On the unsteady rotational flow of a fractional second grade fluid through a circular cylinder
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Here the velocity field and the associated tangential stress corresponding to the rotational flow of a generalized second grade fluid within an infinite circular cylinder are determined by means of the Laplace and finite Hankel transforms. At time t=0 the fluid is at rest and the motion is produced by the rotation of the cylinder around its axis. The solutions that have been obtained are presented under series form in terms of the generalized Gfunctions. The similar solutions for ordinary second grade and Newtonian fluids are obtained from general solution for β→1, respectively, β→1 and α _{1}→0. Finally, the influences of the pertinent parameters on the fluid motion, as well as a comparison between models, is underlined by graphical illustrations.
 Rajagopal KR (1983) Longitudinal and torsional oscillations of a rod in a nonNewtonian fluid. Acta Mech 49:281–285 CrossRef
 Erdogan ME (1995) Plane surface suddenly set in motion in a nonNewtonian fluid. Acta Mech 108:179–187 CrossRef
 Erdogan ME, Imrak CE (2005) Effects of the side walls on starting flows in ducts. Int J NonLinear Mech 40:107–111 CrossRef
 Nadeem S, Asghar S, Hayat T (2008) The Rayleigh Stokes problem for rectangular pipe in Maxwell and second grade fluid. Meccanica 43:495–504 CrossRef
 Fetecau C, Vieru D, Fetecau C (2008) A note on the second problem of Stokes for Newtonian fluids. Int J NonLinear Mech 43:451–457 CrossRef
 Rajagopal KR (1984) On the creeping flow of the second order fluid. J NonNewton Fluid Mech 15:239–246 CrossRef
 Fetecau C, Fetecau C, Zierep J (2002) Decay of potential vortex and propagation of a heat wave in a second grade fluid. Int J NonLinear Mech 37:1051–1056 CrossRef
 Hayat T, Elahi R, Asghar S, Siddiqui AM (2004) Flow induced by a noncoaxial rotation of a porous disk executing nontorsional oscillations and a second grade fluid at infinity. Appl Math Model 28:591–605 CrossRef
 Hayat T, Hameed MI, Asghar S, Siddiqui AM (2004) Some steady MHD flows of the second order fluid. Meccanica 39:345–355 CrossRef
 Fetecau C, Fetecau C (2005) Starting solutions for some unsteady unidirectional flows of a second grade fluid. Int J Eng Sci 43:781–789 CrossRef
 Vieru D, Akhtar W, Fetecau C, Fetecau C (2007) Starting solutions for the oscillating motion of a Maxwell fluid in cylindrical domains. Meccanica 42:573–583 CrossRef
 Fetecau C, Fetecau C (2006) Starting solutions for the motion of second grade fluid due to longitudinal and torsional oscillations of a circular cylinder. Int J Eng Sci 44:788–796 CrossRef
 Fetecau C, Fetecau C, Vieru D (2007) On some helical flows of OldroydB fluids. Acta Mech 189:53–63 CrossRef
 Bagley RL (1983) A theoretical basis for the application of fractional calculus to viscoelasticity. J Rheol 27:201–210 CrossRef
 Friedrich C (1991) Relaxation and retardation function of the Maxwell model with fractional derivatives. Rheol Acta 30:151–158 CrossRef
 He G, Junqi H, Liu C (1995) General second order fluid flow in pipe. Appl Math Mech 16:767–773
 Junqi H, He G, Liu C (1997) Analysis of general second order fluid flow in double cylinder rheometer. Sci China Ser A 40:183–190
 Xu MY, Tan WC (2001) Theoretical analysis of the velocity field, stress field and vortex sheet of generalized second order fluid with fractional anomalous diffusion. Sci China Ser A 44:1387–1399 CrossRef
 Xu MY, Tan WC (2002) The representation of the constitutive equation of viscoelastic materials by the generalized fractional element networks and its generalized solution. Sci China Ser A 32:673–681
 Tan WC, Xu MY (2002) Plane surface suddenly set in motion in a viscoelastic fluid with fractional Maxwell Model. Acta Mech Sin 18:342–349 CrossRef
 Tan WC, Xian F, Wei L (2002) An exact solution of Couette flow of generalized second grade fluid. Chin Sci Bull 47:1783–1785 CrossRef
 Tan WC, Pan WX, Xu MY (2003) A note on unsteady flows of a viscoelastic fluid with fractional Maxwell model between two parallel plates. Int J NonLinear Mech 38:645–650 CrossRef
 Tan WC, Xu MY (2004) Unsteady flows of a generalized second grade fluid with fractional derivative model between two parallel plates. Acta Mech Sin 20:471–476 CrossRef
 Bandelli R, Rajagopal KR (1995) Startup flows of second grade fluids in domains with one finite dimension. Int J NonLinear Mech 30:817–839 CrossRef
 Fetecau C, Fetecau C (2006) Starting solutions for the motion of second grade fluid due to longitudinal and torsional oscillations of a circular cylinder. Int J Eng Sci 44:788–796 CrossRef
 Podlubny I (1999) Fractional differential equations. Academic Press, San Diego
 Tong D, Liu Y (2005) Exact solutions for the unsteady rotational flow of nonNewtonian fluid in an annular pipe. Int J Eng Sci 43:281–289 CrossRef
 Lorenzo CF, Hartley TT (1999) Generalized functions for the fractional calculus. NASA/TP1999209424/REV1
 Title
 On the unsteady rotational flow of a fractional second grade fluid through a circular cylinder
 Journal

Meccanica
Volume 47, Issue 3 , pp 603611
 Cover Date
 20120301
 DOI
 10.1007/s1101201093731
 Print ISSN
 00256455
 Online ISSN
 15729648
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 Generalized second grade fluid
 Velocity field
 Shear stress
 Exact solutions
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