Exact Solutions on the Oscillating Plate of Maxwell Fluids

Abstract

This work is related to establish the exact solutions of sine hyperbolic and cosine hyperbolic oscillations of Maxwell fluid over the velocity field and shear stress. Under the effects of sine hyperbolic and cosine hyperbolic oscillations, the general solutions are derived for the motions of incompressible Maxwell fluid. For the sack of the general solutions the mathematical techniques of integral transformations (Laplace and Fourier Sine transforms) are applied. We have expressed the obtained solutions under form of theorem of convolutions product and integral notation, satisfying the boundary and initial conditions. The expressions for similar solutions are specialized as a limiting case of Newtonian fluid