Effects Of Thermal Relaxation Time Research Articles

Flexural response of thermoelastic thin beam resonators due to thermal and mechanical loads

The flexural vibrations of homogeneous, transversely isotropic, generalized (non-Fourier) thermoelastic simply-supported thin beam resonators due to thermal and mechanical loads have been investigated under Euler–Bernoulli hypothesis. The model equation governing the transverse vibrations has been solved by using double Laplace transform technique (LTT) with respect to space and time. A mesh-less computational method, Adomian decomposition method (ADM), has also been employed to solve the model equation in the space domain for the comparison purpose. The inversion of the transformed solution has been carried out by using Durbin׳s technique in order to obtain the results in physical time domain. The natural frequencies and the corresponding mode shapes of the beam have been computed. The effects of thermal variations and other parameters on the deflection and temperature profiles of the thin beam have been studied. The effect of thermal relaxation time (second sound) on the vibration characteristics of beam has also been observed. The results computed by using LTT and ADM have been compared and are found to be in good agreement. It is noticed that ADM is an accurate, computer friendly and provides a unified, systematic powerful mathematical tool for solving the static and dynamic vibration problems for the considered beams.

Dynamic response of functionally graded cylinders due to time-dependent heat flux

In this paper, analytical solution has been obtained for a functionally graded, transversely isotropic, thermoelastic thick walled hollow cylinder (or disk) subjected to a thermal source. The linear theory of generalized thermoelasticity (Lord–Shulman model) has been employed to model the problem. The material stiffness and thermal conductivity have been assumed to vary as a simple power of the radial coordinate only. Keeping the inner and outer surfaces of the hollow cylinder traction free, a heat flux has been supplied on the inner surface to excite the body and outer surface is kept isothermal. The axisymmetry and plain strain (for cylinder) or plain stress (for disk) conditions have been considered here. The two coupled partial differential equations have been clubbed to obtain the general solution in Laplace domain. The residue calculus method has been employed to invert the transform to obtain the solution in physical domain. The solutions in case of classical coupled and uncoupled thermoelasticity; solid cylinder and infinite solid with cylindrical hole have been deduced as special cases of the present analysis. The results have also been validated with the existing one available in literature at various stages. The analytical results have been computed numerically and presented graphically for solid helium material. The effect of thermal relaxation time and grading parameter on the stresses, strains and temperature change produced in the FGM cylinder have been illustrated through the graphs. A comparative analysis has been done for homogeneous and functionally graded media for the distribution of radial stress, hoop stress, radial strain, hoop strain, radial displacement and temperature change with time, thermal relaxation time and thickness of the FGM cylinder.

On Reflection and Transmission of p- and Sv-Waves Phenomena at the Interface Between Solid-Liquid Media with Magnetic Field and Two Thermal Relaxation Times

In this research, we studied the reflection and transmission of thermoelastic wave at a solid-liquid interface under influence of two thermal relaxation times and magnetic field. The governing equations are introduced taking into consideration Green-Lindsay theory and Maxwell's stresses. After solving the governing equations, we found the two reflections and transmission coefficients of incident p-(primary) and SV- (Shear Vertical) waves in the presence of thermal relaxation times and a magnetic field. The boundary conditions at the interface have been applied. The appropriate expressions to find the amplitude ratios for the two incidence waves (p- and SV-waves) have been obtained. A numerical calculation is made for the reflection and transmitted coefficients of the incident waves, in which we study the effect of thermal relaxation times and magnetic field. The results obtained are presented graphically for the effect of magnetic field and relaxation times to display the phenomena physical meaning.

Fibre-Reinforced Generalized Thermoelastic Medium Subjected to Gravity Field

The present paper is aimed at studying the effects of thermal relaxation time and gravity of a two-dimensional problem with anisotropic semi-infinite solid media with the deformation of fiber-reinforced generalized thermoplastic. The harmonic function techniques are used. The thermal stresses, temperature and displacement have been obtained. These expressions are calculated numerically for two values of elastic constants for mediums M1 and M2 respectively. The results obtained are displayed by graphs to clear the phenomena physical meaning. The results indicate that the effect of gravity, relaxation times and parameters of fibre-reinforced of the material medium are very pronounced.

