This article presents a mathematical analysis of thermoelastic skin tissue using an improved thermal conduction theory known as the refined three-phase-lag (TPL) theory. By accounting for the effects of multiple time derivatives, this advanced model provides a more accurate representation of how skin tissue behaves under different temperature conditions. The thin skin tissue is considered to have mechanically clamped surfaces, which are assumed to be one-dimensional. Furthermore, the skin tissue experiences a thermal shock load on its outer surface while maintaining a constant temperature on its inner surface. The proposed model has led to the derivation of certain generalized thermoelasticity theories in previous studies. The Laplace transform and its associated numerical inversion method are employed to calculate the distributions of temperature, displacement, dilatation, and stress in the system. The obtained outcomes are explicitly depicted to analyze the significant influences on the distributions of the field variables. These findings shed light on the behavior of skin tissue when subjected to a particular temperature distribution at the boundary condition, enhancing our knowledge in this area.

In this article, using memory-dependent derivative (MDD) on three-phase-lag model of thermoelasticity, a new generalized model of thermoelasticity theory with time delay and kernel function is constructed. The governing coupled equations of the new generalized thermoelasticity with time delay and kernel function are applied to two-dimensional problem of an isotropic plate. The two-dimensional equations of generalized thermoelasticity with MDD are solved using state space approach. Numerical inversion method is employed for the inversion of Laplace and Fourier transforms. The displacements, temperature and stress components for different thermoelastic models are presented graphically and the effect of different kernel and time delay on the considered parameters are observed.

The present paper is dealing with the propagation of Rayleigh surface waves in a homogeneous transversely isotropic medium. This thermo-dynamical analysis is carried out in the context of three-phase-lags thermo elasticity model. three phase lag model is very much useful in the problems of nuclear boiling, exothermic catalytic reactions, phonon-electron interactions, phonon scattering etc. The normal mode analysis is employed to obtain the exact expressions of the considered variables. The frequency equations for thermally insulated and isothermal surface in the closed form are derived. Some special cases of frequency equation are also discussed. In order to illustrate the analytical developments, the numerical solution is carried out and the computer simulated results in respect of phase velocity and attenuation coefficient are presented graphically. It is found that the results obtained in the present problem agree with that of the existing results obtained by various researchers. This study may find its applications in the design of surface acoustic waves (SAW) devices, structural health monitoring and damage characterization of materials.

In this paper, a new mathematical model of a Kelvin-Voigt type thermo-visco-elastic, infinite thermally conducting medium has been considered in the context of a new consideration of heat conduction having a non-local fractional order due to the presence of periodically varying heat sources. three-phase-lag thermoelastic model, Green Naghdi models II and III (i.e., the models which predicts thermoelasticity without energy dissipation (TEWOED) and with energy dissipation (TEWED)) are employed to study the thermo-mechanical coupling, thermal and mechanical relaxation effects. In the absence of mechanical relaxations (viscous effect), the results for various generalized theories of thermoelasticity may be obtained as particular cases. The governing equations are expressed in Laplace-Fourier double transform domain. The inversion of the Fourier transform is carried out using residual calculus, where the poles of the integrand are obtained numerically in complex domain by using laguerre's method and the inversion of the Laplace transform is done numerically using a method based on Fourier series expansion technique. Some comparisons have been shown in the form of the graphical representations to estimate the effect of the non-local fractional parameter and the effect of viscosity is also shown.

The reflection of harmonic waves, like sound or light, has diverse applications, including sonar for object location, understanding seismic waves in geophysics, and even in the human eye's ability to see. The reflection of plane waves with constant material properties is available in existing literature, but very little attention has been given to the temperature-dependent modulus of elasticity. A novel model is proposed to study the propagation of harmonic plane waves through a nonlocal micropolar medium with temperature-dependent material properties. The influence of nonlocality, rotation effects, and the constant magnetic field is also taken into account. The precise formulations of the field quantities are presented and examined using the normal mode approach. The phase lag (TPL) theory is applied to model and solve the governing equations. The effects of rotation, temperature-dependent constants, and the nonlocality parameter on the different physical quantities have been examined and displayed graphically. Energy ratios are also computed by using the amplitude ratios. It is concluded that in a nonlocal, rotating, micropolar medium, reflection of harmonic waves provides four coupled quasi-waves, namely, quasi-transverse, quasi-longitudinal, quasi-micro rotational, and quasi-thermal, with different speeds, and the energy ratios and reflection coefficients are affected by nonlocal parameters, rotation, and micropolarity.

Herein, the free vibrations of inhomogeneous nonlocal visco thermoelastic sphere with three-phase-lag model of generalized thermoelasticity have been addressed. The governing equations and constitutive relations with three-phase-lag model have been solved by using non-dimensional quantities. The simple power law has been presumed to take the material in radial direction. The series solution has been established to derive the solution analytically. The relations of frequency equations for the continuation of viable modes are developed in dense form. The analytical results have been authenticated by the reduction of nonlocal and three– phase– lag parameters. To investigate the quality of vibrations, frequency equations are determined by applying the numerical iteration method. MATLAB software tools have been used for numerical computations and simulations to present the results graphically subject to natural frequencies, frequency shift, and thermoelastic damping. The numerical results clearly show that the variation of vibrations is slightly larger in case of nonlocal elastic sphere in contrast to elastic sphere.

The three-phase-lag model and Green–Naghdi theory without energy dissipation are employed to study the deformation of a two-temperature fiber-reinforced medium with an internal heat source that is moving with a constant speed under a hydrostatic initial stress and the gravity field. The modulus of the elasticity is given as a linear function of the reference temperature. The exact expressions for the displacement components, force stresses, thermal temperature and conductive temperature are obtained by using normal mode analysis. The variations of the considered variables with the horizontal distance are illustrated graphically. A comparison is made with the results of the two theories for two different values of a hydrostatic initial stress. Comparisons are also made with the results of the two theories in the absence and presence of the gravity field as well as the linear temperature coefficient.

The present investigation deals with study of thermoelastic damping and frequency shift of Kirchhoff plate resonators by using generalized thermoelasticity theory of dual-phase-lag model. The basic equations of motion and heat conduction equation are written with the help of Kirchhoff-Love plate theory and dual phase lag model. The analytical expressions for thermoelastic damping and frequency shift of modified couple stress dual-phase-lag thermoelastic plate have been obtained. A computer algorithm has been constructed to obtain the numerical results. Influences of modified couple stress dual-phase-lag thermoelastic plate; dualphase-lag thermoelastic plate and Lord-Shulman (L-S, 1967) thermoelastic plate with few vibration modes on the thermoelastic damping and frequency shift are examined. The thermoelastic damping and frequency shift with varying values of length and thickness are shown graphically for clamped-clamped and simply supported boundary conditions. It is observed from the results that the damping factor and frequency shift have noticed larger value in the presence of couple stress for varying values of length but opposite effect are shown for varying values of thickness in case of both vibration modes and boundary conditions.