Unsteady flows of a generalized second grade fluid with the fractional derivative model between two parallel plates

Acta Mechanica Sinica/Lixue Xuebao

Volumn 20, Issue 5, 2004, Pages 471-476

  Tan, Wenchang ^a   Xu, Mingyu ^b  

^a PEKING UNIVERSITY   (China)

^b SHANDONG UNIVERSITY   (China)

Author keywords

Fractional derivative; Generalized second grade fluid; Parallel plates; Unsteady flows

Indexed keywords

FOURIER TRANSFORMS; LAPLACE TRANSFORMS; OSCILLATIONS; PLATES (STRUCTURAL COMPONENTS); SHEAR STRESS;

CONSTITUTIVE RELATIONSHIP MODEL; FRACTIONAL DERIVATIVE MODEL; GENERALIZED SECOND GRADE FLUID; NON NEWTONIAN FLUID; PARALLEL PLATES;

UNSTEADY FLOW;

EID: 11144231363     PISSN: 05677718     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf02484269     Document Type: Article

References (25)

1. Ghosh NC, Ghosh BC, Debnath L. The hydromagnetic flow of a dusty visco-elastic fluid between two infinite parallel plates. Computers and Math With Applications, 2000, 39: 103-116
2. Rajagopal KR, Bhatnagar KR. Exact solutions for some simple flows of an Oldroyd-B fluid. Acta Mechanica, 1995, 113: 233-239
3. Erdogan ME. Plane surface suddenly set in motion in a non-Newtonian fluid. Acta Mechanica, 1995, 108: 179-187
4. Siddiqui AM, Hayat T, Asghar S. Periodic flows of a non-Newtonian fluid between two parallel plates. Int J of Non-Linear Mechanics, 1999, 34: 895-899
5. Hayat T, Asghar S, Siddiqui AM. Periodic unsteady flows of a non-Newtonian fluid. Acta Mechanica, 1998, 131: 169-175
6. Siddiqui AM. Certain inverse solutions of the plane creeping flow of a second-order fluid, Acta Mechanica, 1998, 129: 263-271
7. Rajagopal KR. A note on unsteady unidirectional flows of a non-Newtonian fluid. Int J Non-Linear Mechanics, 1982, 17(5): 369-373
8. Hayat T, Asghar S, Siddiqui AM. Some unsteady unidirectional flows of a non-Newtonian fluid. Int J of Eng Sci, 2000, 38: 337-346
9. Rossihin YA, Shitikova MV. A new method for solving dynamic problems of fractional derivative viscoelasticity. Int J of Eng Sci, 2001, 39: 149-176
10. Friedrich C. Relaxation and retardation function of the Maxwell model with fractional derivative. Rheology Acta, 1998, 30: 151-158
11. Huang JQ, He GY, Liu CQ. Analysis of general second-order fluid flow in double cylinder rheometer. Science in China (Series A), 1997, 40(2): 183-190
12. Xu MY, Tan WC. Theoretical analysis of the velocity field, stress field and vortex sheet of generalized second order fluid with fractional anomalous diffusion. Science in China (Series A), 2001, 44(11): 1387-1399
13. Tan WC, Xu MY. The impulsive motion of flat plate in a generalized second grade fluid. Mechanics Research Communications, 2002, 29(1): 3-9
14. Tan WC, Pan WX, Xu MY. A note on unsteady flows of a viscoelastic fluid with the fractional Maxwell model between two parallel plates. Int J of Non-Linear Mech, 2003, 38(5): 645-650
15. Li J, Jiang TQ. The Research on Viscoelastic Constitutive Relationship Model with Fractional Derivative Operator. Guangzhou: South China Technological University Press, 1993 (in Chinese)
16. Song DY. Study of rheological characterization of fenugreek gum with modified Maxwell. J Chem Eng, 2000, 8: 85-88
17. Song DY, Jiang TQ. Study on the constitutive equation with fractional derivative for the viscoelastic fluids-modified Jeffreys model and its application. Rheologica Acta, 1998, 27: 512-517
18. Schiessel H, Metzler R, Blumen A, et al. Generalized viscoelastic models: their fractional equations with solutions. J Phys A: Math Gen, 1995, 28: 6567-6584
19. Palade LI, Attane P, Huilgol RR, et al. Anomalous stability behavior of a properly invariant constitutive equation which generalizes fractional derivative models. Int J of Eng Sci, 1999, 37: 315-329
20. Rossihin YA, Shitikova MV. A new method for solving dynamic problems of fractional derivative viscoelasticity. Int J of Eng Sci, 2001, 39: 149-176
21. Bagley RL. A theoretical basis for the application of fractional calculus to viscoelasticity. J of Rheology, 1983, 27(3): 201-210
22. Podlubny I. Fractional Differential Equations. San Diego: Academic Press, 1999
23. Metzler R, Klafter J. Boundary value problems for fractional diffusion equations. Physica A, 2000, 278: 107-125
24. Hilfer R. Applications of Fractional Calculus in Physics. Singapore: World Scientific Press, 2000
25. Tan WC, Xu MY. Plane surface suddenly set in motion in a viscoelastic fluid with fractional Maxwell model. Acta Mechanica Sinica, 2002, 18(4): 342-349