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.

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

沈芳^1,2, 谭文长^1,3, 赵耀华⁴, T·增冈隆士³

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

收稿日期:2002-12-29 修回日期:2004-03-12 出版日期:2004-10-18 发布日期:2004-10-18
通讯作者: TAN Wen-chang(Tel:+86-10-62754244;Fax:+86-10-62751812;E-mail:tanwch@mech.pku.edu.cn) E-mail:tanwch@mech.pku.edu.cn
基金资助:
the Society Promotion Science Foundation of Japan(P02325),the National Natural Science Foundation of China(10372007)

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)

摘要/Abstract

摘要： 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.

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

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

中图分类号:

O357.1

沈芳;谭文长;赵耀华;T·增冈隆士. DECAY OF VORTEX VELOCITY AND DIFFUSION OF TEMPERATURE IN A GENERALIZED SECOND GRADE FLUID[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(10): 1151-1159.

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

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

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

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