Dual Phase Lag Model on Magneto-Thermoelasticity Infinite Non-Homogeneous Solid Having a Spherical Cavity

In this article, the induced displacement, temperature and stress fields in an infinite non-homogeneous elastic medium with a spherical cavity are obtained in the context dual-phase-lag model. The surface of the cavity is stress free and is subjected to a thermal shock. The material is assumed to be elastic and has an inhomogeneity in the radial direction. The type of non-homogeneity is such that the elastic constants, thermal conductivity and density are proportional to the n ^th power of the radial distance. The solutions are obtained analytically employing the Laplace transforms technique. The numerical inversion of the transforms is carried out using Fourier series expansions. The stresses components, temperature and displacement are computed numerically and presented graphically. A comparison of the results is made for different theories. If the magnetic field is neglected, the results obtained are deduced as a special case from this study.     

Dynamic response of an infinite medium with a spherical cavity on temperature-dependent properties subjected to a thermal shock under fractional-order theory of thermoelasticity

In this work, we consider the problem for an infinite medium with a spherical cavity on temperature-dependent properties subjected to a stress shock and thermal shock under the fractional-order theory of generalized thermoelasticity. The modulus of elasticity and the coe?cient of thermal conductivity are taken as linear function of temperature. The governing equations for the problem are formulated and then solved by Laplace transform together with its numerical inversion. The nondimensional temperature, displacement, radial stress, and hoop stress are obtained and illustrated graphically. In the calculation, the emphasis is focused on investigating the effect of temperature-dependent properties on the variations of the considered variables. The graphical results indicate that the temperature-dependent modulus of elasticity plays a significant role on all the physical quantities.     

Generalized Thermoelastic Problem of a Spherically Isotropic Infinite Elastic Medium Containing a Spherical Cavity

This paper is concerned with the determination of thermoelastic stresses and temperature in a spherically isotropic infinite elastic medium having a spherical cavity in the context of the linear theory of generalized thermoelasticity with two relaxation time parameters (Green and Lindsay theory). The surface of the cavity is stress free and is subjected to a thermal shock. The basic equations have been written in the form of a vector-matrix differential equation in the Laplace transform domain, which is then solved by the eigenvalue approach. The numerical inversion of the transforms is carried out using the Bellman method. The stresses and temperature are computed and presented graphically. A comparison with isotropic body has also been studied.     

A SHORT TIME SOLUTION FOR A PROBLEM IN THERMOELASTICITY OF AN INFINITE MEDIUM WITH A SPHERICAL CAVITY

The problem of a thermoelastic infinite medium with a spherical cavity is considered within the context of the theory of thermoelasticity with two relaxation times. The surface of the cavity is stress free and suddenly subjected to a time-dependent thermal shock. Laplace transform techniques are used. The inverse Laplace transforms are obtained analytically using asymptotic expansions valid for small values of time. Numerical computations for the temperature, the displacement, and stress distribution are carried out and represented graphically.     

Memory response on thermal wave propagation emanating from a cavity in an unbounded elastic solid

The present paper deals with the thermal memory response of wave propagation in an unbounded, homogeneous, isotropic elastic body, emanating from a spherical cavity. To analyze the memory response, the generalized heat conduction model with the fractional order as well as memory-dependent-derivatives (MDDs) concepts are considered. The solution space is obtained in Laplace transform domain by using the eigenfunction expansion method to the vector-matrix form of the corresponding governing equations. Finally, a comparison study is furnished for thermal displacement, stresses, and temperature changes in the space-time domain and is presented graphically.     

Influence of moving heat source on skin tissue in the context of two-temperature memory-dependent heat transport law

Abstract

Modeling and understanding heat transport and temperature variations within biological tissues and body organs are key issues in medical thermal therapeutic applications, such as hyperthermia cancer treatment. In the present analysis, the bioheat equation is studied in the context of memory responses. The heat transport equation for this problem involving the memory-dependent derivative (MDD) on a slipping interval in the context of three-phase (3P) lag model under two-temperature theory is formulated and is then used to study the thermal damage within the skin tissue during the thermal therapy. Laplace transform technique is implemented to solve the governing equations. The influences of the MDD and moving heat source velocity on the temperature of skin tissues are precisely investigated. The numerical inversion of the Laplace transform is carried out using Zakian method. The numerical outcomes of temperatures are represented graphically. Excellent predictive capability is demonstrated for identification of an appropriate procedure to select different kernel functions to reach effective heating in hyperthermia treatment. Significant effect of thermal therapy is reported due to the effect of delay time and the velocity of moving heat source as well.     

EFFECTS OF THERMAL RELAXATIONS ON THERMOVISCOELASTIC INTERACTIONS IN AN UNBOUNDED BODY WITH A SPHERICAL CAVITY SUBJECTED TO A PERIODIC LOADING ON THE BOUNDARY

Thermoviscoelastic interactions in an infinite homogeneous viscoelastic medium with a spherical cavity are studied. The cavity surface is subjected to a periodic loading and zero temperature change. The classical dynamical theory of thermoelasticity as well as the generalized theories of thermoelasticity are applied to consider the thermoelastic coupling. The analytical expressions for the closed-form solutions of displacement, temperature, and stresses are obtained; and the thermal relaxation effects on the interactions are studied to compare the three theories. The numerical values of the physical quantities are computed for a suitable material. The results are presented graphically to illustrate the problem.     

