Font Size:
Some exact solutions for the rotational flow of a generalized second-grade fluid between two circular cylinders
Arch. Mech. 60 (5), 385-401, 2008
Keywords: generalized second-grade fluid; velocity field; shear stress; fractional calculus; Hankel and Laplace transforms
Abstract
The velocity field and the associated tangential stress corresponding to the flow of a generalized second-grade fluid between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. At time t = 0, the fluid is at rest and at t = 0+ the cylinders suddenly begin to rotate about their common axis with a constant angular acceleration. The solutions that have been obtained satisfy the governing differential equations and all the imposed initial and boundary conditions. The similar solutions for a second-grade fluid and Newtonian fluid are recovered from our general solutions. The influence of the fractional coefficient on the velocity of the fluid is also analyzed by graphical illustrations.