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

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.