Exact solutions for some oscillating motions of a fractional Burgers' fluid

Mathematical and Computer Modelling

Volumn 51, Issue 5-6, 2010, Pages 682-692

  Khan, M ^a   Anjum, Asia ^a   Fetecau, C ^b   Qi, Haitao ^c  

^a QUAID I AZAM UNIVERSITY   (Pakistan)

^b GHEORGHE ASACHI TECHNICAL UNIVERSITY OF IASI   (Romania)

^c SHANDONG UNIVERSITY   (China)

Author keywords

Burgers' fluid; Exact solutions; Fractional model; Oscillating motions

Indexed keywords

BURGERS' FLUID; CONSTITUTIVE RELATIONSHIP MODEL; CONTOUR INTEGRALS; EXACT SOLUTION; FLAT PLATE; FLOW PARAMETERS; FOURIER; FRACTIONAL CALCULUS; FRACTIONAL DERIVATIVES; FRACTIONAL MODEL; G FUNCTION; GENERAL SOLUTIONS; INTEGRAL TRANSFORM; LAPLACE TRANSFORM METHOD; LIMITING CASE; NEWTONIAN FLUIDS; OLDROYD-B; OSCILLATING FLOWS; OSCILLATING MOTION; OSCILLATING PRESSURE GRADIENT; SECOND-GRADE FLUID; SIMILAR SOLUTION; STARTING SOLUTIONS; VELOCITY FIELD;

COSINE TRANSFORMS; FLUIDS; INTEGRAL EQUATIONS; LAPLACE TRANSFORMS; MAXWELL EQUATIONS;

OSCILLATING FLOW;

EID: 74149090249     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2009.10.040     Document Type: Article

References (53)

