Unified GN model of electro thermoelasticity theories with fractional order of heat transfer
A unified mathematical model of electro thermoelasticity has been constructed in the context of a new consideration of heat conduction law with fractional order derivative. Some essential theories follow as limit cases. The governing coupled equations are applied to several concrete problems: (a) time dependent thermal shock problem; (b) a problem for a half space subjected to an arbitrary heating and (c) a layer media problem. Laplace transforms are used to derive the solution in the Laplace transform domain. 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. The predictions of the theory are discussed and compared with dynamic classical coupled theory, Lord Shulman, Green Naghdi (GN) and fractional coupled thermoelasticity theories. The result provides a motivation to investigate conducting fractional thermoelectric materials as a new class of applicable materials.