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Volumn 16, Issue 1, 2011, Pages 226-238

Exact solutions for the unsteady axial flow of Non-Newtonian fluids through a circular cylinder

Author keywords

Exact solutions; Fractional calculus; Generalized Oldroyd B fluid; Longitudinal shear stress; Velocity field

Indexed keywords

CALCULATIONS; CIRCULAR CYLINDERS; LAPLACE TRANSFORMS; NON NEWTONIAN FLOW; NON NEWTONIAN LIQUIDS; SHEAR FLOW; VELOCITY;

EID: 77955516145     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2010.03.010     Document Type: Article
Times cited : (25)

References (46)
  • 1
    • 0029289811 scopus 로고
    • Fluids of differential type: critical review and thermodynamic analysis
    • Dunn J.E., Rajagopal K.R. Fluids of differential type: critical review and thermodynamic analysis. Int J Eng Sci 1995, 33(5):689-729.
    • (1995) Int J Eng Sci , vol.33 , Issue.5 , pp. 689-729
    • Dunn, J.E.1    Rajagopal, K.R.2
  • 2
    • 0001634191 scopus 로고
    • Mechanics of non-Newtonian fluids
    • Longman, New York, Recent developments in theoretical fluids mechanics
    • Rajagopal K.R. Mechanics of non-Newtonian fluids. Pirman research notes in mathematics 1993, vol. 291:129-162. Longman, New York.
    • (1993) Pirman research notes in mathematics , vol.291 , pp. 129-162
    • Rajagopal, K.R.1
  • 3
    • 0001086663 scopus 로고
    • On the formulation of rheological equations of state
    • Oldroyd J.G. On the formulation of rheological equations of state. Proc Roy Soc Lond A 1950, 200:523-541.
    • (1950) Proc Roy Soc Lond A , vol.200 , pp. 523-541
    • Oldroyd, J.G.1
  • 4
    • 0033997971 scopus 로고    scopus 로고
    • A thermodynamical frame-work for rate type fluid models
    • Rajagopal K.R., Srinivasa A.R. A thermodynamical frame-work for rate type fluid models. J Non-Newtonian Fluid Mech 2000, 88:207-227.
    • (2000) J Non-Newtonian Fluid Mech , vol.88 , pp. 207-227
    • Rajagopal, K.R.1    Srinivasa, A.R.2
  • 7
    • 0035217253 scopus 로고    scopus 로고
    • Some simple flows of an Oldroyd-B fluid
    • Hayat T., Siddiqui A.M., Asghar S. Some simple flows of an Oldroyd-B fluid. Int J Eng Sci 2001, 39:135-147.
    • (2001) Int J Eng Sci , vol.39 , pp. 135-147
    • Hayat, T.1    Siddiqui, A.M.2    Asghar, S.3
  • 8
    • 0037567572 scopus 로고    scopus 로고
    • Analytical solutions for non-Newtonian fluid flow in pipe-like domains
    • Fetecau C. Analytical solutions for non-Newtonian fluid flow in pipe-like domains. Int J Nonlinear Mech 2004, 39:225-231.
    • (2004) Int J Nonlinear Mech , vol.39 , pp. 225-231
    • Fetecau, C.1
  • 9
    • 0029490406 scopus 로고
    • Exact solutions for some simple flows of an Oldroyd-B fluid
    • Rajagopal K.R., Bhatnagar R.K. Exact solutions for some simple flows of an Oldroyd-B fluid. Acta Mech 1995, 113:233-239.
    • (1995) Acta Mech , vol.113 , pp. 233-239
    • Rajagopal, K.R.1    Bhatnagar, R.K.2
  • 10
    • 10644240598 scopus 로고    scopus 로고
    • Unsteady unidirectional flow of an Oldroyd-B fluid in a circular duct with different given volume flow rate conditions
    • Chen C.I., Chen C.K., Yong Y.T. Unsteady unidirectional flow of an Oldroyd-B fluid in a circular duct with different given volume flow rate conditions. Heat Mass Transfer 2004, 40:203-209.
    • (2004) Heat Mass Transfer , vol.40 , pp. 203-209
    • Chen, C.I.1    Chen, C.K.2    Yong, Y.T.3
  • 11
    • 33847302855 scopus 로고    scopus 로고
    • On some helical flows of Oldroyd-B fluids
    • Fetecau C., Fetecau Corina, Vieru D. On some helical flows of Oldroyd-B fluids. Acta Mech 2007, 189:53-63.
    • (2007) Acta Mech , vol.189 , pp. 53-63
