang, S., Wen-chang, T., Yao-hua, Z. et al. Decay of vortex velocity and diffusion of temperature in a generalized second grade fluid. Appl Math Mech 25, 1151–1159 (2004). https://doi.org/10.1007/BF02439867

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  • DOI: https://doi.org/10.1007/BF02439867

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2000 Mathematics subject classification

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