Flow and heat transfer of viscoelastic fluid with a novel space distributed-order constitution relationship

被引：10

作者：

Yang, Weidong ^{[1
,2
]}

Chen, Xuehui ^{[1
]}

Zhang, Xinru ^{[2
]}

Zheng, Liancun ^{[1
]}

Liu, Fawang ^{[3
]}

机构：

[1] Univ Sci & Technol Beijing, Sch Math & Phys, Beijing 100083, Peoples R China

[2] Univ Sci & Technol Beijing, Sch Energy & Environm Engn, Beijing 100083, Peoples R China

[3] Queensland Univ Technol, Sch Math Sci, Brisbane, Qld 4001, Australia

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2021年 / 94卷

基金：

中国国家自然科学基金;

关键词：

Distributed-order boundary layer equations; Solvability; Convergence; Flow; Heat transfer; Numerical solution; FRACTIONAL DIFFUSION EQUATION; NUMERICAL-METHOD; SIMILARITY SOLUTION; MHD FLUID; MODEL; RELAXATION; STABILITY; MOTION;

D O I：

10.1016/j.camwa.2021.04.023

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The space distributed-order constitution relationship is firstly formulated to study the flow and heat transfer in the boundary layer. The distributed-order boundary layer equations are derived and approximated by a multi space fractional order ones, which are then solved by the implicit difference schemes. By comparing the analytical solutions of special boundary conditions, the validity of the present numerical method is examined. Then, the stability and convergence of the implicit finite difference scheme are analysed systematically. Finally, we present two practical examples to illustrate the effectiveness of our numerical method. Furthermore, the numerical technique in this study can be extended to others distributed-order boundary layer models.

引用

页码：94 / 103

页数：10

共 32 条

[1] Comparison of mathematical models with fractional derivative for the heat conduction inverse problem based on the measurements of temperature in porous aluminum [J].

Brociek, Rafal ;

Slota, Damian ;

Krol, Mariusz ;

Matula, Grzegorz ;

Kwasny, Waldemar .

INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER, 2019, 143

[2]

Caputo M., 1969, ELASTICITA DISSIPAZI

[3]

Caputo M., 1995, ANN U FERRARA SEZ 7, VXLI, P73

[4] Retarding subdiffusion and accelerating superdiffusion governed by distributed-order fractional diffusion equations [J].

Chechkin, AV ;

Gorenflo, R ;

Sokolov, IM .

PHYSICAL REVIEW E, 2002, 66 (04) :7-046129

[5] Unsteady boundary layer flow of viscoelastic MHD fluid with a double fractional Maxwell model [J].

Chen, Xuehui ;

Yang, Weidong ;

Zhang, Xinru ;

Liu, Fawang .

APPLIED MATHEMATICS LETTERS, 2019, 95 :143-149

[6]

Chen XH, 2018, COMPUT MATH APPL, V75, P3002, DOI [10.1016/J.camwa.2018.01.028, 10.1016/j.camwa.2018.01.028]

[7] A numerical method for solving the two-dimensional distributed order space-fractional diffusion equation on an irregular convex domain [J].

Fan, Wenping ;

Liu, Fawang .

APPLIED MATHEMATICS LETTERS, 2018, 77 :114-121

[8] RELAXATION AND RETARDATION FUNCTIONS OF THE MAXWELL MODEL WITH FRACTIONAL DERIVATIVES [J].

FRIEDRICH, C .

RHEOLOGICA ACTA, 1991, 30 (02) :151-158

[9] Finite difference/spectral-Galerkin method for a two-dimensional distributed-order time-space fractional reaction-diffusion equation [J].

Guo, Shimin ;

Mei, Liquan ;

Zhang, Zhengqiang ;

Jiang, Yutao .

APPLIED MATHEMATICS LETTERS, 2018, 85 :157-163

[10] On the MHD flow of fractional generalized Burgers' fluid with modified Darcy's law [J].

Hayat, T. ;

Khan, M. ;

Asghar, S. .

ACTA MECHANICA SINICA, 2007, 23 (03) :257-261

← 1 2 3 4 →