1887
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
oa
Helical flows of fractionalized Burgers' fluids
Rent:
Rent this article for
Access full text Article
/content/aip/journal/adva/2/1/10.1063/1.3694982
1.
1. R. S. Lakes, Viscoelastic Solids, Boca Raton, FL: CRC Press, (1999).
2.
2. R. G. Larson, The Structure and Rheology of Complex Fluids, Oxford University Press, NewYork, (1999).
3.
3. D. Craiem, F. J. Rojo, J. M. Atienza, R. L. Armentano, G. V. Guinea, Fractional-order viscoelasticity applied to describe uniaxial stress relaxation of human arteries, Phys. Med. Biol. 53, 4543 (2008).
http://dx.doi.org/10.1088/0031-9155/53/17/006
4.
4. D. Craiem, R. L. Armentano, A fractional derivative model to describe arterial viscoelasticity, Biorheology 44 251263 (2007).
5.
5. A. Mahmood, Saifullah, G. Bolat, Some exact solutions for the rotational flow of a generalized second-grade fluid between two circular cylinders, Arch. Mech. 60, 385401 (2008).
6.
6. C. Fetecau, A. Mahmood, Corina Fetecau, D. Vieru, Some exact solutions for the helical flow of a generalized Oldroyd-B fluid in a circular cylinder, Comput. Math. Appl. 56, 30963108 (2008).
http://dx.doi.org/10.1016/j.camwa.2008.07.003
7.
7. H. T. Qi, H. Jin, Unsteady helical flow of a generalized Oldroyd-B fluid with fractional derivative, Nonlinear Anal.: Real World Appl. 10, 27002708 (2009).
http://dx.doi.org/10.1016/j.nonrwa.2008.07.008
8.
8. M. Khan, S. Hyder Ali, H. Qi, On accelerated flows of a viscoelastic fluid with the fractional Burgers’ model, Nonlinear Anal.: Real World Appl. 10, 22862296 (2009).
http://dx.doi.org/10.1016/j.nonrwa.2008.04.015
9.
9. D. Tong, L. T. Shan, Exact solution for generalized Burgers’ fluid in an annular pipe, Meccanica 44, 427431 (2009).
http://dx.doi.org/10.1007/s11012-008-9179-6
10.
10. M. Khan, A. S. Hyder, H. T. Qi, Exact solutions of starting flows for a fractional Burgers’ fluid between coaxial cylinders, Nonlinear Anal.: Real World Appl. 10, 17751783 (2009).
http://dx.doi.org/10.1016/j.nonrwa.2008.02.015
11.
11. M. Khan, S. Hyder Ali, H. T. Qi, On accelerated flows of a viscoelastic fluid with the fractional Burgers’ model, Nonlinear Anal.: Real World Appl. 10, 22862296 (2009).
http://dx.doi.org/10.1016/j.nonrwa.2008.04.015
12.
12. M. Khan, Asia Anjum, C. Fetecau, H. Qi, Exact solutions for some oscillating motions of a fractional Burgers’ fluid, Math. and Comput. Modelling 51, 682692 (2010).
http://dx.doi.org/10.1016/j.mcm.2009.10.040
13.
13. Corina Fetecau, T. Hayat, M. Khan, C. Fetecau, A note on longitudinal oscillations of a generalized Burgers fluid in cylindrical domains, J. of Non-Newtonian Fluid Mech. 165, 350361 (2010).
http://dx.doi.org/10.1016/j.jnnfm.2010.01.009
14.
14. S. H. A. M. Shah, Some helical flows of a Burgers’ fluid with fractional derivative, Meccanica 45, 143151 (2010).
http://dx.doi.org/10.1007/s11012-009-9233-z
15.
15. D. Tong, Starting solutions for oscillating motions of a generalized Burgers’ fluid in cylindrical domains, Acta Mech. 214, 395407 (2010).
http://dx.doi.org/10.1007/s00707-010-0288-7
16.
16. I. Siddique, Exact solutions for the longitudinal flow of a generalized Maxwell fluid in a circular cylinder, Arch. Mech. 62, 305317 (2010).
17.
17. A. Mahmood, C. Fetecau, N. A. Khan, M. Jamil, Some exact solutions of the oscillatory motion of a generalized second grade fluid in an annular region of two cylinders, Acta Mech Sin 26, 541550 (2010).
http://dx.doi.org/10.1007/s10409-010-0353-4
18.
18. C. Fetecau, A. Mahmood, M. Jamil, Exact solutions for the flow of a viscoelastic fluid induced by a circular cylinder subject to a time dependent shear stress, Commun Nonlinear Sci Numer Simulat 15, 39313938 (2010).
http://dx.doi.org/10.1016/j.cnsns.2010.01.012
19.
19. M. Jamil, A. Rauf, A. A. Zafar, N. A. Khan, New exact analytical solutions for Stokes’ first problem of Maxwell fluid with fractional derivative approach, Comput. Math. Appl. 62, 10131023 (2011).
http://dx.doi.org/10.1016/j.camwa.2011.03.022
20.
20. M. Jamil, N. A. Khan, A. A. Zafar, Translational flows of an Oldroyd-B fluid with fractional derivatives, Comput. Math. Appl. 62, 15401553 (2011).
http://dx.doi.org/10.1016/j.camwa.2011.03.090
21.
21. H. T. Qi, J. G. Liu, Some duct flows of a fractional Maxwell fluid, Eur. Phys. J. Special Topics 193, 7179 (2011).
http://dx.doi.org/10.1140/epjst/e2011-01382-6
22.
22. P. Sollich, F. Lequeux, P. Hébraud, M. E. Cates, Rheology of soft glassy materials, Phys. Rev. Lett. 78, 20202023 (1997).
http://dx.doi.org/10.1103/PhysRevLett.78.2020
23.
23. P. Sollich, Rheological constitutive equation for a model of soft glassy materials, Phys. Rev. E 58, 738759 (1998).
http://dx.doi.org/10.1103/PhysRevE.58.738
24.
24. D. Stamenović, N. Rosenblatt, M. Montoya-Zavala, B. D. Matthews, S. Hu, B. Suki, N. Wang, D. E. Ingber, Rheological behavior of living cells is timescale-dependent, Biophys. J. 93, 3941 (2007).
http://dx.doi.org/10.1529/biophysj.107.116582
25.
25. Q. Chen, B. Suki, An K-N. Dynamic mechanical properties of agarose gels modeled by a fractional derivative model, J Biomech Eng 126, 66671 (2004).
http://dx.doi.org/10.1115/1.1797991
26.
26. M. Z. Kiss, T. Varghese, T. J. Hall, Viscoelastic characterization of in vitro canine tissue, Phys Med Biol 49, 420718 (2004).
http://dx.doi.org/10.1088/0031-9155/49/18/002
27.
27. D. Klatt, U. Hamhaber, P. Asbach, J. Braun, I. Sack, Noninvasive assessment of the rheological behavior of human organs using multifrequency mrelastography: a study of brain and liver viscoelasticity, Phys Med Biol 52, 728194 (2007).
http://dx.doi.org/10.1088/0031-9155/52/24/006
28.
28. R. Sinkus, K. Siegmann, T. Xydeas, M. Tanter, C. Claussen, M. Fink, Mr elastography of breast lesions: understanding the solid/liquid duality can improve the specificity of contrast-enhanced mr mammography, Magn Reson Med 58, 113544 (2007).
http://dx.doi.org/10.1002/mrm.21404
29.
29. D. Craiem1, R. L. Magin, Fractional order models of viscoelasticity as an alternative in the analysis of red blood cell (RBC) membrane mechanics, Phys. Biol. 7, 013001 (2010).
http://dx.doi.org/10.1088/1478-3975/7/1/013001
30.
30. F. C. Meral, T. J. Royston, R. Magin, Fractional calculus in viscoelasticity: An experimental study, Commun Nonlinear Sci Numer Simulat 15, 939945 (2010).
http://dx.doi.org/10.1016/j.cnsns.2009.05.004
31.
31. R. L. Magin, Fractional calculus models of complex dynamics in biological tissues, Comput. Math. Appl. 59, 15861593 (2010).
http://dx.doi.org/10.1016/j.camwa.2009.08.039
32.
32. I. Podlubny, Fractional Differential Equations, Academic press, San Diego, (1999).
33.
33. F. Mainardi, Frcational calculus and waves in linear viscoelasticity: An itroduction to mathemtical models, Imperial College Press, London, (2010).
34.
34. L. Debnath, D. Bhatta, Integral Transforms and Their Applications (Second Edition), Chapman & Hall/CRC, (2007).
35.
35. C. F. Lorenzo, T. T. Hartley, Generalized Functions for the Fractional Calculus, NASA/TP-1999-209424, (1999).
http://aip.metastore.ingenta.com/content/aip/journal/adva/2/1/10.1063/1.3694982
Loading
/content/aip/journal/adva/2/1/10.1063/1.3694982
Loading

