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Thermoelectric Viscoelastic Fluid with Fractional Integral and Derivative Heat Transfer

Published online by Cambridge University Press:  29 May 2015

Magdy A. Ezzat ,
A. S. Sabbah ,
A. A. El-Bary  and
S. M. Ezzat
Magdy A. Ezzat*
Affiliation:
Department of Mathematics, Faculty of Education, Alexandria University, Alexandria, Egypt
A. S. Sabbah
Affiliation:
Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt
A. A. El-Bary
Affiliation:
Arab Academy for Science and Technology, P.O. Box 1029, Alexandria, Egypt
S. M. Ezzat
Affiliation:
Department of Mathematics, Faculty of Education, Alexandria University, Alexandria, Egypt
*
*Corresponding author. Email: [email protected] (M. A. Ezzat)
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Abstract

A new mathematical model of magnetohydrodynamic (MHD) theory has been constructed in the context of a new consideration of heat conduction with a time-fractional derivative of order 0 < α ≤ 1 and a time-fractional integral of order 0 < γ ≤ 2. This model is applied to one-dimensional problems for a thermoelectric viscoelastic fluid flow in the absence or presence of heat sources. Laplace transforms and state-space techniques will be used to obtain the general solution for any set of boundary conditions. According to the numerical results and its graphs, conclusion about the new theory has been constructed. Some comparisons have been shown in figures to estimate the effects of the fractional order parameters on all the studied fields.

Keywords

65M1078A48Viscoelastic fluidmodified Fourier’s and Ohm’s lawsmodified Riemann-Liouville fractional integralnew fractional Taylor’s seriesstate space approachfractional calculus
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 7 , Issue 4 , August 2015 , pp. 528 - 548
Copyright
Copyright © Global-Science Press 2015 

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