Thermoelastic transient response of an infinitely long annular multilayered cylinder

Thermoelastic transient response of multilayered annular cylinders of infinite lengths subjected to known temperature at traction-free inner and outer surfaces are considered. A method based on the Laplace transformation and finite difference method has been developed to analyze the thermoelasticity problem. Using the Laplace transform with respect to time, the general solutions of the governing equation are obtained in transform domain. The solution is obtained by using the matrix similarity transformation and inverse Laplace transform. Solutions for the temperature and thermal stress distributions in a transient state were obtained. It was found that the temperature distribution, the displacement and the thermal stresses change slightly as time increases. There is no limit of number of annular layers of the cylinder in the presented computational procedures.     

Dynamic analysis of functionally graded plates using the hybrid Fourier-Laplace transform under thermomechanical loading

In this study, the analytical solution is presented for dynamic response of a simply supported functionally graded rectangular plate subjected to a lateral thermomechanical loading. The first-order and third-order shear deformation theories and the hybrid Fourier-Laplace transform method are used. The material properties of the plate, except Poisson’s ratio, are assumed to be graded in the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. The plate is subjected to a heat flux on the bottom surface and convection on the upper surface. A third-order polynomial temperature profile is considered across the plate thickness with unknown constants. The constants are obtained by substituting the profile into the energy equation and applying the Galerkin method. The obtained temperature profile is considered along with the equations of motion. The governing partial differential equations are solved using the finite Fourier transformation method. Using the Laplace transform, the unknown variables are obtained in the Laplace domain. Applying the analytical Laplace inverse method, the solution in the time domain is derived. The computed results for static, free vibration, and dynamic problems are presented for different power law indices for a plate with simply supported boundary conditions. The results are validated with the known data reported in the literature. Furthermore, the results calculated by the analytical Laplace inversion method are compared with those obtained by the numerical Newmark method.     

Coupling model for unsteady MHD flow of generalized Maxwell fluid with radiation thermal transform

This paper introduces a new model for the Fourier law of heat conduction with the time-fractional order to the generalized Maxwell fluid. The flow is influenced by magnetic field, radiation heat, and heat source. A fractional calculus approach is used to establish the constitutive relationship coupling model of a viscoelastic fluid. We use the Laplace transform and solve ordinary differential equations with a matrix form to obtain the velocity and temperature in the Laplace domain. To obtain solutions from the Laplace space back to the original space, the numerical inversion of the Laplace transform is used. According to the results and graphs, a new theory can be constructed. Comparisons of the associated parameters and the corresponding flow and heat transfer characteristics are presented and analyzed in detail.     

Non-Fourier heat conduction in an exponentially graded slab

The present article investigates one-dimensional non-Fourier heat conduction in a functionally graded material by using the differential transformation method. The studied geometry is a finite functionally graded slab, which is initially at a uniform temperature and suddenly experiences a temperature rise at one side, while the other side is kept insulated. A general non-Fourier heat transfer equation related to the functionally graded slab is derived. The problem is solved in the Laplace domain analytically, and the final results in the time domain are obtained by using numerical inversion of the Laplace transform. The obtained results are compared with the exact solution to verify the accuracy of the proposed method, which shows excellent agreement.     

A half-space problem in the theory of generalized thermoelastic diffusion

In this work we consider the problem of a thermoelastic half-space with a permeating substance in contact with the bounding plane in the context of the theory of generalized thermoelastic diffusion with one relaxation time. The bounding surface of the half-space is taken to be traction free and subjected to a time dependent thermal shock. The chemical potential is also assumed to be a known function of time on the bounding plane. Laplace transform techniques are used. The solution is obtained in the Laplace transform domain by using a direct approach. The solution of the problem in the physical domain is obtained numerically using a numerical method for the inversion of the Laplace transform based on Fourier expansion techniques.The temperature, displacement, stress and concentration as well as the chemical potential are obtained. Numerical computations are carried out and represented graphically.     

Transient thermopiezoelectric response of a one-dimensional functionally graded piezoelectric medium to a moving heat source

The thermopiezoelectricity problem of a one-dimensional (1-D), finite length, functionally graded medium excited by a moving heat source is investigated in this paper. The Lord and Shulman theory of generalized coupled thermoelasticity is employed to account for both the finite speed of thermal waves and coupling of temperature field with displacement and electric fields. Except thermal relaxation time and specific heat, which are taken to be constant for simplicity, all other properties are assumed to vary exponentially along the length through an arbitrary non-homogeneity index. Laplace transform has been used to eliminate the time effect, and three coupled fields, namely, displacement, temperature, and electric fields are obtained analytically in the Laplace domain. The solutions are then inverted to time domain using a numerical Laplace inversion method. Numerical examples are displayed to illustrate the effects of non-homogeneity index, length and thermal relaxation time on the results. When the medium is homogeneous, the results of the current paper are reduced to exactly the same results available in the literature.     

