A space fractional constitutive equation model for non-Newtonian fluid flow

Sun, HongGuang1; Zhang, Yong1,2; Wei, Song1,4; Zhu, Jianting3; Chen, Wen1

2018-09

10.1016/j.cnsns.2018.02.007

Communications in Nonlinear Science and Numerical Simulation   影响因子和分区

1007-5704

1878-7274

Non-Newtonian fluid flow can be driven by spatially nonlocal velocity, the dynamics of which can be described by promising fractional derivative models. This study reports a left-side, Caputo type, space fractional-order constitutive equation (FCE) using a nonlocal, fractional velocity gradient and then interprets physical properties of non-Newtonian fluids for steady pipe flow. Results show that the generalized FCE model contains previous non-Newtonian fluid flow models as end-members by simply adjusting the order of the fractional index, and a preliminary test shows that the FCE model conveniently captures the observed growth of shear stress for various velocity gradients. Further analysis of the velocity profile, frictional head loss, and Reynolds number using the FCE model also leads to analytical tools and criterion that can extend standard models in quantifying the complex dynamics of non-Newtonian fluid flow with a wide range of spatially nonlocal velocities. Model extension using the general two-side fractional derivative is also briefly discussed. (c) 2018 Elsevier B.V. All rights reserved.

Space fractional constitutive equation Non-Newtonian fluid flow Fractional velocity gradient Fractional Reynolds number

SCI ; EI

英语

其他

National Natural Science Foundation of China[11572112] ; National Natural Science Foundation of China[41628202] ; National Natural Science Foundation of China[11528205] ; National Natural Science Foundation of China[41330632]

Mathematics ; Mechanics ; Physics

Mathematics, Applied ; Mathematics, Interdisciplinary Applications ; Mechanics ; Physics, Fluids & Plasmas ; Physics, Mathematical

WOS:000429332800027

ELSEVIER SCIENCE BV

20181104896349

Constitutive equations ; Flow measurement ; Newtonian flow ; Non Newtonian liquids ; Reynolds equation ; Reynolds number ; Rheology ; Shear flow ; Shear stress ; Velocity ; Viscous flow

Fluid Flow, General:631.1 ; Mathematics:921 ; Mechanics:931.1 ; Physical Properties of Gases, Liquids and Solids:931.2

Web of Science

1.Hohai Univ, Coll Mech & Mat, State Key Lab Hydrol Water Resources & Hydraul En, Nanjing 210098, Jiangsu, Peoples R China
2.Univ Alabama, Dept Geol Sci, Tuscaloosa, AL 35487 USA
3.Univ Wyoming, Dept Civil & Architectural Engn, 1000 E Univ Ave, Laramie, WY 82071 USA
4.Southern Univ Sci & Technol, Sch Environm Sci & Engn, Shenzhen 518055, Peoples R China

Sun, HongGuang,Zhang, Yong,Wei, Song,et al. A space fractional constitutive equation model for non-Newtonian fluid flow[J]. Communications in Nonlinear Science and Numerical Simulation,2018,62:409-417.

Sun, HongGuang,Zhang, Yong,Wei, Song,Zhu, Jianting,&Chen, Wen.(2018).A space fractional constitutive equation model for non-Newtonian fluid flow.Communications in Nonlinear Science and Numerical Simulation,62,409-417.

Sun, HongGuang,et al."A space fractional constitutive equation model for non-Newtonian fluid flow".Communications in Nonlinear Science and Numerical Simulation 62(2018):409-417.