Mathematical Problems in Engineering 
Volume 2008 (2008), Article ID 641431, 10 pages
doi:10.1155/2008/641431
Research Article

Exact Solutions of Rayleigh-Stokes Problem for Heated Generalized Maxwell Fluid in a Porous Half-Space

Changfeng Xue1 and Junxiang Nie2

 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

Recommended by Katica Hedrih

Abstract

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.