An Exact Solution for an Unsteady Flow of a Generalized Burgers' Fluid Induced by an Accelerating Plate

This paper presents a theoretical study on an unsteady flow of a generalized Burgers' fluid on an infinite flat plate subject to a translation motion with a power law time-dependent velocity in its plane. The fractional calculus is used to establish the constitutive relationship of the viscoelastic Burgers' fluid. An exact solution is obtained for velocity field by employing the Fourier sine transform and the fractional Laplace transform in terms of Mittag-Leffler function. It is shown that some classical results in the literature can be considered as special cases of our results. Furthermore, the numerical results are given for different cases and the velocity-field property is discussed.