A modified Green-Naghdi fractional order model and its application to thermoelectric semi-space heated by a moving heat source

Abstract

Classical Green-Naghdi (GN-II) model may have trouble accurately forecasting the thermo-mechanical behavior of electro-thermoelastic materials if memory-dependent impact is not taken into account. As results, we shall construct a new mathematical model of the Green-Naghdi (GN-II) theory, based on fractional order of heat transfer. A few theories are offered as limit examples. The method of the matrix exponential, which constitutes the basis of the state-space approach of modern theory, is used. Laplace transforms are utilized. The formulation is applied to half-space problem exposed to a uniform magnetic field and heated by a moving heat source with a constant speed. A numerical method is employed for the inversion of the Laplace transforms. The effects of several estimates of the figure-of-merit quantity, heat source speed, fractional parameter, magnetic number, and thermal shock parameter are considered.