화학공학소재연구정보센터
Chemical Engineering Communications, Vol.199, No.1, 17-39, 2012
Exact Analytic Solutions for the Flow of a Generalized Burgers Fluid Induced By an Accelerated Shear Stress
The rotational flow of a generalized Burgers fluid between two infinite coaxial cylinders is considered. The flow is produced by the inner cylinder when at time t = 0(+) a torsional time-dependent accelerated shear is applied to the fluid. The exact analytic solutions obtained with the help of Laplace and finite Hankel transforms and presented in series form in terms of Bessel functions of the first and second kinds satisfy all imposed initial and boundary conditions. The similar solutions for Burgers, Maxwell, second grade, and Newtonian fluids are easily obtained as limiting cases of general solutions for generalized Burgers and Oldroyd B fluids. Furthermore, for small values of the appropriate material parameters, the general solutions corresponding to generalized Burgers fluid are reduced to those for Oldroyd B and Newtonian fluids, respectively. Finally, the influence of the pertinent parameters on the fluid motion, as well as a comparison between models, is shown by graphical illustrations.