Dynamic analysis to the fractional order thermoelastic diffusion problem of an infinite body with a spherical cavity and variable material properties

Abstract

Based on the generalized thermoelastic diffusion theory with fractional order derivative, the dynamic response of an infinite thermoelastic medium with a spherical cavity is investigated. The thermoelastic and diffusive properties of the medium are assumed to be temperature-dependent, and the medium is subjected to a thermal shock and a chemical potential shock at the inner surface of the spherical cavity simultaneously. The governing equations of the problem are formulated and then solved by Laplace transform together with its numerical inversion. The distributions of the non-dimensional temperature, displacement, radial stress, concentration and chemical potential are obtained and illustrated graphically. In calculation, the effects of the fractional order parameter and the temperature-dependent properties on the variations of the considered variables are presented and discussed in detail. The results show that the fractional order parameter and the temperature-dependent properties significantly influence the variations of all the considered variables. The present investigation may be valuable in heat and mass transfer, waste disposal or petroleum engineering, etc.     

Reflection of plane waves in an anisotropic magnetothermoelastic diffusive medium with temperature dependent properties

In this article, a model of two dimensional problem of generalized thermoelasticity for an anisotropic magnetothermoelastic diffusive medium under the effect of temperature dependent properties is established. The enunciation is applied to generalized thermoelasticity theory based on Green-Lindsay model. There exist four coupled waves, namely, quasi-longitudinal P-wave (qP), quasi-longitudinal thermal wave (qT), quasi-longitudinal mass diffusive wave (qMD), and quasi-transverse wave (qSV) in the medium. Amplitude and energy ratios for these reflected waves are derived and the numerical computations have been carried out with the help of MATLAB programing. Effects of temperature dependent properties, magnetic and diffusion parameters on the amplitude and energy ratios are depicted graphically. Expressions of energy ratios have also been obtained in explicit form and are shown graphically as functions of angle of incidence. It has been verified that during the reflection phenomenon, the sum of energy ratios is equal to unity at each angle of incidence. Effect of anisotropy is also depicted on velocities of various reflected waves.     

Application of fractional order theory of thermoelasticity to a bilayered structure with interfacial conditions

In this work, fractional order theory of thermoelasticity is applied to a bilayered structure being in imperfect thermal and mechanical contact. The model is subjected to a sudden heating at the traction-free end, assumed to be undisturbed at infinity. The heat conduction in each medium is described by the time-fractional heat conduction equations with two fractional order parameters, respectively. An analytical technique based on Laplace transform is adopted. Numerical results are computed and represented graphically, from which the effects of fractional derivative parameters of both media, thermal contact resistance, elastic wave impedance ratio on the responses are discussed.     

Thermoelastic Wave with Energy Dissipation in an Unbounded Medium with a Spherical Cavity

The generalized linear theory of thermoelasticity has been used to study waves emanating from the boundary of a spherical cavity in a homogeneous and isotropic infinite thermoelastic body. The basic equations are written in the form of a vector-matrix differential equation and solved by an eigenvalue approach. Solutions in closed form have been achieved in the Laplace transform domain, and the inversion in the space-time domain for the field variables are done numerically. Finally, the results are analyzed and represented graphically.     

Analytical and experimental investigation on the operational characteristics and the thermal optimization of a miniature heat pipe with a grooved wick structure

A mathematical model for heat and mass transfer in a miniature heat pipe with a grooved wick structure is developed and solved analytically to yield the maximum heat transport rate and the overall thermal resistance under steady-state conditions. The effects of the liquid-vapor interfacial shear stress, the contact angle, and the amount of initial liquid charge have been considered in the proposed model. In particular, a novel method called a modified Shah method is suggested and validated; this method is an essential feature of the proposed model and accounts for the effect of the liquid-vapor interfacial shear stress. In order to verify the model, experiments for measuring the maximum heat transport rate and the overall thermal resistance are conducted. The analytical results for the maximum heat transport rate and the total thermal resistance based on the proposed model are shown to be in close agreement with the experimental results. From the proposed model, numerical optimization is performed to enhance the thermal performance of the miniature heat pipe. It is estimated that the maximum heat transport rate of outer diameter 3 and 4 mm heat pipes can be enhanced up to 48% and 73%, respectively, when the groove wick structure is optimized from the existing configurations. Similarly, the total thermal resistance of these heat pipes can be reduced by 7% and 11%, respectively, as a result of optimization.     

