Visco-thermodiffusive elastic interactions in plate within the framework of two-temperature fractional thermoelastic models

Extensive advancement in the field of geotechnology, hypersonic transport mediums and design of new materials have attracted researchers to make in-depth study of thermoelastic materials considering diffusion and viscosity effects. Fractional calculus produces more rational results in such studies. In this view, considering two-temperature generalized visco-thermoelastic diffusion with fractional order theory of generalized thermoelasticity, a model is formulated in the context of Lord Shulman (LS) and Green Lindsay (GL) theories of thermoelasticity. The medium considered for study is thermoelastic plate which is kept traction free initially at uniform temperature and is isoconcentrated. The constitutive relations and governing equations are non-dimensionalized and transformed to ordinary differential equation using Laplace transformation with respect to time 't' and Fourier transformation with respect to space variable 'x'. Mechanical and thermal loads are applied on both surfaces of the plate. Solutions in transformed domain are obtained from resulting system of differential equations. Various quantities like stress, temperature field, mass concentration and chemical potential are obtained for copper material in physical domain by numerical inversion of Laplace and Fourier transforms. The numeric results of LS model are presented graphically. The outcome of this work underlines that disturbances in field quantities can be reduced by increasing two-temperature parameter or decreasing fractional order parameter. Also viscosity parameters have significant influence on field quantities. (author)