The two-dimensional Newtonian and non-Newtonian (Carreau viscosity model used) oscillatory flows in straight tubes are studied theoretically and numerically. The corresponding analytical solution of the Newtonian flow and the numerical solution of the Carreau viscosity model flow show differences in velocity and shear rate. Some estimates for the velocity and shear rate differences are theoretically proved. As numerical examples the blood flow in different type of arteries and the polymer flow in pipes are considered.
REFERENCES
1.
A.
Razavi
, E.
Shirani
, and M.R.
Sadeghi
(2011
) Journal of Biomechanics
44
, 2021
–2030
.2.
T. G.
Myers
(2005
) Physical Review E
72
, paper 066302, 11
p.3.
S. S.
Shibeshi
and W. E.
Collins
(2005
) Appl Rheol.
15
, 398
–405
.4.
5.
A.
Valencia
, D.
Ledermann
, E.
Bravo
, and M.
Galvez
(2008
) Numerical Methods in Fluids
58
, 1081
–1100
.6.
S.
Tabakova
, E.
Nikolova
, and S.
Radev
, “Carreau Model for Oscillatory Blood Flow in a Tube
,” in AMi-TaNS’14
, AIP Conference Proceedings
, Vol. 1629
, edited by M.D.
Todorov
, (American Institute of Physics
, Melville, NY
, 2014
), pp. 336
–343
.7.
N.
Kutev
, S.
Tabakova
, and S.
Radev
, “Approximation of the oscillatory blood flow using the Carreau viscosity model
,” in Proceedings of the International Conference on Mechanics – Seventh Polyakhov’s Reading
, 2-6 February 2015
, Saint-Petersburg, Russia
, ISBN , IEEE Catalog Number CFP15A24-ART, 4
p.8.
S.
Tabakova
, N.
Kutev
, and S.
Radev
, “Application of the Carreau viscosity model to the oscillatory fFlow in blood vessels
,” in AMEE’15
, AIP Conference Proceedings
, Vol. 1690
, edited by V.
Pasheva
, et al., (American Institute of Physics
, Melville, NY
, 2015
), paper 040019, 7
p.9.
10.
L.N.
Brush
and S.M.
Roper
(2008
) J. Fluid Mech.
616
, 235
–262
.11.
J. R.
Womersley
(1955
) The Journal of Physiology
127
, 553
–563
.12.
M.H.
Protter
and H. F.
Weinberger
, Maximum Principles in Differential Equations
(Springer-Verlag
, New York
, 1984
), p. 261
.
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