Hall effects on unsteady motions of a generalized second-grade fluid through a porous medium

Journal of Porous Media

Volumn 9, Issue 8, 2006, Pages 779-788

  Nadeem, S ^a  

^a QUAID I AZAM UNIVERSITY   (Pakistan)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIATION (CALCULUS); LAPLACE TRANSFORMS; POROUS MATERIALS; UNSTEADY FLOW;

FRACTIONAL CALCULUS; FRACTIONAL DERIVATIVES; IMPULSIVE FLOW;

HALL EFFECT;

EID: 33847672710     PISSN: 1091028X     EISSN: None     Source Type: Journal    
DOI: 10.1615/JPorMedia.v9.i8.60     Document Type: Article

References (40)

1. Ariel, P. D., Flow of a third grade fluid through a porous flat channel, Int. J. Eng. Sci., vol. 41, pp. 1267-1285, 2003.
2. Asghar, S., Parveen, S., Hanif, S., Siddiqui, A. M., and Hayat, T., Hall effects on the unsteady hydromagnetic flows of an Oldroyd-B fluid, Int. J. Eng. Sci., vol. 41, pp. 609-619, 2003.
3. Benharbit, A. M., and Siddiqui, A. M., Certain solutions of the equations of the planar motion of a second grade fluid for steady and unsteady cases, Acta Mech., vol. 94, pp. 85-96, 1992.
4. Dunn, J. E., and Rajagopal, K. R., Fluids of differential type-critical review and thermodynamic analysis, Int. J. Eng. Sci., 33, pp. 689-729, 1995.
5. Dunn, J. E., and Fosdick, R. L., Thermodynamic stability and boundedness of fluids of complexity 2 and fluids of second grade, Arch. Rat. Mech. Anal., vol. 56, pp. 191-252, 1974.
6. El-Shahed, M., MHD of a fractional viscoelastic fluid in a circular tube, Mech. Res. Comm., pp. 261-268, 2006.
7. Erdogan, M. E., On the unsteady unidirectional flows generated by impulsive motion of a boundary or sudden application of a pressure gradient, Int. J. Non-Linear Mech., vol. 37, pp. 1091-1106, 2002.
8. Fosdick, R. L., and Rajagopal, K. R., Thermodynamic and stability of fluids of third grade, Proc. Roy. Soc. Lond. A, vol. 339, pp. 351-377, 1980.
9. Hayat, T., Asghar, S., and Siddiqui, A. M., On the moment of a plane disk in a non-Newtonian fluid, Acta Mech., vol. 136, pp. 125-131, 1999.
10. Hayat, T., Asghar, S., and Siddiqui, A. M., Periodic unsteady flows of a non-Newtonian fluid, Acta Mech., vol. 131, pp. 169-175, 1998.
11. Hayat, T., Hutter, K., Nadeem, S., and Asghar, S., Unsteady hydromagnetic rotating flow of a conducting second grade fluid, Z. Angew. Math. Phys., vol. 55, pp. 626-641, 2004.
12. Hayat, T., Wang, Y., and Hutter, K., Hall effects on the unsteady hydromagnetic oscillatory flow of a second grade fluid, Int. J. Non-Linear Mech., vol. 39, pp. 1027-1037, 2004.
13. Hilfer, R., Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
14. Khan, M., Nadeem, S., Hayat, T., and Siddiqui, A. M., Unsteady motions of a generalized second grade fluid, Math. Comp. Modell., vol. 41, pp. 629-637, 2005.
15. Mansutti, D., Pontrelli, G., and Rajagopal, K. R., Non-similar flow of a non-Newtonian fluid past a wedge, Int. J. Eng. Sci., vol. 31, pp. 637-647, 1993.
16. Miller, K. S., and Ross, B., An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, 1993.
17. Nield, D. A., and Bejan, A., Convection in Porous Media, 2nd ed., Springer, Berlin, 1999.
18. Oldroyd, J. G., On the formulation of rheological equations of state, Proc. Roy. Soc. Lond, Ser. A, vol. 200, pp. 523-541, 1950.
19. Palade, L. I., Attane, P., Huilgol, R. R., and Mena, B., Anomalous stability behavior of a properly invariant constitutive equation which generalizes fractional derivative models, Int. J. Eng. Sci., vol. 37, pp. 315-329, 1999.
