Journal ArticleDOI
Study on the constitutive equation with fractional derivative for the viscoelastic fluids – Modified Jeffreys model and its application
Dao Yun Song,Ti Qian Jiang +1 more
TLDR
In this article, a modified version of the classic linear viscoelastic Jeffreys model is proposed and the corresponding five-parameter equation with fractional derivatives of different orders of the stress and rate of strain is stated.Abstract:
Based on the classic linear viscoelastic Jeffreys model, a modified Jeffreys model is suggested. The corresponding five-parameter equation with fractional derivatives of different orders of the stress and rate of strain is stated and the characteristic material functions of the linear viscoelasticity theory, such as the dynamic moduli, are derived. The comparison between the measured dynamic moduli of Sesbania gel and xanthan gum and the theoretical predictions of the proposed phenomenological model shows an excellent agreement.read more
Citations
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Journal ArticleDOI
Identification of the parameters of the Kelvin-Voigt and the Maxwell fractional models, used to modeling of viscoelastic dampers
TL;DR: In this paper, a family of methods for identification of the parameters of both the Kelvin-Voigt fractional model and the Maxwell fractional models are presented in order to describe the behavior of viscoelastic dampers using a small number of parameters.
Journal ArticleDOI
Plane surface suddenly set in motion in a viscoelastic fluid with fractional maxwell model
TL;DR: In this article, the fractional calculus approach in the constitutive relationship model of viscoelastic fluid is introduced and the flow near a wall suddenly set in motion is studied for a non-Newtonian visco-elastic liquid with the fraction fractional Maxwell model.
Journal ArticleDOI
Exact solution for MHD flow of a generalized Oldroyd-B fluid with modified Darcy’s law
TL;DR: In this paper, an exact solution for the magnetohydrodynamic (MHD) flow of a generalized oldroyd-B fluid in a circular pipe is presented. And the velocity field is calculated analytically based on modified Darcy's law.
Journal ArticleDOI
Stokes’ first problem for a viscoelastic fluid with the generalized Oldroyd-B model
Haitao Qi,Mingyu Xu +1 more
TL;DR: In this paper, the authors studied the flow near a wall suddenly set in motion for a viscoelastic fluid with the generalized Oldroyd-B model and obtained exact analytical solutions of velocity and stress by using the discrete Laplace transform of the sequential fractional derivative and the Fox H-function.
Journal ArticleDOI
Exact solutions for the unsteady rotational flow of non-Newtonian fluid in an annular pipe
Dengke Tong,Yusong Liu +1 more
TL;DR: In this article, a generalized Jeffreys model with the fractional calculus is built to deal with some unsteady transient rotational flows of an Oldroyd-B fluid in an annular pipe.
References
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Book
The Fractal Geometry of Nature
TL;DR: This book is a blend of erudition, popularization, and exposition, and the illustrations include many superb examples of computer graphics that are works of art in their own right.
Book
Fractional Integrals and Derivatives: Theory and Applications
TL;DR: Fractional integrals and derivatives on an interval fractional integral integrals on the real axis and half-axis further properties of fractional integral and derivatives, and derivatives of functions of many variables applications to integral equations of the first kind with power and power-logarithmic kernels integral equations with special function kernels applications to differential equations as discussed by the authors.
Book
The science of fractal images
Michael F. Barnsley,Robert L. Devaney,Benoit B. Mandelbrot,Heinz-Otto Peitgen,Dietmar Saupe,Richard F. Voss,Yuval Fisher,Michael McGuire +7 more
TL;DR: Fractal Modelling of Real World Images and a Unified Approach to Fractal Curves and Plants are studied.
Journal ArticleDOI
A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity
Ronald L. Bagley,Peter J. Torvik +1 more
TL;DR: In this article, the authors established a link between molecular theories that predict the macroscopic behavior of certain viscoelastic media and an empirically developed fractional calculus approach to visco-elasticity.
Journal ArticleDOI
On the Fractional Calculus Model of Viscoelastic Behavior
Ronald L. Bagley,Peter J. Torvik +1 more
TL;DR: In this paper, a mathematical model of the viscoelastic phenomenon employing derivatives of fractional order is examined in light of its consistency with thermodynamic principles, which leads the model to predict realistic sinusoidal response as well as realistic relaxation and creep responses.