广义二阶流体涡流速度的衰减和温度扩散

沈芳; 谭文长; 赵耀华; T·增冈隆士

广义二阶流体涡流速度的衰减和温度扩散

1.
北京大学力学与工程科学系,湍流与复杂系统研究国家重点实验室,北京 100871;2.中国科学院空间科学与应用研究中心空间天气学重点实验室,北京 100080;
九州大学机械工程科学系,福冈,812_8581 日本;4.中国科学院工程热物理研究所,北京 100080

基金项目: 日本学术振兴会基金资助项目(P02325);国家自然科学基金资助项目(10372007)

详细信息

作者简介:
沈芳(1977- ),女,河北张家口人,博士(E-mail:fshen@spaceweather.ac.cn);谭文长(联系人.Tel:+86-10-62754244;Fax:+86-10-62751812;E-mail:tanwch@mech.pku.edu.cn).

中图分类号: O357.1
计量
- 文章访问数: 2733
- HTML全文浏览量: 101
- PDF下载量: 578
- 被引次数: 0
出版历程
- 收稿日期: 2002-12-29
- 修回日期: 2004-03-12
- 刊出日期: 2004-10-15

Decay of Vortex Velocity and Diffusion of Temperature in a Generalized Second Grade Fluid

1.
Depar tment of Mechanics and Engineering Science, State Key Labora tory for bulence and Complex System Research, Peking University, Beijing 100871, P. R. China, Chinese Academy of Science, Beijing 100080, P. R. China;
Department of Mechanical Engineering Science, Kyushu University, Fukuoka, 812-8581, Japan;

摘要

摘要: 将分数阶微积分运算引入到二阶流体的本构关系中，建立了带分数阶导数的广义二阶流体模型．研究了广义二阶流体涡流速度的衰减和温度扩散，利用分数阶导数的Laplace变换和广义Mittag-Leffler函数，得到了涡流速度场和温度场的精确解，分析了分数阶指数对涡流速度的衰减和温度扩散的影响．
- 广义二阶流体 /
- 分数阶微积分 /
- 涡流 /
- 温度场 /
- 广义Mittag-Leffler函数
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.
- generalized second grade fluid /
- fractional calculus /
- unsteady flow /
- temperature field /
- generalized Mittag-Leffler function

HTML全文

参考文献(17)

[1]	余钊圣，林建忠．粘弹性二阶流体混合层流场拟序结构的数值研究[J]. 应用数学和力学,1998,19(8):671—677.
[2]	Fetecau C,Fetacau Corina,Zierep J.Decay of a potential vortex and propagation of a heat wave in a second grade fluid[J].International Journal of Non-Linear Mechanics,2002,37(6):1051—1056. doi: 10.1016/S0020-7462(01)00028-2
[3]	Bagley R L. A theoretical basis for the application of fractional calculus to viscoelasticity[J].Journal of Rheology,1983,27(3):201—210. doi: 10.1122/1.549724
[4]	Friedrich C H R.Relaxation and retardation function of the Maxwell model with fractional derivatives[J].Rheol Acta,1991,30(2):151—158. doi: 10.1007/BF01134604
[5]	黄军旗，何光渝, 刘慈群. 双筒流变仪中广义二阶流体运动分析[J].中国科学,A辑,1996,26(10):912—920.
[6]	何光渝，黄军旗，刘慈群．广义二阶流体管内轴向流动[J]．应用数学和力学, 1995,16(9):767—773.
[7]	徐明瑜，谭文长．广义二阶流体分数阶反常扩散速度场、应力场及涡旋层的理论分析[J]．中国科学,A辑,2001,31(7):626—638.
[8]	徐明瑜，谭文长．粘弹性材料本构方程的广义分数阶单元网格表述及其广义解[J]．中国科学,A辑,2002,32(8):673—681.
[9]	谭文长，鲜峰，魏兰．广义二阶流体非定常Couette流动的精确解[J]．科学通报, 2002,47(16):1226—1229.
[10]	TAN Wen-chang,XU Ming-yu.The impulsive motion of flat plate in a general second grade fluid[J].Mechanics Research Communication,2002,29(1):3—9. doi: 10.1016/S0093-6413(02)00223-9
[11]	TAN Wen-chang,XU Ming-yu.Plane surface suddenly set in motion in a viscoelastic fluid with fractional Maxwell model[J].Acta Mechanica Sinica,2002,18(4):342—349. doi: 10.1007/BF02487786
[12]	TAN Wen-chang,PAN Wen-xiao,XU Ming-yu. A note on unsteady flows of a viscoelastic fluid with the fractional Maxwell model between two parallel plates[J].International Journal of Non-Linear Mechanics,2003，38(5)：645—650. doi: 10.1016/S0020-7462(01)00121-4
[13]	李健，江体乾．带分数导数的粘弹性流体本构方程的研究[A]．见：全国流变学学术会议论文集[C]．广州:华南理工大学出版社，1993.
[14]	Song D Y, Jiang T Q. Study on the constitutive equation with fractional derivative for the viscoelastic fluids-modified Jeffreys model and its application [J].Rheologica Acta, 1998,27(5):512—517.
[15]	Podlubny I.Fractional Differential Equations[M].San Diego: Academic Press, 1999, 1—303.
[16]	Paradisi P, Cesari R, Mainardi R，et al. The fractional Fick's law for non-local transport processes[J].Physica A, 2001,293(1):130—142. doi: 10.1016/S0378-4371(00)00491-X
[17]	奥齐西克．热传导[M]．俞昌铭译．北京: 高等教育出版社, 1983, 563—715.

施引文献

资源附件(0)

访问统计

点击查看大图

计量

文章访问数: 2733
HTML全文浏览量: 101
PDF下载量: 578
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

留言板

广义二阶流体涡流速度的衰减和温度扩散

作者简介:
沈芳(1977- ),女,河北张家口人,博士(E-mail:fshen@spaceweather.ac.cn);谭文长(联系人.Tel:+86-10-62754244;Fax:+86-10-62751812;E-mail:tanwch@mech.pku.edu.cn).

计量

Decay of Vortex Velocity and Diffusion of Temperature in a Generalized Second Grade Fluid

计量

目录

留言板

广义二阶流体涡流速度的衰减和温度扩散

作者简介: 沈芳(1977- ),女,河北张家口人,博士(E-mail:fshen@spaceweather.ac.cn);谭文长(联系人.Tel:+86-10-62754244;Fax:+86-10-62751812;E-mail:tanwch@mech.pku.edu.cn).

计量

出版历程

Decay of Vortex Velocity and Diffusion of Temperature in a Generalized Second Grade Fluid

计量

出版历程

目录

作者简介:
沈芳(1977- ),女,河北张家口人,博士(E-mail:fshen@spaceweather.ac.cn);谭文长(联系人.Tel:+86-10-62754244;Fax:+86-10-62751812;E-mail:tanwch@mech.pku.edu.cn).