20. Passerini, A., and Videman, J. H., Decay in time of kinetic energy of second and third grade fluids in unbounded domains, Monteiro Marques, M., and Rodrigues, J. F., (eds), emphTrends in Applications of Mathematics to Mechanics, Longman, New York, pp. 195-208, 1995.
21. Pileckas, K., Sequeira, A., and Videman, J. H., A note on steady flows of non-Newtonian fluids in channels and pipes, EQUADIFF, 95-International Conference on Differential Equations, Magalhaes, L., Rocha, C., and Sanchez, L., (eds), World Scientific, Singapore, pp. 458-467, 1998.
22. Rajagopal, K. R., and Gupta, A. S., An exact solution for the flow of a non-Newtonian fluid past an infinite porous plate, Meccanica, vol. 19, pp. 158-160, 1984.
23. Rajagopal, K. R., On boundary conditions for fluids of differential type, Navier-Stokes Equations and Related Nonlinear Problems, Sequeira, A., (eds), Plenum Press, New York, pp. 273-278, 1995.
24. Rajagopal, K. R., A note on unsteady unidirectional flows of a non-Newtonian fluid, Int. J. Non-Linear Mech., vol. 17, pp. 369-373, 1982.
25. Rajagopal, K. R., and Gupta, A. S., Flow and stability of a second grade fluid between two parallel plates rotating about non-coincident axes, Int. J. Eng. Sci., vol. 19, pp. 1401-1409, 1981.
26. Rajagopal, K. R., and Kaloni, P. N., Some remarks on boundary conditions for fluids of the differential type, Continuum Mechanics and its Applications, Burnby, B. C., (eds), Hemisphere, New York, pp. 935-942, 1989.
27. Rajagopal, K. R., and Na, T. Y., On Stokes problem for a non-Newtonian fluid, Acta Mech., vol. 48, pp. 233-239, 1983.
28. Rajagopal, K. R., Flow of viscoelastic fluids between rotating discs, Theor. Comput. Fluid Dyn., vol. 3, pp. 185-206, 1992.
29. Rajagopal, K. R., Mechanics of non-Newtonian fluids, Recent Developments in Theoretical Fluid Mechanics, Galdi, G. P., and Necas, J., (eds), Longman Scientific and Technical, New York, Pitman Research Notes in Mathematical Series, pp. 129-162, 1993.
30. Rajagopal, K. R., On creeping flow of a second order fluid, J. Non-Newtonian Fluid Mech., vol. 15, pp. 239-246, 1984.
31. Rajagopal, K. R., On the stability of third grade fluids, Arch. Rat. Mech. Anal., vol. 32, pp. 867-875, 1980.
32. Rivlin, R. S., and Ericksen, J. L., Stress-deformation relations for isotropic materials, J. Rat. Mech. Anal., vol. 3, pp. 323-425, 1955.
33. Rossikhin, Y. A., and Shitikova, M. V., A new method for solving dynamical problems of fractional derivative viscoelasticity, Int. J. Eng. Sci., vol. 39, pp. 149-176, 2001.
34. Sahimi, M., Flow phenomena and rocks. From continuum model to fractals, percolation, cellular automata, and simulated annealing, Rev. Mod. Phys., vol. 65, pp. 1393-1534, 1993.
35. Samko, S. G., Kilbas, A. A., and Marichev, O. I., Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, New York, 1993.
36. Siddiqui, A. M., Hayat, T., and Asghar, S., Periodic flows of a non-Newtonian fluid between two parallel plates, Int. J. Non-Linear Mach., vol. 34, pp. 895-899, 1999.
37. Tan, W. C., and Xu, M. Y., The impulsive motion of flat plate in a generalized second grade fluid, Mech. Res. Commun., vol. 29, pp. 3-9, 2002.
38. 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., vol. 38, pp. 615-650, 2003.
39. Tan, W. C., Xian, F., and Wei, L., An exact solution of unsteady Couette flow of generalized second grade fluid, Chin. Sci. Bull., vol. 47, pp. 1783-1785, 2002.
40. Truesdell, C., and Noll, W., The non-linear field theories of mechanics, Handbuch der Physik, W. Flugge (eds), Springer, Berlin, Vol. III/3, 1965.