A semi-analytic solution of a wellbore in a non-isothermal low-permeability porous medium under non-hydrostatic stresses

The transient stress, displacement, pore pressure and temperature fields around a wellbore in a thermo-poro-elastic (THM) medium subject to non-hydrostatic remote stresses are analyzed under non-isothermal plane-strain conditions. The linear THM model proposed by Coussy (1989) is adopted in the analysis with a focus on thermal effects in low-permeability saturated rocks, characterized by a latent heat associated with local changes of fluid mass content. Non-dimensionalized parameters are identified by reformulating the fully-coupled governing equations and boundary conditions. The wellbore problem is simplified by decomposing it into axisymmetric and deviatoric loading cases. The corresponding analytical solutions are obtained in Laplace space. The inverse Laplace transforms are performed numerically to find the time-dependent distributions of field variables in the rock mass around the wellbore. These numerical results show that although the pore pressure diffusion has little influence on temperature and stress, temperature changes can strongly affect the pore pressure and stress around the wellbore. The temperature change can lead to changes in near-well stresses and the resulting significant change in wellbore breakdown pressure illustrates the importance of considering the THM coupling.     

Generalized thermoelastic infinite transversely isotropic body with a cylindrical cavity due to moving heat source and harmonically varying heat

In this paper, the induced temperature, displacement, and stress fields in an infinite transversely isotropic unbounded medium with cylindrical cavity due to a moving heat source and harmonically varying heat are investigated. This problem is solved in the context of the linear theory of generalized thermoelasticity with dual phase lag model. The governing equations are expressed in Laplace transform domain. Based on Fourier series expansion technique the inversion of Laplace transform is done numerically. The numerical estimates of the displacement, temperature and stress are obtained and presented graphically. The theories of coupled thermoelasticity, generalized thermoelasticity with one relaxation time, and thermoelasticity without energy dissipation can extracted as special cases. Some comparisons have been shown in figures to present the effect of the heat source, dual phase lags parameters and the angular frequency of thermal vibration on all the studied fields.     

Dynamic response in two-dimensional transversely isotropic thick plate with spatially varying heat sources and body forces

This paper deals with a two-dimensional (2D) problem for a transverselyisotropic thick plate having heat sources and body forces. The upper surface of the plate is stress free with the prescribed surface temperature, while the lower surface of the plate rests on a rigid foundation and is thermally insulated. The study is carried out in the context of the generalized thermoelasticity proposed by Green and Naghdi. The governing equations for displacement and temperature fields are obtained in the Laplace-Fourier transform domain by applying the Laplace and Fourier transforms. The inversion of the double transform is done numerically. Numerical inversion of the Laplace transform is done based on the Fourier series expansion. Numerical computations are carried out for magnesium (Mg), and the results are presented graphically. The results for an isotropic material (Cu) are obtained numerically and presented graphically to be compared with those of a transversely isotropic material (Mg). The effect of the body forces is also studied.     

A two dimensional problem for a transversely isotropic generalized thermoelastic thick plate with spatially varying heat source

This paper deals with a two dimensional problem for a transversely isotropic thick plate having heat source. The upper surface of the plate is stress free with prescribed surface temperature while the lower surface of the plate rests on a rigid foundation and is thermally insulated. The study is carried out in the context of generalized thermoelasticity proposed by Green and Naghdi. The governing equations for displacement and temperature fields are obtained in Laplace–Fourier transform domain by applying Laplace and Fourier transform techniques. The inversion of double transform has been done numerically. The numerical inversion of Laplace transform is done by using a method based on Fourier Series expansion technique. Numerical computations have been done for magnesium (Mg) and the results are presented graphically. The results for an isotropic material (Cu) have been deduced numerically and presented graphically to compare with those of transversely isotropic material (Mg).     

Thermoelastic solutions for thermal distributions moving over thin slim rod under memory-dependent three-phase lag magneto-thermoelasticity

Abstract

Enlightened by the Caputo fractional derivative, the present study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena due to the influence of magnetic field and moving heat source in a rod in the context of three-phase lag (TPL) theory of thermoelasticity. Both ends of the rod are fixed and heat insulated. Employing Laplace transform as a tool, the problem has been transformed into the space-domain and solved analytically. Finally, solutions in the real-time domain are obtained by applying the inverse Laplace transform. Numerical calculation for stress, displacement, and temperature within the rod is carried out and displayed graphically. The effect of moving heat source speed on temperature, stress, and temperature is studied. It is found from the distributions that the temperature, thermally induced displacement and stress of the rod are found to decrease at large source speed. For the better understanding of the effect of moving heat source on all the distributions, three animations are added.     

