Abstract
The unsteady flow of a generalized Burgers' fluid, between two infinite coaxial circular cylinders, is studied by means of the Laplace and finite Hankel transforms. The motion of the fluid is produced by the inner cylinder that, after the initial moment, applies a longitudinal time dependent shear to the fluid. The solutions that have been obtained, presented in series form in terms of usual Bessel functions, satisfy all imposed initial and boundary conditions. Moreover, the corresponding solutions for Burgers' fluids appear as special cases of present results. For large values of t, these solutions are going to the steady solutions that are the same for both kinds of fluids. Finally, the influence of the material parameters on the fluid motion, as well as a comparison between models, is shown by graphical illustrations.Mathematics Subject Classification (2010). 76A05; 76A10.
Highlights
Considerable attention has been focused to study the behavior of non-Newtonian fluids
Non-Newtonian fluids form a broad class of fluids in which the relation connecting the shear stress and shear rate is nonlinear and there is no universal constitutive model available which exhibits the characteristics of all non-Newtonian fluids
For large values of t, all solutions tend to the steady solutions vS(r,t) and τS(r,t) which are the same for all kinds of fluids the motion of rate type fluids is due to a time dependent shear stress on the boundary
Summary
Considerable attention has been focused to study the behavior of non-Newtonian fluids. The first exact solutions for motions of non-Newtonian fluids due to a circular cylinder that applies a longitudinal or rotational shear stress to the fluid are those of Bandelli and Rajagopal [13, Sects.
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