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

• Published in: Boundary value problems Vol. 2012; no. 1; pp. 1 - 15
• Main Authors: Jamil, Muhammad, Fetecau, Constantin
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 10.02.2012; Hindawi Limited; BioMed Central Ltd
• Subjects: Analysis; Approximations and Expansions; Bessel functions; Boundary value problems; Classification; Computational fluid dynamics; Cylinders; Difference and Functional Equations; Fluid flow; Fluids; Mathematical analysis; Mathematical models; Mathematics; Mathematics and Statistics; Ordinary Differential Equations; Partial Differential Equations; Laplace and Hankel transforms; velocity field; time-dependent shear stress; Generalized Burgers' fluid; coaxial cylinders
• ISSN: 1687-2770; 1687-2762; 1687-2770
• DOI: 10.1186/1687-2770-2012-14

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.