Impact of Two Temperature and Fractional Order Parameters on Visco-thermodiffusive Elastic Plate

In this chapter, the analysis of the transient responses of visco-thermoelastic material in the context of two temperature fractional generalized thermoelastic diffusion models is presented. Here, a thermoelastic plate that is initially kept traction-free at a uniform temperature and subjected to thermal as well as mechanical loadings on both of its surfaces is considered for the study. The basic equations and constitutive relations governing the problem are solved in the Laplace-Fourier transformed domain using boundary restrictions. The expressions thus obtained in the transformed domain are too complex to invert analytically. Hence by applying the numerical inversion technique, results of physical quantities are obtained in the original domain using the physical data of copper material. The impact of viscosity, two temperature, and fractional order parameters on various physical quantities is presented graphically. The outcome of this work underlines that viscosity parameters have a significant influence on the field quantities, and increasing two temperature parameter or decreasing the fractional order parameter leads to their smoother distribution.