    • Fetecau, C.1    Fetecau, C.2    Vieru, D.3
  • 12
    • 77949427345 scopus 로고    scopus 로고
    • Taylor-Couette flow of an Oldroyd-B fluid in a circular cylinder subject to a time-dependent rotation
    • Fetecau C., Awan A.U., Fetecau Corina Taylor-Couette flow of an Oldroyd-B fluid in a circular cylinder subject to a time-dependent rotation. Bull Math Soc Sci Math Roumanie 2009, 52(100)(2):117-128.
    • (2009) Bull Math Soc Sci Math Roumanie , Issue.2 , pp. 117-128
    • Fetecau, C.1    Awan, A.U.2    Fetecau, C.3
  • 13
    • 77952879196 scopus 로고    scopus 로고
    • Axial Couette flow of an Oldroyd-B fluid due to a time dependent shear stress
    • Fetecau Corina, Fetecau C., Imran M. Axial Couette flow of an Oldroyd-B fluid due to a time dependent shear stress. Math Rep 2009, 11(61)(2):145-154.
    • (2009) Math Rep , Issue.2 , pp. 145-154
    • Fetecau, C.1    Fetecau, C.2    Imran, M.3
  • 14
    • 34848840903 scopus 로고    scopus 로고
    • On set of oscillatory convection in a porous cylinder saturated with a viscoelastic fluid
    • Zhang Z.Y., Fu C.J., Tan W.C., Wang C.Y. On set of oscillatory convection in a porous cylinder saturated with a viscoelastic fluid. Phys Fluids 2007, 19:098104.
    • (2007) Phys Fluids , vol.19 , pp. 098104
    • Zhang, Z.Y.1    Fu, C.J.2    Tan, W.C.3    Wang, C.Y.4
  • 15
    • 41349116524 scopus 로고    scopus 로고
    • Stability analysis of double-diffusive convection of Maxwell fluid in a porous medium heated from below
    • Wang S.W., Tan W.C. Stability analysis of double-diffusive convection of Maxwell fluid in a porous medium heated from below. Phys Lett A 2008, 372(17):3046-3050.
    • (2008) Phys Lett A , vol.372 , Issue.17 , pp. 3046-3050
    • Wang, S.W.1    Tan, W.C.2
  • 16
    • 0035216379 scopus 로고    scopus 로고
    • A new method for solving dynamic problems of fractional derivative viscoelasticity
    • Rossihni Y.A., Shitikova M.V. A new method for solving dynamic problems of fractional derivative viscoelasticity. Int J Eng Sci 2001, 39:149-176.
    • (2001) Int J Eng Sci , vol.39 , pp. 149-176
    • Rossihni, Y.A.1    Shitikova, M.V.2
  • 17
    • 0020765202 scopus 로고
    • A theoretical basis for the application of fractional calculus to viscoelasticity
    • Bagley R.L. A theoretical basis for the application of fractional calculus to viscoelasticity. J Rheol 1983, 27:201-210.
    • (1983) J Rheol , vol.27 , pp. 201-210
    • Bagley, R.L.1
  • 18
    • 34147203638 scopus 로고
    • Relaxation and retardation functions of the Maxwell model with fractional derivative
    • Friedrich C. Relaxation and retardation functions of the Maxwell model with fractional derivative. Rheol Acta 1991, 30:151-158.
    • (1991) Rheol Acta , vol.30 , pp. 151-158
    • Friedrich, C.1
  • 21
    • 70449529531 scopus 로고    scopus 로고
    • A new method of finding the fractional Euler-Lagrange and Hamilton equations within Caputo fractional derivatives
    • Baleanu D., Trujillo J.I. A new method of finding the fractional Euler-Lagrange and Hamilton equations within Caputo fractional derivatives. Commun Nonlinear Sci Numer Simul 2010, 15(5):1111-1115.
    • (2010) Commun Nonlinear Sci Numer Simul , vol.15 , Issue.5 , pp. 1111-1115
    • Baleanu, D.1    Trujillo, J.I.2
  • 23
    • 85196213986 scopus 로고    scopus 로고
    • Study on the constitutive equation with fractional derivative for the viscoelastic fluids - modified Jeffers model and its application
    • Song D.Y., Jiang T.Q. Study on the constitutive equation with fractional derivative for the viscoelastic fluids - modified Jeffers model and its application. Rheol Acta 1998, 27:217-512.
    • (1998) Rheol Acta , vol.27 , pp. 217-512
