Domain of influence on generalized thermoelastic diffusion theory

Abstract

The aim of this research work is to establish the theory of the domain of influence of diffusion disturbance with potential-temperature disturbance under the theory of generalized thermo-elastic diffusion using Lord and Shulman model. For a finite time t > 0, it has been proved that the potential due to displacement, temperature and diffusion effect does not produce any disturbances outside a bounded domain and the domain of influence is dependent on the support of thermo-elasto-diffusive load, the thermo-elasto-diffusive coupling constant and the phase-lag parameters. It has been shown that the domain of influence of the present case reduce to the domain of influence for classical thermo-elasticity theory with or without diffusion and the thermo-elasticity theory with one relaxation parameter without diffusion. Also, the effect of diffusion on thermal wave propagation is shown. This theorem will be applicable to analyze the deformation occur in elastic solids due to internal and external loads for the thermo-elasto-diffusive models and problems based on it in the field of engineering physics like solid-state-physics, physical metallurgy (fabrication of semi-conductor devices in mixture metals and molten semi-conductor), material engineering (separation of polymers), aircraft engineering, mechanical engineering and also in the industries like oil extraction from hydrocarbon and manipulation of macro-molecules like DNA etc.