First Problem of Stokes for Generalized Burgers' Fluids

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.