    • Song, D.Y.1    Jiang, T.Q.2
  • 24
    • 33646699530 scopus 로고    scopus 로고
    • A note on unsteady flows of a viscoelastic fluid with the fractional Maxwell model between two parallel plates
    • Tan W.C., Pan W.X., Xu M.Y. A note on unsteady flows of a viscoelastic fluid with the fractional Maxwell model between two parallel plates. Int J Non-Linear Mech 2003, 38:615-620.
    • (2003) Int J Non-Linear Mech , vol.38 , pp. 615-620
    • Tan, W.C.1    Pan, W.X.2    Xu, M.Y.3
  • 25
    • 11144231363 scopus 로고    scopus 로고
    • Unsteady flows of a generalized second grade fluid with the fractional derivative model between two parallel plates
    • Tan W.C., Xu M.Y. Unsteady flows of a generalized second grade fluid with the fractional derivative model between two parallel plates. Acta Mech Sin 2004, 20:471-476.
    • (2004) Acta Mech Sin , vol.20 , pp. 471-476
    • Tan, W.C.1    Xu, M.Y.2
  • 26
    • 14544294370 scopus 로고    scopus 로고
    • Exact solutions for the unsteady rotational flow of non-Newtonian fluid in an annular pipe
    • Tong D.K., Liu Y.S. Exact solutions for the unsteady rotational flow of non-Newtonian fluid in an annular pipe. Int J Eng Sci 2005, 43:281-289.
    • (2005) Int J Eng Sci , vol.43 , pp. 281-289
    • Tong, D.K.1    Liu, Y.S.2
  • 27
    • 33644649045 scopus 로고    scopus 로고
    • Exact solutions for the flow of non-Newtonian fluid with fractional derivative in an annular pipe
    • Tong D., Ruihe W., Heshan W. Exact solutions for the flow of non-Newtonian fluid with fractional derivative in an annular pipe. Sci China, Ser G Phys, Mech Astron 2005, 48:485-495.
    • (2005) Sci China, Ser G Phys, Mech Astron , vol.48 , pp. 485-495
    • Tong, D.1    Ruihe, W.2    Heshan, W.3
  • 28
    • 33750495838 scopus 로고    scopus 로고
    • Unsteady flow of viscoelastic fluid with fractional Maxwell model
    • Qi H.T., Xu M.Y. Unsteady flow of viscoelastic fluid with fractional Maxwell model. Mech Res Commun 2007, 34:210-212.
    • (2007) Mech Res Commun , vol.34 , pp. 210-212
    • Qi, H.T.1    Xu, M.Y.2
  • 29
    • 44649157180 scopus 로고    scopus 로고
    • Flow of a generalized Oldroyd-B fluid due to a constantly accelerating plate
    • Vieru D., Fetecau C., Fetecau C. Flow of a generalized Oldroyd-B fluid due to a constantly accelerating plate. Appl Math Comp 2008, 201:834-842.
    • (2008) Appl Math Comp , vol.201 , pp. 834-842
    • Vieru, D.1    Fetecau, C.2    Fetecau, C.3
  • 30
    • 56549125687 scopus 로고    scopus 로고
    • Axial Couette flow of two kinds of fractional viscoelastic fluids in an annulus
    • Wang S.W., Xu M.Y. Axial Couette flow of two kinds of fractional viscoelastic fluids in an annulus. Non linear Anal Real World Appl 2009, 10:1087-1096.
    • (2009) Non linear Anal Real World Appl , vol.10 , pp. 1087-1096
    • Wang, S.W.1    Xu, M.Y.2
  • 31
    • 77952240591 scopus 로고    scopus 로고
    • Some helical flow of a generalized Oldroyd-B fluid in a circular cylinder
    • Fetecau C., Mahmood A., Fetecau C., Veiru D. Some helical flow of a generalized Oldroyd-B fluid in a circular cylinder. Nonlinear Anal Real World Appl 2009, 56:3096-3108.
    • (2009) Nonlinear Anal Real World Appl , vol.56 , pp. 3096-3108
    • Fetecau, C.1    Mahmood, A.2    Fetecau, C.3    Veiru, D.4
  • 32
    • 48249084496 scopus 로고    scopus 로고
    • Some exact solutions for fractional generalized Burger's fluid in a porous space
    • Khan M., Hayat T. Some exact solutions for fractional generalized Burger's fluid in a porous space. Nonlinear Anal: Real World Appl 2007, 9:1965-1975.
    • (2007) Nonlinear Anal: Real World Appl , vol.9 , pp. 1965-1975
    • Khan, M.1    Hayat, T.2
  • 33
    • 77955922917 scopus 로고    scopus 로고
    • Exact solutions of generalized Oldroyd-B fluid subject to a time-dependent shear stress in a pipe
    • Rubbab Qammar, Husnain S.M., Mahmood A. Exact solutions of generalized Oldroyd-B fluid subject to a time-dependent shear stress in a pipe. J Prime Res Math 2009, 5:139-148.
    • (2009) J Prime Res Math , vol.5 , pp. 139-148
    • Rubbab, Q.1    Husnain, S.M.2    Mahmood, A.3
  • 34
    • 85196192493 scopus 로고    scopus 로고
    • Generalized functions for the fractional calculus. NASA/TP-1999-209424/Rev1
    • Lorenzo CF, Hartley TT. Generalized functions for the fractional calculus. NASA/TP-1999-209424/Rev1; 1999.
    • (1999)
    • Lorenzo, C.F.1    Hartley, T.T.2
  • 40
    • 85196139915 scopus 로고
    • Handbook of mathematical functions. NBS, Appl Math Ser, Washington, DC
    • Abramowitz M, Stegun IA. Handbook of mathematical functions. NBS, Appl Math Ser, vol. 55, Washington, DC; 1964.
    • (1964) , vol.55
    • Abramowitz, M.1    Stegun, I.A.2
  • 41
    • 85196168140 scopus 로고
    • Transformation integral et calculus operational. Editions Mir-Moscou
    • Ditkin V, Proudnicov A, Transformation integral et calculus operational. Editions Mir-Moscou; 1987.
    • (1987)
    • Ditkin, V.1    Proudnicov, A.2
  • 42
    • 77953926210 scopus 로고    scopus 로고
    • Exact solution of some helical flows of Newtonian fluids
    • Siddique I. Exact solution of some helical flows of Newtonian fluids. Proc World Acad Sci, Eng Tech 2008, 33:664-667.
    • (2008) Proc World Acad Sci, Eng Tech , vol.33 , pp. 664-667
    • Siddique, I.1
  • 43
    • 85196207386 scopus 로고    scopus 로고
    • On the helical flow of Newtonian fluid induced by time dependent shear. In: Proceedings of the tenth int conf Zargoza-Pau on appl math and statistics. Jaca, september, in press
    • Akhtar W, Nazar M. On the helical flow of Newtonian fluid induced by time dependent shear. In: Proceedings of the tenth int conf Zargoza-Pau on appl math and statistics. Jaca, september 2008, in press.
    • (2008)
    • Akhtar, W.1    Nazar, M.2
  • 44
    • 85196216261 scopus 로고    scopus 로고
    • Axial Couette flow for a second grade fluid due to a longitudinal time-dependent shear stress. In: Proceedings of the tenth int conf Zaragoza-Pau on appl math and statistics. Jaca, september, in press
    • Nazar M, Akhtar M, Akhtar W. Axial Couette flow for a second grade fluid due to a longitudinal time-dependent shear stress. In: Proceedings of the tenth int conf Zaragoza-Pau on appl math and statistics. Jaca, september 2008, in press.
    • (2008)
    • Nazar, M.1    Akhtar, M.2    Akhtar, W.3
  • 45
    • 85015257003 scopus 로고    scopus 로고
    • On the axial Couette flow for a Maxwell fluid due to a longitudinal time-dependent shear stress
    • Akhtar W., Jamil M. On the axial Couette flow for a Maxwell fluid due to a longitudinal time-dependent shear stress. Bull Inst Poly Iasi 2009, 55(59)(1):11-17.
    • (2009) Bull Inst Poly Iasi , Issue.1 , pp. 11-17
    • Akhtar, W.1    Jamil, M.2
  • 46
    • 77955771349 scopus 로고    scopus 로고
    • A note on the unsteady flow of a generalized second-grade fluid through a circular cylinder subject to a time-dependent shear stress
    • doi: 10.1016/j.nonrwa.2009.06.010
    • Nazar M, Fetecau Corina, Awan AU. A note on the unsteady flow of a generalized second-grade fluid through a circular cylinder subject to a time-dependent shear stress. Nonlinear Anal: Real World Appl. doi: 10.1016/j.nonrwa.2009.06.010.
    • Nonlinear Anal: Real World Appl.
    • Nazar, M.1    Corina, F.2    Awan, A.U.3


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