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

Boundary value problems

Muhammad Jamil²  Constantin Fetecau³ 

[1] Technology, Pakistan;Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan;Department of Mathematics, NED University of Engineering &

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

DOI  :  10.1186/1687-2770-2012-14

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY