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Advances in Materials Science and Engineering
Volume 2015, Article ID 391454, 16 pages
http://dx.doi.org/10.1155/2015/391454
Research Article

Thermomechanical Fractional Model of Two Immiscible TEMHD

1Department of Mathematics, Faculty of Science, University of Alexandria, Alexandria 21511, Egypt
2Department of Mathematics, Faculty of Science, University of Damanhour, Damanhour 22111, Egypt

Received 29 January 2015; Revised 15 April 2015; Accepted 18 April 2015

Academic Editor: Somchai Thongtem

Copyright © 2015 F. Hamza et al. 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.

Abstract

We introduce a mathematical model of unsteady thermoelectric MHD flow and heat transfer of two immiscible fractional second-grade fluids, with thermal fractional parameters and mechanical fractional parameters , . The Laplace transform with respect to time is used to obtain the solution in the transformed domain. The inversion of Laplace transform is obtained by using numerical method based on a Fourier-series expansion. The numerical results for temperature, velocity, and the stress distributions are represented graphically for different values of and . The graphs describe the fractional thermomechanical parameters effect on the case of two immiscible fluids and the case of a single fluid.