Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 641431, 10 pages
Exact Solutions of Rayleigh-Stokes Problem for Heated Generalized Maxwell Fluid in a Porous Half-Space
1Department of Fundamental Sciences, Yancheng Institute of Technology, Yancheng, Jiangsu 224003, China
2Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing 100044, China
Received 8 October 2007; Accepted 24 April 2008
Academic Editor: Katica Hedrih
Copyright © 2008 Changfeng Xue and Junxiang Nie. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The Rayleigh-Stokes problem for a generalized Maxwell fluid in a porous
half-space with a heated flat plate is investigated. For the description of such a
viscoelastic fluid, a fractional calculus approach in the constitutive relationship
model is used. By using the Fourier sine transform and the fractional Laplace
transform, exact solutions of the velocity and the temperature are obtained.
Some classical results can be regarded as particular cases of our results, such
as the classical solutions of the first problem of Stokes for Newtonian viscous
fluids, Maxwell fluids, and Maxwell fluids in a porous half-space.