Open Access Research

Starting solutions for the motion of a generalized Burgers' fluid between coaxial cylinders

Muhammad Jamil12* and Constantin Fetecau13

Author Affiliations

1 Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan

2 Department of Mathematics, NED University of Engineering & Technology, Karachi-75270, Pakistan

3 Department of Mathematics, Technical University of Iasi, Iasi-700050, Associate member of Academy of Romanian Scientists, 050094 Bucarest, Romania

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Boundary Value Problems 2012, 2012:14  doi:10.1186/1687-2770-2012-14

Published: 10 February 2012

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.

Keywords:
Generalized Burgers' fluid; coaxial cylinders; velocity field; time-dependent shear stress; Laplace and Hankel transforms