On the comparison of the solutions obtained by using two different transform methods for the second problem of Stokes for Newtonian fluids


Erdogan M. E. , İmrak C. E.

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, vol.44, no.1, pp.27-30, 2009 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 44 Issue: 1
  • Publication Date: 2009
  • Doi Number: 10.1016/j.ijnonlinmec.2008.08.004
  • Title of Journal : INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS
  • Page Numbers: pp.27-30

Abstract

The unsteady flow over a plane wall which is initially at rest and the plate begins suddenly to oscillate in own plane is considered. The Solution subject to the boundary and initial conditions is obtained by applying to the governing equation the Laplace transform method or Fourier transform method. A comparison of the solutions obtained by two transform methods for flow considered is given. It is shown that the solution obtained by the Laplace transform method or Fourier transform method is the sum of the steady-state and the transient parts. The transient parts are found in terms of definite integrands whose integrals are oscillatory functions. Therefore, the transient parts are expressed in terms of the tabulated functions. (C) 2008 Elsevier Ltd. All rights reserved.