On solutions of some non-linear differential equations arising in third grade fluid flows

Abstract Numerical solutions for a class of non-linear second order differential equations arising in third grade fluid flows between rotating cylinders are obtained. Furthermore, using the Schauder theory and perturbation technique, existence, uniqueness and analyticity results are established. Moreover, the exact analytical solutions (in integral form) are obtained and are compared with the corresponding numerical solutions. The results obtained for the flow characteristics reveal many interesting behaviors that warrant further study of the effects of rotation on the flow characteristics.

[1]  K. Rajagopal,et al.  An exact solution for the flow of a non-newtonian fluid past an infinite porous plate , 1984 .

[2]  C. Truesdell,et al.  The Non-Linear Field Theories Of Mechanics , 1992 .

[3]  Kuppalapalle Vajravelu,et al.  Analytical and Numerical Solutions of Nonlinear Differential Equations Arising in Non-Newtonian Fluid Flows , 2000 .

[4]  J. E. Dunn,et al.  Thermodynamics, stability, and boundedness of fluids of complexity 2 and fluids of second grade , 1974 .

[5]  J. Lumley,et al.  Mechanics of non-Newtonian fluids , 1978 .

[6]  Kumbakonam R. Rajagopal,et al.  On the creeping flow of the second-order fluid , 1984 .

[7]  R. Rivlin,et al.  Stress-Deformation Relations for Isotropic Materials , 1955 .

[8]  Wilhelm Dipl.-Ing. Dr. techn Schneider,et al.  Trends in applications of mathematics to mechanics , 1991 .

[9]  G. Graham,et al.  Continuum mechanics and its applications , 1990 .

[10]  J. Oldroyd.  On the formulation of rheological equations of state , 1950, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[11]  K. Rajagopal.  On Boundary Conditions for Fluids of the Differential Type , 1995 .

[12]  Kumbakonam R. Rajagopal,et al.  Thermodynamics and stability of fluids of third grade , 1980, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[13]  M. C. Patria,et al.  Existence, uniqueness and stability of steady flows of second and third grade fluids in an unbounded “pipe-like” domain , 2000 .

[14]  Giovanni P. Galdi,et al.  Navier-Stokes Equations and Related Nonlinear Problems , 1995 .