Effect of a Temperature-Dependent Thermal Conductivity on a Fixed Unbounded Solid with a Cylindrical Cavity (original) (raw)
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Thermal Conductivity Study of an Orthotropic Medium Containing a Cylindrical Cavity
Symmetry
An interesting feature that appears in the thermoelastic interaction in an orthotropic material containing cylindrical cavities is addressed in this study. For this purpose, the Finite Element Method is applied to analyze a generalized thermoelasticity theory with a relaxation time. For the development of the model, a thermal conductivity that is dependent on the temperature of the orthotropic medium was considered. The boundary condition for the internal surface of a cylindrical hollow is defined by the thermal shocks and the traction on the free surface. The nonlinear formulations of thermoelastic based on thermal relaxation time in orthotropic mediums are abbreviated using the Finite Element Method. The nonlinear equations without Kirchhoff’s transformations are presented. The results are graphically represented to demonstrate how changing thermal conductivity affects all physical values.
Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, 2017
In this work, the generalized thermoelasticity theory with phase lags is used to solve a thermoelastic problem for an orthotropic infinite unbounded body containing a cylindrical cavity by approximate techniques. The thermal conductivity of the present body is assumed to vary linearly with the temperature. The surface of the cylinder is traction free and subjected to a uniform step temperature. The general solutions for the temperature, displacement, and thermal stresses are obtained by the method of Laplace transforms. The effects of dual phase lags and the variable thermal conductivity parameter on the studied fields for a cobalt material are discussed.
Honam Mathematical Journal, 2016
This paper investigates the effect of dual-phase-lags on a thermoviscoelastic orthotropic solid with a cylindrical cavity. The cylindrical cavity is subjected to a thermal shock varying heat and its material is taken to be of Kelvin-Voigt type. The phase-lag thermoelastic model, Lord and Shulman's model and the coupled thermoelasticity model are employed to study the thermomechanical coupling, thermal and mechanical relaxation (viscous) effects. Numerical solutions for temperature, displacement and thermal stresses are obtained by using the method of Laplace transforms. Numerical results are plotted to illustrate the effect phase-lags, viscoelasticity, and the variability thermal conductivity parameter on the studied fields. The variations of all field quantities in the context of dual-phase-lags and coupled thermoelasticity models follow similar trends while the Lord and Shulman's model may be different. The influence of viscosity parameter and variability of thermal conductivity is very pronounced on temperature and thermal stresses of the thermoviscoelastic solids.
Mathematics
The current article introduces the thermoelastic coupled response of an unbounded solid with a cylindrical hole under a traveling heat source and harmonically altering heat. A refined dual-phase-lag thermoelasticity theory is used for this purpose. A generalized thermoelastic coupled solution is developed by using Laplace’s transforms technique. Field quantities are graphically displayed and discussed to illustrate the effects of heat source, phase-lag parameters, and the angular frequency of thermal vibration on the field quantities. Some comparisons are made with and without the inclusion of a moving heat source. The outcomes described here using the refined dual-phase-lag thermoelasticity theory are the most accurate and are provided as benchmarks for other researchers.
Archive of Mechanical Engineering
In the present article, we introduced a new model of the equations of generalized thermoelasticity for unbounded orthotropic body containing a cylindrical cavity. We applied this model in the context of generalized thermoelasticity with phase-lags under the effect of rotation. In this case, the thermal conductivity of the material is considered to be variable. In addition, the cylinder surface is traction free and subjected to a uniform unit step temperature. Using the Laplace transform technique, the distributions of the temperature, displacement, radial stress and hoop stress are determined. A detailed analysis of the effects of rotation, phase-lags and the variability thermal conductivity parameters on the studied fields is discussed. Numerical results for the studied fields are illustrated graphically in the presence and absence of rotation.
A study of generalized thermoelastic interactions in an unbounded medium with a spherical cavity
Computers & Mathematics with Applications, 2008
The aim of the present paper is to study the thermoelastic interactions in an unbounded elastic medium with a spherical cavity in the context of four different theories of thermoelasticity, namely: the classical coupled dynamical thermoelasticity, the extended thermoelasticity, the temperature-rate-dependent thermoelasticity and the thermoelasticity without energy dissipation in a unified way. The cavity surface is assumed to be stress free and is subjected to a smooth and time-dependent-heating effect. The solutions for displacement, temperature and stresses are obtained with the help of the Laplace transform procedure. Firstly the short-time approximated solutions for four different theories have been obtained analytically. Then following the numerical method proposed by Bellman et al. [R. Bellmen, R.E. Kolaba, J.A. Lockette, Numerical Inversion of the Laplace Transform, American Elsevier Pub. Co., New York, 1966] for the inversion of Laplace transforms, the numerical values of the physical quantities are also computed for the copper material and results are displayed in graphical forms to compare the results obtained for the theory of thermoelasticity without energy dissipation with the results of other thermoelasticity theories.
2015
This article presents an analytical solution for the effect of phase-lags on a generalized plane strain thermoviscoelastic orthotropic medium with a cylindrical cavity subjected to a thermal shock from varying heat. It is assumed that the cylindrical cavity is made of Kelvin–Vogt type material. The general solutions for field quantities are obtained using the method of Laplace transforms. The results are graphically presented to illustrate the effect of phase-lags, viscoelasticity and variability of thermal conductivity on the studied fields. Comparisons are also presented with those in the absence of viscosity and variability of thermal conductivity.
Materials Research Express
The linear generalized Green-Naghdi thermoelasticity theory without energy dissipation is employed. The study of thermoelastic interactions in a hollow cylinder under a continuous heat source is carried out. Firstly, Laplace and Hankel transforms are employed to solve the problem without the time domain. Then, the state space approach is employed to get the exact solution of the problem in the space domain. Once again, the inverse Laplace transforms is used to get the solutions in the time domain. Accurate terminologies for the temperature, thermoelastic potential, axial displacement, dilatation, and stresses are derived. Numerical outcomes for field variables are presented with the view of illustrating the theoretical results.
Journal of Thermal Science and Technology, 2015
In this paper, the thermoelastic interactions in an orthotropic unbounded body containing a cylindrical cavity are studied. This problem is solved by using the Green and Naghdi's (GN) generalized thermoelasticity model. The thermal material characteristic of the GN theory is taken as linear function of temperature. The surface of the cylinder is constrained and subjected to an exponentially decaying pulse boundary heat flux. The Laplace transform is used to remove the time dependency from the governing field equations. Finally, the transformed equations are inverted by the numerical inversion of the Laplace transform. Numerical results are shown graphically to estimate the effect of the thermal material coefficient and time of the pulse heat parameters. The distributions of all the studied felids in the space-time domain are also investigated.
Generalized thermoelastic infinite medium with spherical cavity subjected to moving heat source
Computational Mathematics and Modeling, 2010
This paper deals with a problem of thermoelastic interactions in an isotropic unbounded medium with cylindrical cavity due to the presence of moving heat sources in the context of the linear theory of generalized thermoelasticity with one relaxation time. The governing equations are expressed in Laplace transform domain and solved in that domain. The inversion of the Laplace transform is done numerically using the Riemann-sum approximation method. The numerical estimates of the displacement, temperature, stress and strain are obtained for a hypothetical material. The results obtained are presented graphically to show the effect of the heat source velocity and the relaxation time parameters on displacement, temperature, stress and strain.