http://www.ikb.poznan.pl/roman.lewandowski/Passive/jabartosz.pdf

Identification of the parameters of the Kelvin-Voigt and the Maxwell fractional models, used to modeling of viscoelastic dampers

The fractional calculus approach in the constitutive relationship model of viscoelastic fluid is introduced. The flow near a wall suddenly set in motion is studied for a non-Newtonian viscoelastic fluid with the fractional Maxwell model. Exact solutions of velocity and stress are obtained by using the discrete inverse Laplace transform of the sequential fractional derivatives. It is found that the effect of the fractional orders in the constitutive relationship on the flow field is significant. The results show that for small times there are appreciable viscoelastic effects on the shear stress at the plate, for large times the viscoelastic effects become weak.

Plane surface suddenly set in motion in a viscoelastic fluid with fractional maxwell model

http://streaming.ictp.it/preprints/P/05/074.pdf

Exact solution for MHD flow of a generalized Oldroyd-B fluid with modified Darcy’s law

The flow near a wall suddenly set in motion for a viscoelastic fluid with the generalized Oldroyd-B model is studied. The fractional calculus approach is used in the constitutive relationship of fluid model. Exact analytical solutions of velocity and stress are obtained by using the discrete Laplace transform of the sequential fractional derivative and the Fox H-function. The obtained results indicate that some well known solutions for the Newtonian fluid, the generalized second grade fluid as well as the ordinary Oldroyd-B fluid, as limiting cases, are included in our solutions.

Stokes’ first problem for a viscoelastic fluid with the generalized Oldroyd-B model

Exact solutions for the unsteady rotational flow of non-Newtonian fluid in an annular pipe

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.

Ti Qian Jiang

Papers

Study on the constitutive equation with fractional derivative for the viscoelastic fluids – Modified Jeffreys model and its application