Two-temperature theory in magneto-thermoelasticity with fractional order dual-phase-lag heat transfer

A new mathematical model of two-temperature magneto-thermoelasticity is constructed where the fractional order dual-phase-lag heat conduction law is considered. The state space approach developed in Ezzat (2008) is adopted for the solution of one-dimensional application for a perfect conducting half-space of elastic material, which is thermally shocked in the presence of a transverse magnetic field. The Laplace transform technique is used. A numerical method is employed for the inversion of the Laplace transforms. According to the numerical results and its graphs, conclusion about the new theory has been constructed. Some theories of generalized thermoelasticity follow as limit cases. Some comparisons have been shown in figures to estimate effects of temperature discrepancy and fractional order parameter on all the studied fields.

► We model fractional order dual-phase-lag heat conduction law. ► We applied the model on a perfect conducting half-space of elastic material. ► Some theories of generalized thermoelasticity follow as limit cases. ► State space approach is adopted for the solution of one-dimensional problems. ► The model will improve the efficiency of thermoelectric material.