Exact solutions of accelerated flows for a Burgers' fluid. I. The case γ<λ2/4

In this paper, we derive the exact solutions of accelerated flows for a Burgers' fluid. The expressions for the velocity field and the associated tangential stress to the flows of a Burgers' fluid induced by the accelerating flat plate are established when the relaxation times satisfy the condition γ<λ2/4. Employing the Laplace transform, the exact solutions are developed for the following two problems: (i) constantly accelerating flow and (ii) variable accelerating flow. The corresponding solutions for a Newtonian, second grade, Maxwell and Oldroyd-B fluids appear as the limiting cases of the presented analysis.