Exact solutions of nonlinear differential equations arising in third grade fluid flows
Abbreviated Journal Title
Int. J. Non-Linear Mech.
closed form solution; third grade fluid; rotating cylinder; STABILITY; THERMODYNAMICS; UNIQUENESS; EXISTENCE; Mechanics
Exact solutions for a class of non-linear second-order differential equations arising in a third grade fluid flow, at a rotating cylinder (unbounded domain case) and between rotating cylinders (bounded domain case), are obtained. Furthermore, the exact solutions are compared with the numerical ones. It is observed that the difference between the exact and the numerical solutions is about 1% for small R (the non-dimensional distance between the cylinders) and is about 3% when R = 100. This difference increases with an increasing R. Moreover, for large R it is not easy to obtain meaningful results numerically. Hence, these exact solutions for various values of the parameters R and omega (rotation parameter) are useful for experimental and numerical studies, and warrant further study. (C) 2004 Elsevier Ltd. All rights reserved.
International Journal of Non-Linear Mechanics
"Exact solutions of nonlinear differential equations arising in third grade fluid flows" (2004). Faculty Bibliography 2000s. 4178.