First Problem of Stokes for Generalized Burgers' Fluids

Muhammad Jamil

doi:10.5402/2012/831063

Abstract

The velocity field and the adequate shear stress corresponding to the first problem of Stokes for generalized Burgers’ fluids are determined in simple forms by means of integral transforms. The solutions that have been obtained, presented as a sum of steady and transient solutions, satisfy all imposed initial and boundary conditions. They can be easily reduced to the similar solutions for Burgers, Oldroyd-B, Maxwell, and second-grade and Newtonian fluids. Furthermore, as a check of our calculi, for small values of the corresponding material parameters, their diagrams are almost identical to those corresponding to the known solutions for Newtonian and Oldroyd-B fluids. Finally, the influence of the rheological parameters on the fluid motions, as well as a comparison between models, is graphically illustrated. The non-Newtonian effects disappear in time, and the required time to reach steady-state is the lowest for Newtonian fluids.

Highlights

There is evidence that the interest of the workers in non-Newtonian fluids is on the leading edge during the last few years
In spite of several challenges, ISRN Mathematical Physics many investigations regarding the analytic solutions for flows of non-Newtonian fluids have been performed 4–19
The purpose of this work is to established exact solutions corresponding to the first problem of Stokes for generalized Burgers’ fluids

Summary

Introduction

There is evidence that the interest of the workers in non-Newtonian fluids is on the leading edge during the last few years. Many researchers have the opinion that flows of such fluids are important in industry and technology. It is an established fact that unlike the Newtonian fluids, the flows of non-Newtonian fluids cannot be analyzed by a single constitutive equation. This is due to the rheological properties of non-Newtonian fluids. To obtain an analytic solution for such flows is not an easy task. In spite of several challenges, ISRN Mathematical Physics many investigations regarding the analytic solutions for flows of non-Newtonian fluids have been performed 4–19

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Conclusion