1. Rajagopal K.R. A note on unsteady unidirectional flows of a non-Newtonian fluid. Internat. J. Non-Linear Mech. 17 (1982) 369-373
2. Bandelli R., and Rajagopal K.R. Start-up flows of second grade fluid in domain with one finite dimension. Internat. J. Non-Linear Mech. 30 (1995) 817-839
3. Rajagopal K.R. On the creeping flow of the second-order fluid. J. Non-Newton. Fluid Mech. 15 (1984) 239-246
4. Khan M., Fetecau C., and Hayat T. MHD transient flows in a channel of rectangular cross-section with porous medium. Phys. Lett. A 369 (2007) 44-54
5. Khan M., Ali S.H., Fetecau C., and Hayat T. MHD flow of a second grade fluid between two side walls perpendicular to a plate through a porous medium. Internat. J. Non-Linear Mech. 43 (2008) 302-319
6. Erdogan M.E., and Imrak C.E. On some unsteady flows of a non-Newtonian fluids. Appl. Math. Model. 31 (2007) 170-180
7. Fetecau C., Prasad S.C., and Rajagopal K.R. A note on the flow induced by a constantly accelerating plate in an Oldroyd-B fluid. Appl. Math. Model. 31 (2007) 647-654
8. Hayat T., Khan M., and Ayub M. Exact solutions of flow problem of an Oldroyd-B fluid. Appl. Math. Comput. 151 (2004) 105-119
9. Ariel P.D. On exact solutions of flow problems of a second grade fluid through two parallel porous walls. Internat. J. Engrg. Sci. 40 (2002) 913-941
10. Tan W.C., and Masuoka T. Stokes' first problem for an Oldroyd-B fluid in a porous half space. Phys. Fluids 17 (2005) 023101
11. Zhang Z., Fu C., Tan W.C., and Wang C.Y. Onset of oscillatory convection in a porous cylinder saturated with a viscoelastic fluid. Phys. Fluids 19 (2007) 098104
12. Fu C., Zhang Z., and Tan W.C. Numerical simulation of thermal convection of a viscoelastic fluid in a porous square box heated from below. Phys. Fluids 19 (2007) 104107
13. Tana W.C., and Masuoka T. Stability analysis of a Maxwell fluid in a porous medium heated from below. Phys. Lett. A 360 (2007) 454-460
14. Zhang Z., Fu C., and Tan W. Linear and nonlinear stability analyses of thermal convection for Oldroyd-B fluids in porous media heated from below. Phys. Fluids 20 (2008) 084103
15. Wanga S., and Tan W.C. Stability analysis of double-diffusive convection of Maxwell fluid in a porous medium heated from below. Phys. Lett. A 372 (2008) 3046-3050
16. Burgers J.M. Mechanical considerations-model system-phenomenological theories of relaxation of viscosity. In: Burgers J.M. (Ed). First Report on Viscosity and Plasticity (1935), Nordemann Publishing Company, New York
17. Krishnan J.M., and Rajagopal K.R. A thermodynamic framework for the constitutive modeling of asphalt concrete: Theory and application. J. Mater. Civ. Eng. 16 (2004) 155-166
18. Tovar C.A., Cerdeirina C.A., Romani L., Prieto B., and Carballo J. Viscoelastic behavior of Arzua-Ulloa cheese. J. Texture Stud. 34 (2003) 115-129
19. Wang M.C., and Lee K.Y. Creep behavior of cement stabilized soils. Highway Res. Record 442 (1973) 58-69
20. Krishnan J.M., and Rajagopal K.R. Review of the uses and modeling of bitumen from and ancient to modern times. ASME Mech. Rev. 56 (2003) 199-214
21. Ravindran P., Krishnan J.M., and Rajagopal K.R. A note on the flow of a Burgers' fluid in an orthogonal rheometer. Internat. J. Engrg. Sci. 42 (2004) 1973-1985
22. Fetecau C., Hayat T., and Fetecau C. Steady state solutions for some simple flows of generalized Burgers' fluid. Internat. J. Non-Linear Mech. 41 (2006) 880-887
23. Chen C.I., Hayat T., and Chen J.L. Exact solutions for the unsteady flow of a Burgers' fluid in a duct induced by time-dependent prescribed volume flow rate. Heat Mass Transfer 43 (2006) 85-90
24. Hayat T., Fetecau C., and Asghar S. Some simple flows of a Burgers' fluid. Internat. J. Engrg. Sci. 40 (2006) 1423-1431
25. Hayat T., Hussain M., and Khan M. Effect of Hall current on the flows of a Burgers' fluid through a porous medium. Transp. Porous Media 68 (2007) 249-263
26. Hayat T., Khan M., and Asghar S. On the MHD flow of fractional generalized Burgers' fluid with modified Darcy's law. Acta Mech. Sin. 23 (2007) 257-261
27. Hayat T., Maqbool M., and Khan M. Hall and heat transfer effects on the steady flow of a generalized Burgers' fluid induced by sudden pull of eccentric rotating disks. Nonlinear Dynam. 51 (2008) 267-276
28. Hayat T., Khan S.B., and Khan M. Influence of Hall current on the rotating flow of a Burgers' fluid through a porous space. J. Porous Med. 11 (2008) 277-287
29. 2 / 4. Appl. Math. Comput. 203 (2008) 881-894
30. Khan M., and Hayat T. Some exact solutions for fractional generalized Burgers' fluid in a porous space. Nonlinear Anal. RWA 9 (2008) 1952-1965
31. Penton R. The transient for Stokes' oscillating plane: A solution in terms of tabulated functions. J. Fluid Mech. 31 (1968) 810-825
32. Erdogan M.E. A note on an unsteady flow of a viscous fluid due to an oscillating plane wall. Internat. J. Non-Linear Mech. 35 (2000) 1-6
33. Rajagopal K.R. Longitudinal and torsional oscillations of a rod in a non-Newtonian fluid. Acta Mech. 49 (1983) 281-285
34. Rajagopal K.R., and Bhatnagar R.K. Exact solutions for some simple flows of an Oldroyd-B fluid. Acta Mech. 113 (1995) 233-239
35. Hayat T., Siddiqui A.M., and Asghar S. Some simple flows of an Oldroyd-B fluid. Internat. J. Engrg. Sci. 39 (2001) 135-147
36. Aksel N., Fetecau C., and Scholle M. Starting solutions for some unsteady unidirectional flows of Oldroyd-B fluids. Z. Angew. Math. Phys. 57 (2006) 815-831
37. Khan M., Asghar S., and Hayat T. Hall effect on the pipe flow of a Burgers' fluid: An exact solution. Nonlinear Anal. RWA 10 (2009) 974-979
38. Fetecau C., and Fetecau C. Starting solutions for some unsteady unidirectional flows a of a second grade fluid. Internat. J. Engrg. Sci. 43 (2005) 781-789
39. Fetecau C., and Fetecau C. Starting solutions for the motion of a second grade fluid due to longitudinal and torsional oscillations of a circular cylinder. Internat. J. Engrg. Sci. 44 (2006) 788-796
40. Bagley R.L. A theoretical basis for the application of fractional calculus to viscoelasticity. J. Rheol. 27 (1983) 201-210
41. Song D.Y. Study of rheological characterization of Fenu-Greek gum with modified Maxwell. J. Chem. Eng. 8 (2000) 85-88
42. Tan W.C., and Xu M.Y. Unsteady flows of a generalized second grade fluid with the fractional derivative model between two parallel plates. Acta Mech. Sin. 20 (2004) 471-476
43. Qi H.T., and Xu M.Y. Unsteady flow of viscoelastic fluid with fractional Maxwell model. Mech. Res. Comm. 34 (2007) 210-212
44. Qi H.T., and Xu M.Y. Stokes' first problem for a viscoelastic fluid with the generalized Oldroyd-B model. Acta Mech. Sin. 23 (2007) 463-469
45. Khan M., Maqbool K., and Hayat T. Influence of hall current on the flows of a generalized Oldroyd-B fluid in the porous space. Acta Mech. 184 (2006) 1-13
46. Khan M., and Wang S.W. Flow of a generalized second grade fluid between two side walls perpendicular to a plate with a fractional derivative model. Nonlinear Anal. RWA 10 (2009) 203-208
47. Fetecau C., Fetecau C., Khan M., and Vieru D. Decay of a potential vortex in a generalized Oldroyd-B fluid. Appl. Math. Comput. 205 (2008) 497-506
48. Tan W.C., Fu C., Fu C., Xie W., and Cheng H. An anomalous subdiffusion model for calcium spark in cardiac myocytes. Appl. Phys. Lett. 91 (2007) 183901
49. Podlubny I. Fractional Differential Equations (1999), Academic Press, Sen Diego
50. Sneddon I.N. Fourier Transforms (1951), McGraw-Hill Company, New York, Toronato, London
51. Stehfest H. Algorithms 368 numerical inversion of Laplace transform. Commun. ACM 13 (1970) 47-49
52. Stehfest H. Remark on algorithm 368 numerical inversion of Laplace transform. Commun. ACM 13 (1970) 624-625
53. Heibig A., and Palade L.I. On the rest state stability of an objective fractional derivative viscoelastic fluid model. J. Math. Phys. 49 (2008) 043101