Magneto-thermoelasticity with thermoelectric properties and fractional derivative heat transfer

In this work, a new model of the magneto-thermoelasticity theory has been constructed in the context of a new consideration of heat conduction with fractional derivative. A one-dimensional application for a conducting half-space of thermoelectric elastic material, which is thermally shocked in the presence of a magnetic field, has been solved using Laplace transform and state-space techniques (Ezzat, 2008 [1]). According to the numerical results and its graphs, a conclusion about the new theory of magneto-thermoelasticity has been constructed. The theories of coupled magneto-thermoelasticity and of generalized magneto-thermoelasticity with one relaxation time follow as limited cases. The result provides a motivation to investigate conducting thermoelectric materials as a new class of applicable materials.