Exact solutions of Stokes' first problem for heated generalized Burgers' fluid in a porous half-space

Nonlinear Analysis: Real World Applications

Volumn 9, Issue 4, 2008, Pages 1628-1637

  Xue, Changfeng ^a   Nie, Junxiang ^b  

^a YANCHENG INSTITUTE OF TECHNOLOGY   (China)

^b BEIJING JIAOTONG UNIVERSITY   (China)

Author keywords

Burgers' fluid; Fractional calculus; Heat transfer; Porous medium; Stokes' first problem

Indexed keywords

COMPUTATION THEORY; FLUID DYNAMICS; HEAT TRANSFER; LAPLACE TRANSFORMS; MAXWELL EQUATIONS; NAVIER STOKES EQUATIONS;

FOURIER SINE TRANSFORMS; FRACTIONAL CALCULUS; HEATED BURGER'S FLUID; STOKES' FIRST PROBLEM;

NONLINEAR ANALYSIS;

EID: 43649105279     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2007.04.007     Document Type: Article

References (39)

1. Al-Hadhrami A.K., Elliott L.D.B., and Ingham D.B. Combined free and forced convection in vertical channels of porous media. Transp. Porous Med. 49 (2002) 265-289
2. Al-Hadhrami A.K., Elliott L.D.B., and Ingham D.B. A new model for viscous dissipation in porous media across a range of permeability values. Transp. Porous Med. 53 (2003) 117-122
3. Bagley R.L. A theoretical basis for the application of fractional calculus to viscoelasticity. J. Rheol. 27 (1983) 201-210
4. Bandelli R., and Rajagopal K.R. Start-up flows of second grade fluids in domains with one finite dimension. Int. J. Non-Linear Mech. 30 (1995) 817-839
5. Eckert E.R.G., and Drake R.M. Analysis of Heat and Mass Transfer (1977), McGraw-Hill, New York
6. Fetecau C., and Fetecau C. The Rayleigh-Stokes problem for heated second grade fluids. Int. J. Non-Linear Mech. 37 (2002) 1011-1015
7. Friedrich C.H.R. Relaxation and retardation function of the Maxwell model with fractional derivatives. Rheol. Acta 30 (1991) 151-158
8. He G.Y., Huang J.Q., and Liu C.Q. General second order fluid flow in a pipe. Appl. Math. Mech. 16 (1995) 767-773
9. Huang J.Q., He G.Y., and Liu C.Q. Analysis of general second-order fluid flow in double cylinder rheometer. Sci. China (Ser. A) 40 (1997) 183-190
10. Huilgol R.R. Vortex sheet in viscoelastic liquids-the Rayleigh problem. J. Non-Newtonian Fluid Mech. 8 (1981) 337-347
11. Jordan P.M., Puri A., and Boros G. On a new exact solution to Stokes' first problem for Maxwell fluids. Int. J. Non-Linear Mech. 39 (2004) 1371-1377
12. Jordan P.M., and Puri P. Stokes' first problem for a Rivlin-Ericksen fluid of second grade in a porous half-space. Int. J. Non-Linear Mech. 38 (2003) 1019-1025
13. Luchini P., and Bottaro A. Linear stability and receptivity analyses of the Stokes layer produced by an impulsively started plate. Phys. Fluids 13 (2001) 1668-1678
14. Masuoka T., and Takatsu Y. Turbulence characteristics in porous media. In: Derek B.I., and Pop I. (Eds). Transport Phenomena in Porous Media vol. II (2002), Elsevier, Boston 231-256
15. Morrison J.A. Wave propagation in rods of Voigt material and viscoelastic material with three parameter models. Q. J. Mech. Appl. Math. 14 (1956) 153-162
16. Nield D.A., and Adrian B. Convection in Porous Media. second ed. (1999), Springer, Berlin
17. Nield D.A., Kuznetsov A.V., and Xing M. Thermally developing forced convection in a porous medium: parallel plate channel with walls at uniform temperature, with axial conduction and viscous dissipation effects. Int. J. Heat Mass Transfer 46 (2003) 643-651
18. Phan-Thien N., and Chew Y.T. On the Rayleigh problem for a viscoelastic fluid. J. Non-Newtonian Fluid Mech. 28 (1988) 117-127
19. Podlubny I. Fractional Differential Equations (1999), Academic Press, San Diego pp. 1-303
20. Preziosi L., and Joseph D.D. Stokes first problem for viscoelastic fluids. J. Non-Newtonian Fluid Mech. 25 (1987) 239-259
21. Schlichting H., and Gersten K. Boundary Layer Theory. eighth ed. (2000), Springer, Berlin
22. Shen F., Tan W.C., Zhao Y.H., and Masuoka T. Decay of vortex and diffusion of temperature in a generalized second grade fluid. Appl. Math. Mech. 25 (2004) 1151-1159
23. Shen F., Tan W.C., Zhao Y.H., and Masuoka T. The Rayleigh-Stokes problem for a heated generalized second grade fluid with fractional derivative model. Nonlinear Anal.: Real World Appl. 7 (2006) 1072-1080
24. Tan W.C. Velocity overshoot of start-up flow for a Maxwell fluid in a porous half-space. Chin. Phys. 15 (2006) 2644-2650
25. Tan W.C., and Masuoka T. Stokes' first problem for a second grade fluid in a porous half-space with heated boundary. Int. J. Non-Linear Mech. 40 (2005) 515-522
26. Tan W.C., and Masuoka T. Stokes' first problem for an Oldroyd-B fluid in a porous half-space. Phys. Fluids 17 (2005) 023101-7
27. Tan 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
28. Tan W.C., Pan W.X., and 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. 38 (2003) 645-650
29. Tan W.C., Xian F., and Wei L. An exact solution of unsteady Couette flow of generalized second grade fluid. Chin. Sci. Bull. 47 (2002) 1783-1785
30. Tan W.C., and Xu M.Y. The impulsive motion of flat plate in a general second grade fluid. Mech. Res. Commun. 29 (2002) 3-9
31. Tan W.C., and Xu M.Y. Plane surface suddenly set in motion in a viscoelastic fluid with fractional Maxwell mode. Acta Mech. Sin. 18 (2002) 342-349
32. 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
33. Tanner R. Notes on the Rayleigh parallel problem for a viscoelastic fluid. Z Angew. Math. Phys. 13 (1962) 573-579
34. Teipel I. The impulsive motion of a flat plate in a viscoelastic fluid. Acta Mech. 39 (1981) 277-279
35. Vafai K., and Tien C.L. Boundary and inertia effects on flow and heat transfer in porous media. Int. J. Heat Mass Transfer 24 (1981) 195
36. Xu M.Y., and Tan W.C. 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 (2001) 1387-1399
37. Xu M.Y., and Tan W.C. The representation of the constitutive equation of viscoelastic materials by the generalized fractional element networks and its generalized solutions. Sci. China (Ser. A) 32 (2002) 673-681
38. Xu M.Y., and Tan W.C. Intermediate processes and critical phenomena: theory, method and progress of fractional operators and their applications to modern mechanics. Sci. China (Ser. G) 49 (2006) 257-272
39. Younes A. On modeling the multidimensional coupled fluid flow and heat or mass transport in porous media. Int. J. Heat Mass Transfer 46 (2003) 367-379