On the Starting Solutions for Oscillating Motions of a Burgers Fluid

Abstract

In this thesis, a theoretical investigation is undertaken into some oscillatory ‡ motions uid generated in various geometries for a non-Newtonian ‡ uid. Exactly, we establish exact solutions for the fully developed laminar ‡ ows of an incompressible Burgers ‡ uid. The main theme of this work is to present the starting solutions concerning some fundamental ‡ ows with technical relevance in a Burgers ‡ for di¤erent ‡ geometries. The oscillating uid ow motion over a rigid plate when the relaxation time satis...es the conditions 2 =4 and > 2 < 2 =4; = =4; the oscillating ‡ between two side walls perpendicular to the plate and ow the ‡ generated by an oscillating pressure gradient as well as the ‡ due to the oscillation ow ow of a rectangular duct parallel to its length are considered. The analytical expressions for the velocity ...eld and the associated tangential stress are obtained in simple forms by means of integral transforms. These solutions, depending on the initial and boundary conditions, are presented as a sum of steady and transient solutions. A salient feature of the present study is that the corresponding solutions for Stokes’...rst problem and ‡ induced by a constant ow pressure gradient appear as the limiting cases of the presented results. In all cases studied the analytical procedure adopted yields consistent results and comparison with limiting solutions shows interesting aspects of the solutions. In order to shed light on some relevant physical aspects of the obtained results, the in‡ uence of the material parameters on the ‡ uid motion as well as comparison amongst models are underlined by graphical illustrations. It is worth pointing out that the velocity pro...le is found to be quite sensitive to the changes in the rheological parameter of the Burgers ‡ uid.