Data & Media loading...

Loading

Article metrics loading...

/content/aip/journal/adva/2/1/10.1063/1.3694982
2012-03-07
2014-07-28

Abstract

The unsteady flows of Burgers’ fluid with fractional derivatives model, through a circular cylinder, is studied by means of the Laplace and finite Hankel transforms. The motion is produced by the cylinder that at the initial moment begins to rotate around its axis with an angular velocity Ωt, and to slide along the same axis with linear velocity Ut. The solutions that have been obtained, presented in series form in terms of the generalized G a,b,c (•, t) functions, satisfy all imposed initial and boundary conditions. Moreover, the corresponding solutions for fractionalized Oldroyd-B, Maxwell and second grade fluids appear as special cases of the present results. Furthermore, the solutions for ordinary Burgers’, Oldroyd-B, Maxwell, second grade and Newtonian performing the same motion, are also obtained as special cases of general solutions by substituting fractional parameters α = β = 1. Finally, the influence of the pertinent parameters on the fluid motion, as well as a comparison among models, is shown by graphical illustrations.

Loading

Full text loading...

/deliver/fulltext/aip/journal/adva/2/1/1.3694982.html;jsessionid=1fkfrvkgivtaf.x-aip-live-06?itemId=/content/aip/journal/adva/2/1/10.1063/1.3694982&mimeType=html&fmt=ahah&containerItemId=content/aip/journal/adva
true
true
This is a required field
Please enter a valid email address
This feature is disabled while Scitation upgrades its access control system.
This feature is disabled while Scitation upgrades its access control system.
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Helical flows of fractionalized Burgers' fluids
http://aip.metastore.ingenta.com/content/aip/journal/adva/2/1/10.1063/1.3694982
10.1063/1.3694982
SEARCH_EXPAND_ITEM