State space approach to two-dimensional magneto-thermoelasticity with fractional order heat transfer in a medium of perfect conductivity

Article type: Research Article

Authors: Ezzat, M.A.^a | El-Bary, A.A.^{b; *}

Affiliations: [a] Department of Mathematics, Faculty of Education, Alexandria University, Alexandria, Egypt | [b] Arab Academy for Science and Technology, Alexandria, Egypt

Correspondence: [*] Corresponding author: A.A. El-Bary, Arab Academy for Science and Technology, P.O. Box 1029, Alexandria, Egypt. E-mail:aaelbary@aast.edu

Abstract: The model of the two-dimensional equations of magneto-thermoelasticity with fractional order heat transfer in a perfectly conducting medium is established. The method of the matrix exponential which constitutes the basis of the state-space approach of modern control theory is applied to the non-dimensional equations. Laplace and Fourier integral transforms are used. In this formulation, the governing equations are transformed into a matrix equation whose solution enables us to write the solution of any two-dimensional problem in terms of the boundary conditions. The resulting formulation is applied to a perfect conducting half-space problem. Some comparisons are shown in figures to estimate the effects of the Alfven velocity and the fractional order on all the considered fields.

Keywords: Magneto-thermoelasticity, new fractional taylor's series, state space approach, fractional calculus, numerical results

DOI: 10.3233/JAE-150095

Journal: International Journal of Applied Electromagnetics and Mechanics, vol. 49, no. 4, pp. 607-625, 2015