Some oscillating motions of a Burgers' fluid

In this work, the exact analytic solutions for some unsteady oscillating flows of an incompressible Burgers' fluid in a duct of rectangular cross-section are considered. Here, two types of flows, namely, (1) flow due to the oscillating pressure gradient, and (2) flow due to the oscillation of duct parallel to its length, were considered. The exact analytical expressions for the velocity field and the adequate shear stress are determined by means of the Laplace and Fourier sine transforms. They are written as a sum of steady and transient solutions and satisfy all imposed initial and boundary conditions. The effects of the indispensable parameters of the flow are graphically analyzed. Moreover, similar solutions for Oldroyd-B, Maxwell, Newtonian fluid, and for the flows induced by a constant pressure gradient and impulsive motion of duct are obtained as the limiting cases of the presented solutions.