Generalized magneto-thermoelasticity in a perfectly conducting medium

A model of the equations of generalized magneto-thermoelasticity in a perfectly conducting medium is given. The formulation is applied to generalizations, Lord–Shulman theory with one relaxation time and the Green–Lindsay theory with two relaxation times, as well as to the coupled theory.Laplace transforms and Fourier transforms techniques are used to get the solution. The resulting formulation is used to solve a specific two-dimensional problem. The inverses of Fourier transforms are obtained analytically.Laplace transforms are obtained using the complex inversion formula of the transform together with Fourier expansion techniques.Numerical results for the temperature distribution, thermal stress and displacement components are represented graphically. A comparison was made with the results predicted by the three theories.     

Effect of rotation in magneto-thermoelastic transversely isotropic hollow cylinder with three-phase-lag model

This article deals with the various heat source responses in a transversely isotropic hollow cylinder under the purview of three-phase-lag (TPL) generalized thermoelasticity theory. In presence of magnetic field and due to the rotating behavior of the cylinder, the governing equations are redefined for generalized thermoelasticity with thermal time delay. In order to obtain the stress, displacement and temperature field, the field functions are expressed in terms of modified Bessel functions in Laplace transformed domain. When the outer radius of hollow cylinder tends to infinity, the corresponding results are discussed. Finally an appropriate Laplace transform inversion technique is adopted.     

MHD natural convection flow with radiative heat transfer past an impulsively moving plate with ramped wall temperature

Influence of radiation on unsteady hydromagnetic natural convection transient flow near an impulsively moving vertical flat plate with ramped wall temperature in a porous medium is studied. Exact solution of momentum and energy equations, under Boussinesq approximation, is obtained in closed form by Laplace transform technique. The variations in fluid velocity and temperature are shown graphically whereas numerical values of skin friction and Nusselt number are presented in tabular form.     

半无限长压电杆的瞬态热冲击问题

采用具有一个热松弛时间的L－S广义热弹性理论，研究了一维半无限长压电杆在一端受到热冲击时的边值问题。借助拉普拉斯正，反变换技术，在所考虑时间非常短的情况下，对问题进行了求解，得到了压电杆上的位移，压力及温度分布的近似解析解，发现应力及温度分布中分别存在两个阶跃点，并给出了算例。     

Dependence of modulus of elasticity and thermal conductivity on reference temperature in generalized thermoelasticity for an infinite material with a spherical cavity

Introduction Thetheoryofgeneralizedthermoelasticitywithonerelaxationtimebasedonamodified Fourier’slawofheatconductionwasdevelopedbyLordandShulman[1].Thistheoryallowsfor theso_calledsecond_soundeffectsinsolids,hencethermaldisturbancespropagatewithfinite wavespeeds. Themathematicalmodelofthegeneralizedthermoelasticitytheoryisofacomplicatednature thathindersthepossibilityofderivingananalyticalsolution.Mostattemptsdealingwiththese equationsarebasedoneithershort_timesolution[2-4]. Modernstructur…     

THE ANALYTICAL STUDY ON THE LASER INDUCED REVERSE－PLUGGING EFFECT BY USING THE CLASSICAL ELASTIC PLATE THEORY（Ⅰ）－TEMPERATURE FIELDS

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Two-temperature theory in generalized magneto-thermoelasticity with two relaxation times

The model of one-dimensional equations of the two-temperature generalized magneto-thermoelasticity theory with two relaxation times in a perfect electric conducting medium is established. The state space approach developed in Ezzat (Can J. Phys. Rev. 86(11):1241–1250, 2008) is adopted for the solution of one-dimensional problems. The resulting formulation together with the Laplace transform techniques are applied to a specific problem of a half-space subjected to thermal shock and traction-free surface. The inversion of the Laplace transforms is carried out using a numerical approach. Some comparisons have been shown in figures to estimate the effects of the temperature discrepancy and the applied magnetic field.     

State space approach to magnetohydrodynamic flow of perfectly conducting micropolar fluid with stretch

In this work we introduce a model of the boundary layer equations for a perfect conducting micropolar fluid with stretch, bounded by an infinite vertical flat plane surface of a constant temperature. This model is applied to study the effects of free convection currents on the flow of the fluid in the presence of a constant magnetic field. The state space technique is adopted for the solution of a one‐dimensional problem for any set of boundary conditions. The resulting formulation together with the Laplace transform techniques are applied to a thermal shock problem. The inversion of the Laplace transforms is carried out using a numerical approach. Numerical results are given and illustrated graphically for the problem. Copyright © 2011 John Wiley & Sons, Ltd.     

Deflection of transient thermoelastic circular plate by Marchi-Zgrablich and Laplace integral transform technique

This paper deals with the determination of temperature distribution and thermal deflection function of a thin circular plate with the stated conditions. The transient heat conduction equation is solved by using Marchi-Zgrablich transform and Laplace transform simultaneously and the results of temperature distribution and thermal deflection function are obtained in terms of infinite series of Bessel function and it is solved for special case by using Mathcad 2007 software and represented graphically by using Microsoft excel 2007.