GENERALIZED THERMOELASTICITY OF AN INFINITE BODY WITH A CYLINDRICAL CAVITY AND VARIABLE MATERIAL PROPERTIES

ABSTRACT

The equations of generalized thermoelasticity with one relaxation time in an isotropic elastic medium with temperature-dependent mechanical and thermal properties are established. The modulus of elasticity and the thermal conductivity are taken as linear function of temperature. A problem of an infinite body with a cylindrical cavity has been solved by using Laplace transform techniques. The interior surface of the cavity is subjected to thermal and mechanical shocks. The inverse of the Laplace transform is done numerically using a method based on Fourier expansion techniques. The temperature, the displacement, and the stress distributions are represented graphically. A comparison was made with the results obtained in the case of temperature-independent mechanical and thermal properties.     

Semi-analytical solutions for the dual phase lag heat conduction in multilayered media

A semi-analytical solution procedure for transient heat transfer in composite mediums consisting of multi-layers within the framework of the dual phase lag model is presented. The procedure is then used to derive solutions for the temperature-, temperature gradient-, and heat flux distributions in a two-layer composite planar slab, a bi-layered solid-cylinder and sphere. The solutions obtained are applicable to the classical Fourier heat diffusion, hyperbolic heat conduction, phonon–electron interaction, and phonon scattering models with perfect or imperfect contact and with layers of different materials. The interfacial contact resistance, the heat flux and temperature gradient phase lags, thermal diffusivities and conductivities, initial temperatures of the composite medium and a general time-dependent boundary heat flux enter the solutions as parameters, allowing the solutions obtained to be applicable to a wide range of arrangements including perfect and imperfect contact. Analysis of thermal wave propagation, transmission and reflection in planar, cylindrical and spherical geometries with imperfect interfaces are presented, and geometrical—as well as the temperature gradient phase lag—effects on the thermal lagging behavior in different layered media are discussed.     

A thermoelastic spherical shell with and without energy dissipation

In this work, we apply the Green and Naghdi generalized thermoelasticity theory to a one-dimensional problem of distribution of thermal stresses and temperature in a generalized thermoelastic medium in the form of a spherical shell subjected to sudden change in the temperature of its external boundary. The results are compared to the generalized thermoelasticity theory with one relaxation time. Numerical results are computed and represented graphically for temperature, displacement, and stress distributions.     

THERMAL STRESSES FOR AN INFINITE BODY WITH A SPHERICAL CAVITY WITH TWO RELAXATION TIMES

Thermoelastic interactions caused in a homogeneous and isotropic infinite body with a spherical cavity are considered for the two different theories of generalized thermoelasticity, that is, Lord, and Shulman's theory and Green and Lindsay's theory. Analytical expressions for the temperature, displacement, and thermal stress fields are obtained; and the results are compared with the classical dynamical coupled theory.     

A Two-Dimensional Generalized Thermoelasticity Problem for a Half-Space Under the Action of a Body Force

In this work, we consider a two-dimensional problem of distribution of thermal stresses and temperature in a generalized thermoelastic half-space under the action of a body force and subjected to a thermal shock on the bounding plane. Laplace and exponential Fourier transform techniques are used. The solution in the transformed domain is obtained by a direct approach. The inverse double transform is evaluated numerically. Numerical results are obtained and represented graphically.     

Thermal stress analysis of laminated structures by a variable kinematic MITC9 shell element

A linear static thermal stress analysis of composite shell structures is carried out by means of a shell finite element with variable through-the-thickness kinematic. The refined models used are both Equivalent Single Layer (ESL) and Layer Wise (LW) and they are grouped in the Unified Formulation by Carrera (CUF). These models permit the distribution of displacements, stresses and temperature along the thickness of the multilayered shell to be accurately described. The Principle of Virtual Displacement (PVD) is employed to derive the governing equations. The Mixed Interpolation of Tensorial Components (MITC) method is used to contrast the membrane and shear locking phenomenon for a nine-node shell element. Cross-ply plate, cylindrical and spherical shells with simply supported edges and subjected to bi-sinusoidal thermal load are analyzed and various thickness ratios are considered. The results, obtained with different theories contained in the CUF, are compared with both the elasticity solutions given in the literature and the analytical solutions obtained using higher-order models and Navier's method. From the analysis, one can conclude that the shell element based on the CUF is very efficient, and its use leads to reach higher accuracy than classical models in the study of layered structures.     

Geometrical nonlinear free vibration analysis of FGM spherical panel under nonlinear thermal loading with TD and TID properties

In this article, the nonlinear free vibration behavior of functionally graded (FG) spherical shell panel is examined under nonlinear temperature field. The functionally graded material (FGM) constituents are assumed to be the function of temperature and the thermal conductivity. The effective \hboxmaterial properties of the FGM are obtained using the Voigt micromechanical model through power-law distribution. The mathematical model of the shell panel is developed using Green–Lagrange nonlinear kinematics in the framework of the higher order shear deformation theory. The desired governing \hboxequation of the FG shell panel under thermal environment is obtained using the classical Hamilton's principle. The domain is discretized with the help of the \hboxisoparametric finite element steps and the responses are computed using the direct \hboxiterative method. The convergence behavior of the present nonlinear numerical model has been checked and compared with the previous reported results. Numerous examples have been demonstrated for the FG spherical panel to show the influence of different geometrical and material parameters and support conditions on the linear and nonlinear frequency parameters.