Showing papers by "Santwana Mukhopadhyay published in 2017"

On electromagneto-thermoelastic plane waves under Green–Naghdi theory of thermoelasticity-II

Abstract: The present work attempts to investigate the propagation of one-dimensional electromagneto-thermoelastic plane waves in an isotropic unbounded thermally and electrically conducting media with finite conductivity in the context of the theory of thermoelasticity of Green and Naghdi type-II. The heat conduction equation is affected with the Thomson coefficient. Basic governing equations are modified by using Green–Naghdi theory of type-II. Our problem formulation derives two different systems. The first system is found to be coupled with the thermal field and represents the longitudinal wave. However, the second system represents transverse wave that is uncoupled with the thermal field. In both the cases, we identify waves that are affected with the magnetic field. Asymptotic expansions of dispersion relation solutions and various components of plane waves such as phase velocity, specific loss, and penetration depth are derived analytically for high- and low-frequency values in all cases. Analytical re...

Some theorems on linear theory of thermoelasticity for an anisotropic medium under an exact heat conduction model with a delay

Abstract: The present work is concerned with a very recently proposed heat conduction model—an exact heat conduction model with a delay term for an anisotropic and inhomogeneous material—and some important t...

An in-depth investigation on plane harmonic waves under two-temperature thermoelasticity with two relaxation parameters

Abstract: The present work is concerned with an in-depth analysis of plane harmonic waves in a thermoelastic medium under two-temperature thermoelasticity with two relaxation parameters. After the mathematical formulation of the present problem, we obtain the dispersion relation solution of harmonic plane waves propagating in the medium. The transverse wave is observed to be not affected by the thermal field and the longitudinal wave is coupled with the thermal field. Hence, special attention is paid on two different modes of longitudinal plane wave. One is predominantly elastic and the other is predominantly thermal in nature. The asymptotic expressions for the phase velocity, specific loss and many other important wave characteristics are derived in the cases of very high- and low-frequency regions for both the elastic and thermal mode longitudinal waves. Numerical results of these wave components are obtained for the intermediate values of frequency and the results are illustrated graphically in order to verify ...

Fundamental solutions of thermoelasticity with a recent heat conduction model with a single delay term

Abstract: The present work is concerned with the thermoelasticity theory based on a very recently proposed heat conduction model—a heat conduction model with a delay term introduced by Quintanilla. Here we aim to obtain the fundamental solutions of thermoelasticity in the context of this theory. We derive the solution of Galerkin-type field equations for the case of homogeneous and isotropic bodies. With the help of this solution, we determine the effects of concentrated heat sources and body forces in an unbounded medium. We further obtain the fundamental solutions of the field equations in case of steady vibrations.

On harmonic plane wave propagation under fractional order thermoelasticity: an analysis of fractional order heat conduction equation

Abstract: In the present paper, we investigate the propagation of an harmonic plane wave propagating with assigned frequency by implementing the thermoelasticity theory based on a fractional order heat conduction law where the fractional order parameter α satisfies 0<α<1. After formulating the problem, the exact dispersion relation solutions for the plane wave are determined analytically and asymptotic expressions of different characterization of the wave are analyzed in two special cases, namely for a high-frequency field and low-frequency field. We consider the case of longitudinal wave which is coupled with the thermal field and we ignore the transverse wave as it is observed to be independent to the thermal field. Two different modes: predominantly thermal and predominantly elastic mode longitudinal waves are found. Finally we compute wave characterizations for the intermediate values of frequency and verify our analytical results for the limiting cases of wave frequency. A detailed analysis is presented to hig...

A note on a two-temperature model in linear thermoelasticity

Abstract: We discuss the so-called two-temperature model in linear thermoelasticity and provide a Hilbert space framework for proving well-posedness of the equations under consideration. With the abstract perspective of evolutionary equations, the two-temperature model turns out to be a coupled system of the elastic equations and an abstract ordinary differential equation (ODE). Following this line of reasoning, we propose another model which is entirely an abstract ODE. We also highlight an alternative method for a two-temperature model, which might be of independent interest.

A domain of influence theorem for thermoelasticity without energy dissipation

Abstract: The present work is concerned with the thermoelasticity theory of Green and Naghdi of type I, II and III. By considering a mixed initial-boundary value problem for an isotropic medium in the context of all three models of type I, II and III in a unified way, we derive an identity in terms of the temperature and potential. On the basis of this identity, we establish the domain of influence theorem for the Green–Naghdi-II model. This theorem implies that for a given bounded support of thermomechanical loading, the thermoelastic disturbance generated by the pair of temperature and potential of the system vanishes outside a well-defined bounded domain. This domain is shown to depend on the support of the load, that is, on the initial and boundary data. It is also shown that under Green–Naghdi-II model, the thermoelastic disturbance propagates with a finite speed that is dependent on the thermoelastic parameters.

Investigation on the effects of temperature dependency of material parameters on a thermoelastic loading problem

Abstract: The present work is concerned with the investigation of thermoelastic interactions inside a spherical shell with temperature-dependent material parameters. We employ the heat conduction model with a single delay term. The problem is studied by considering three different kinds of time-dependent temperature and stress distributions applied at the inner and outer surfaces of the shell. The problem is formulated by considering that the thermal properties vary as linear function of temperature that yield nonlinear governing equations. The problem is solved by applying Kirchhoff transformation along with integral transform technique. The numerical results of the field variables are shown in the different graphs to study the influence of temperature-dependent thermal parameters in various cases. It has been shown that the temperature-dependent effect is more prominent in case of stress distribution as compared to other fields and also the effect is significant in case of thermal shock applied at the two boundary surfaces of the spherical shell.