Travelling wave solutions to Stokes' problem for a fourth grade fluid

Applied Mathematical Modelling

Volumn 33, Issue 3, 2009, Pages 1613-1619

  Hayat, T ^a,b   Kara, A H ^b   Momoniat, E ^b  

^a QUAID I AZAM UNIVERSITY   (Pakistan)

^b UNIVERSITY OF THE WITWATERSRAND   (South Africa)

Author keywords

Fourth grade fluid; Lie point symmetries; Numerical solution; Stokes' problem

Indexed keywords

SOLUTIONS; WAVE TRANSMISSION;

FOURTH GRADE FLUID; LIE POINT SYMMETRIES; LINEAR PARTIAL DIFFERENTIAL EQUATIONS; MODEL EQUATIONS; NUMERICAL SOLUTION; STOKES' PROBLEM; TRAVELLING WAVES;

LINEAR EQUATIONS;

EID: 55549111597     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2008.02.014     Document Type: Article

References (21)

1. Rajagopal K.R. On boundary conditions for fluids of the differential type. In: Sequira A. (Ed). Navier-Stokes Equations and Related Non-linear Problems (1995), Plenum Press, New York 273-278
2. Rajagopal K.R. Boundedness and uniqueness of fluids of the differential type. Acta Cienca Indica 18 (1982) 1-11
3. Rajagopal K.R., Szeri A.Z., and Troy W. An existence theorem for the flow of a non-Newtonian fluid past an infinite porous plate. Int. J. Non-linear Mech. 21 (1986) 279-289
4. Rajagopal K.R., and Kaloni P.N. Some remarks on boundary conditions for fluids of differential type. In: Graham G.A.C., and Malik S.K. (Eds). Continuum Mechanics and its Applications (1989), Hemisphere, New York 935-942
5. Rajagopal K.R., and Gupta A.S. An exact solution for the flow of a non-Newtonian fluid past an infinite plate. Meccanica 19 (1984) 158-160
6. Schowalter W.R. Mechanics of Non-Newtonian Fluids (1978), Oxford, Pergamon
7. Huilgol R.R. Continuum Mechanics of Viscoelastic Liquids (1975), Hindustan Publishing Corporation, Delshi
8. Rajagopal K.R. Mechanics of non-Newtonian fluids. In: Galdi G.P.J. (Ed). Recent developments in theoretical fluid mechanics. Pitman Res. Notes Math. Ser. 291 (1983) 129-162
9. Beavers G.S., and Joseph D.D. The rotating rod viscometer. J. Fluid Mech. 69 (1975) 475-511
10. Joseph D.D., Beavers G.S., and Fosdick R.L. The free surface on a liquid between cylinders rotating at different speeds Part II. Arch. Ration. Mech. Anal. 49 (1973) 381-401
11. Straughan B. Explosive Instabilities in Mechanics (1998), Springer
12. Rajagopal K.R., and Na T.Y. On Stoke's problem for a non-Newtonian fluid. Acta Mech. 48 (1983) 233-239
13. Erdogan M.E. Plane surface suddenly set in motion in a non-Newtonain fluid. Acta Mech. 108 (1995) 179-187
14. Akylidiz F.T. A note on the flow of non-Newtonian fluid film. Int. J. Non-linear Mech. 33 (1998) 1061-1067
15. Mollica F., and Rajagopal K.R. Secondary flows due to axial shearing of a third grade fluid between two eccentrically placed cylinders. Int. J. Eng. Sci. 37 (1999) 411-429
16. Hayat T., Wang Y., and Hutter K. Flow of fourth grade fluid. Math. Models Methods Appl. Sci. 12 (2002) 797-811
17. Dunn J.E., and Fosdick R.L. Thermodynamics stability and boundedness of fluids of complexity 2 and fluids of second grade. Arch. Ration. Mech. Anal. 56 (1974) 191-252
18. Fosdick R.L., and Rajagopal K.R. Anomalous features in the model of second-order fluids. Proc. Roy. Soc. Lond. A339 (1980) 351-377
19. Dunn J.E., and Rajagopal K.R. Fluids of differential type-critical review and thermodynamic analysis. Int. J. Eng. Sci. 33 (1995) 689-729
20. Bluman G., and Kumei S. Symmetries and Differential Equations (1986), Springer, New York
21. Olver P. Applications of Lie Groups to Differential Equations (1986), Springer, New York