Effect of thermal relaxation time on heat transfer in a two layer composite system of living tissues

In this paper, we have numerically studied the heat transfer in a composite system of living tissues by taking into consideration the effect of thermal relaxation time. The composite system of living tissues comprises two layers in which the heat transfer takes place in one layer due to pure diffusion, while in the other layer due to both perfusion and diffusion. The modified Pennes bioheat equation is considered by introducing a thermal relaxation time which is the ratio of the thermal diffusion to the square of the heat propagation velocity in the medium. We assume that heat mainly propagates in the direction perpendicular to the skin surface. The problem is solved numerically by developing the Crank–Nicolson implicit finite difference scheme. With an aim to validate our numerical results, a comparison has been made with the previous solution and shows excellent agreement. The study shows that the relaxation time has a significant impact on the temperature distribution in a two layer composite system of living tissues.

Reflection of plane waves from a thermo-microstretch elastic solid with temperature dependent elastic properties

Purpose– The purpose of this paper is to study the reflection of a plane harmonic wave at the interface of thermo-microstretch elastic half space. The modulus of elasticity is taken as a linear function of reference temperature. The formulation is applied to generalized thermoelasticity theories, the Lord-Shulman and Green-Lindsay theories, as well as the classical dynamical coupled theory. Using potential function, the governing equations reduce to ten-order differential equation.Design/methodology/approach– Coefficient ratios of reflection of different waves with the angle of incidence are obtained using continuous boundary conditions. By numerical calculations, the variation of coefficient ratios of reflection with the angle of incidence is illustrated graphically for magnesium crystal micropolar material under three theories.Findings– The effect of different temperature-dependent constants and frequency on the coefficient ratios of reflection is illustrated graphically in context of Lord-Shulman theory.Originality/value– The reflection coefficient ratios are given analytically and illustrated graphically. The effects of thermal relaxation times are very small on reflection coefficient ratio. The temperature-dependent constant and wave frequency have a strong effect on the reflection coefficient ratios.

Reflection and Refraction of Coupled Transverse and Micro-Rotational Wave at Interface between Two Micropolar Elastic Solid

Using the model of micropolar generalized magneto-thermo-elasticity, the coupled transverse and micro-rotational wave at an interface between two micropolar solid mediums is discussed in the presence of a constant magnetic field. The model can be applied to the coupled theory as well as to five generalizations: the Lord-Shulman theory with one relaxation time, the Green-Lindsay theory with two relaxation times, the Green-Naghdi theories of type II(without energy dissipation) and of type III, and the theory with dual-phase-lag. Using continuous conditions at the interface, the amplitude ratios of reflected and refracted longitudinal displacement waves, longitudinal micro-rotational waves and the coupled transverse and micro-rotational waves are studied for incident coupled transverse and micro-rotational wave. The effect of thermal relaxation is discussed for C-D theory, G-L theory and L-S theory. The numerical results show that the effects of thermal relaxation times are very significant on the amplitude ratios.

Effect of Thermal Relaxation on Propagation of Longitudinal Displacement Wave

The micropolar elasticity theory takes into consideration the granular character of the medium, describes deformations by a microrotation and a microdisplacement. A model can be applied to the coupled theory as well as to five generalizations, such as L-S theory, G-L theory, H-I theory, G-N theory of type (II) and C-T theory. And if some parameters in this model are taken as given values, we can easily deduce the known models of Kelvin-Voigt model and other generalized micropolar/magneto/thermo/viscoelastic theory model. Employing the model of micropolar generalized magneto-thermo-elasticity, reflection and refraction of longitudinal displacement wave at interface of two welded micropolar elastic media are studied. The amplitude ratios of reflected and refracted micropolar magneto-thermoelastic longitudinal displacement waves, longitudinal microrotational waves and the coupled transverse and microrotational waves are studied for incident longitudinal displacement wave. The numerical results show that the effects of thermal relaxation times are very significant on the amplitude ratios.

The effect of thermal relaxation times on wave propagation of micropolar thermoelastic medium with voids due to various sources

PurposeThe purpose of this paper is to formulate a model of the equations of a two‐dimensional problem with the deformation of micropolar generalized thermoelastic medium with voids under the influence of various sources in the context of the Lord‐Shulman, Green‐Lindsay theories, as well as the classical dynamical coupled theory.Design/methodology/approachThe normal mode analysis was used to obtain the exact expressions of the displacement components, force stress, coupled stress, change in volume fraction field and temperature distribution. Numerical results were given and illustrated graphically when the volume source was applied.FindingsThe presence of voids plays a significant role on all the physical quantities. The value of normal displacement and normal force stress increases while the temperature, tangential force stress and the couple stress increase and then decrease due to the presence of voids. The value of all the physical quantities converges to zero with increase in distance z.Originality/valueComparisons are made with the results predicted by the three theories in the presence and the absence of material constants due to voids.

Effects of thermal relaxation time on plane wave propagation under two-temperature thermoelasticity

The present paper is concerned with an in-depth investigation of the propagation of harmonic plane waves in elastic media in the context of the linear theory of two-temperature generalized thermoelasticity. The exact dispersion relation solutions for the longitudinal plane wave are determined analytically. Asymptotic expansions of several characterizations of the wave field, like phase velocity, specific loss and penetration depth of the dilatational waves, are obtained for both the high frequency as well as low frequency values. The effects of thermal relaxation parameter on the plane wave is analyzed in details by comparing the theoretical as well as numerical results of the present work with the corresponding results in the context of classical two-temperature thermoelasticity theory as reported earlier.

WITHDRAWN: The effect of thermal relaxation time on magneto-hydrodynamic visco-elastic fluid layer heated from below

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Nonlinear Analysis of Rubber-Based Polymeric Materials with Thermal Relaxation Models

ABSTRACT Using mathematical modeling and computer simulation, nonlinear dynamics of rubber-based polymers has been studied with due regard for the effect of thermal relaxation. Main results have been obtained for the case of elongational oscillations of a ring-shaped body subjected to periodic (“internal”)boundary conditions. Particular emphasis has been placed on high-frequency and short spatial variations of temperature and displacement, in which the role of nonlinearities in the dynamics of the material and their close connection with the effect of thermal relaxation time can be best appreciated. It is shown how the vanishing relaxation time can lead to an attenuation of nonlinear effects in the thermomechanical system.

Thermoelastic waves in an anisotropic infinite plate

An analysis of the propogation of thermoelastic waves in a homogeneous, anisotropic, thermally conducting plate has been presented in the context of the generalized Lord-Shulman theory of thermoelasticity. Three different methods are used in this analysis: two of them are exact and the third is a semianalytic finite element method (SAFE). In our exact analysis, two different approaches are used. The first one, which is applicable to transversely isotropic plate, is based on introducing displacement potential functions, whereas in the second approach, which is applicable to any triclinic material, we rewrite the governing equations and boundary conditions in a matrix form. Finally, in the SAFE method, the plate is discretized along its thickness using N parallel, homogeneous layers, which are perfectly bonded together. Frequency spectrum and dispersion curves are obtained using the three methods and are shown to agree well with each other. The effects of thermal relaxation time and coupling term are also investigated. Numerical calculations have been presented for a silicon nitride (Si3N4) plate. However, the methods can be used for other materials as well.

The effect of thermal relaxation time on a electrohydrodynamic viscoelastic fluid layer heated from below

The problem of the onset of stability in a horizontal layer of a viscoelastic dielectric liquid with one relaxation time heated from below under the action of a vertical ac electric field is analyzed. Linear stability theory is used to derive an eigenvalue system of order eight and an exact eigenvalue equation for a neutral instability is obtained. Under somewhat artificial boundary conditions, this equation can be solved exactly to yield the required eigenvalue relationship from which various critical values are determined in detail. The critical Rayleigh number and wave number for the onset of instability are presented graphically as functions of the Grashof number for various values of the Prandtl number and one relaxation time. A comparison is made with the results obtained in the absence of an electric field. PACS No.: 47.27.T

The non-Fourier effect on the fin performance under periodic thermal conditions

This paper investigates the effect of thermal relaxation time (the non-Fourier effect) on the thermal performance of a convective fin under periodic thermal conditions. The environment heat transfer coefficient is assumed to be spatially varying. The periodic oscillation of the base temperature is considered. An efficient numerical scheme involving the hybrid application of the Laplace transform and control volume methods in conjunction with hyperbolic shape functions is used to solve the linear hyperbolic heat conduction equation. The thermal performance of the fin predicted by using the non-Fourier heat conduction model is compared with that predicted by using the Fourier model. Results show that the effects of the thermal relaxation time on the fin performance are significant for a short time after the initial transient. For the steady state, the non-Fourier effect is still great if the frequency of the temperature oscillation is high.

Spherically symmetric thermoelastic waves in a temperature-rate dependent medium with a spherical cavity

The temperature-rate dependent thermoelasticity theory is employed to study spherically symmetric thermoelastic waves in an infinite medium with a spherical cavity whose inner boundary is subjected to (i) unit-step in temperature change and zero stress and (ii) unit-step in stress and zero temperature change. The effect of thermal relaxation times on the thermoelastic disturbances being short-lived, short-time approximations of the solutions for deformation, temperature and stresses have been considered. It is observed that the temperature and deformation are discontinuous at both the wave fronts while the stresses suffer delta-function singularities in case (i) and in case (ii), the deformation and temperature are continuous at both the wave fronts, while the stresses are discontinuous at these locations.