Solutions of Stokes Second Problem for Casson Fluid over an Infinite Plate: A Comparison of the Laplace and Fourier Transforms

Abstract

The unsteady flow of Casson fluid over a plane wall, which is initially at rest and the plate suddenly starts oscillations in its own plane is studied by mean of Laplace transform method and Fourier transform method. The solutions are obtained as a sum of steady and transient solutions, which satisfy the governing equation and all impose initial and boundary conditions. The comparison of the solutions obtained by two integral transform methods is presented in graphical illustrations. The transient parts are found in terms of definite integrands whose integral are oscillatory function. Finally, these solutions are graphically shown and discussed.