Generalized thermoelastic diffusion problem for an infinitely long hollow cylinder for short times

In this work, we consider the problem of a thermoelastic infinitely long hollow cylinder in the context of the theory of generalized thermoelastic diffusion with one relaxation time. The outer surface of the cylinder is taken traction free and subjected to a thermal shock, while the inner surface is taken to be in contact with a rigid surface and is thermally insulated. 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.     

Problem in electromagneto thermoelasticity for an infinitely long solid conducting circular cylinder with thermal relaxation

The problem of an infinitely long solid conducting circular cylinder whose lateral surface is traction free and subjected to known surrounding temperatures in the presence of a uniform magnetic field in the direction of the axis is considered. The problem is in the context of generalized magneto-thermo-elasticity theory with one relaxation time. The solution is obtained by a direct approach without the customary use of potential functions. Laplace transform techniques are used to derive the solution in the Laplace transform domain. The inversion process is carried out using a numerical method based on Fourier series expansions.Numerical computations for the temperature, the displacement and stress distributions as well as for the induced magnetic and electric fields are carried out and represented graphically. Comparison is made with the results obtained when using the coupled equation of heat conduction.     

Torsional impact of a layer or a cylinder bonded to an elastic half-space

In this paper two torsional impact problems are considered. The first problem deals with the solution of a layer bonded to an elastic half-space when the layer is driven by the torsional impact over a bonded rigid circular disc. In the second problem sudden torsion by a rigid disc attached over the plane face of a circular cylinder is considered and the rest of the plane surface of the cylinder is stress free. The cylinder is bonded to the half-space, making use of Laplace and Hankel transforms the solution of each problem is reduced into Fredholm integral equations of the second kind. A numerical Laplace inversion technique is then used to recover the time depencence of the solution. The numerical values for the applied torque at the surface of rigid disc are calculated for each problem and then are displayed graphically.     

Transient heat conduction analysis in functionally graded materials by the meshless local boundary integral equation method

Advanced computational method for transient heat conduction analysis in continuously nonhomogeneous functionally graded materials (FGM) is proposed. The method is based on the local boundary integral equations with moving least square approximation of the temperature and heat flux. The initial-boundary value problem is solved by the Laplace transform technique. Both Papoulis and Stehfest algorithms are applied for the numerical Laplace inversion to obtain the time-dependent solutions. Numerical results are presented for a finite strip and a hollow cylinder with an exponential spatial variation of material parameters.     

Thermal shock analysis and thermo-elastic stress waves in functionally graded thick hollow cylinders using analytical method

Transient stress field and thermo-elastic stress wave propagation are studied in functionally graded thick hollow cylinder under arbitrary thermo-mechanical shock loading, in this article. Thermo-mechanical properties of functionally graded (FG) cylinder are assumed to be temperature independent and vary continuously and smoothly in the radial direction. The governing dynamic equations are analytically solved in temperature and elastic fields. To solve the problem, Laplace transform is used respect to time in all constitutive equations and boundary conditions. At first, temperature field equation analytically solved using Laplace transform and series method. The dynamic behaviors of thermo-elastic stresses are illustrated and discussed for various grading patterns of thermo-mechanical properties in several points across the thickness of FG cylinder. Time history of temperature field and thermal stresses are obtained using the residual theorem and the fast Laplace inverse transform method (FLIT), respectively. Also, the effects of the cylinder thickness and convection heat transfer coefficient on dynamic response of FG cylinder are revealed and discussed. The presented analytical method provides a ground to study the time histories of radial and hoop stresses in FG cylinders with different thickness and various volume fraction exponents. The advantage of this method is its mathematical ability to support simple and complicated mathematical function for the thermo-mechanical boundary conditions. A reasonable agreement can be seen in comparison of obtained results based on the presented analytical method with published data.     

Asymptotic analysis of axisymmetric plane strain problem involving fractional order heat conduction

This work is concerned with the asymptotic solutions of the axisymmetric plane strain problem involving the fractional order heat conduction. The governing equations for the axisymmetric plane strain problem are derived by means of fractional calculus. The Laplace transform technique is used to obtain the general solutions for any set of boundary conditions in the physical domain. The asymptotic solutions for a specific problem of an infinite cylinder with the boundary subjected to a thermal shock is derived by means of the limit theorem of Laplace transform. Utilizing these solutions, the thermoelastic behavior induced by transient thermal shock can be clearly illustrated, and the jumps locating at the position of each wavefront can also be accurately captured. Some comparisons for the predictions of thermoelastic response are conducted to estimate the effect of the fractional order parameter on the thermoelastic behavior.     

Method of Summation‐Integral Equations for Solving the Mixed Problem of Nonstationary Heat Conduction

The solution of a mixed axisymmetric nonstationary problem of heat conduction is obtained in the region of Laplace transforms. In solution of this problem, there occur summation–integral equations with the parameter of the integral Laplace transform (Lparameter) and the additional parameter of the finite integral Hankel transform (Hparameter). The laws governing the development of spatial nonstationary temperature fields in a bounded cylinder and a halfspace when one end surface of the cylinder is in contact with the surface of the halfspace in a circular region are determined.     

Transient solution of temperature field in functionally graded hollow cylinder with finite length using multi layered approach

In this paper by using a multi-layered approach based on the theory of laminated composites, the solution of temperature in functionally graded circular hollow cylinders subjected to transient thermal boundary conditions are presented. The material properties are assumed to be temperature-independent and radially dependent. The cylinder has finite length and is subjected to axisymmetric thermal loads. It is assumed that the functionally graded circular hollow cylinder is composed of N fictitious layers and the properties of each layer are assumed to be homogeneous and isotropic. Employing Laplace transform techniques and series solving method for two-dimensional heat conduction equation in the cylinder, solutions for the variation of temperature with time as well as temperature distribution through the cylinder are obtained.     

Transient Heat Conduction in a Functionally Graded Cylindrical Panel Based on the Dual Phase Lag Theory

The transient heat conduction in a functionally graded cylindrical panel is investigated based on the dual phase lag (DPL) theory in this article. Except for the phase lags which are assumed to be constant, all the other material properties of the panel are assumed to change continuously along the radial direction according to a power-law formulation with different non-homogeneity indices. The heat conduction equations based on the DPL theory in the cylindrical coordinate system are written in a general form which are then used for the analyses of four different geometries: (1) a hollow cylinder of an infinite length; (2) a hollow cylinder of a finite length; (3) a cylindrical panel of an infinite length; and (4) a cylindrical panel of a finite length. Using the Laplace transform, the analytical solutions for temperature and heat flux are obtained in the Laplace domain. The solutions are then converted into the time domain by employing the fast Laplace inversion technique. The exact expressions for the radial thermal wave speed are obtained for the four different geometries. The numerical results are displayed to reveal the effect of different approximations of the DPL theory on the temperature distribution for various non-homogeneity indices. The results are verified with those reported in the literature.     

Calculating the heating of a massive cylinder by the sweep method

Numerical solution of the heat conduction problem for a massive cylinder with allowance for heat transfer by radiation at the cylinder surface and for the furnace time lag is considered.     

Solution of Mixed Contact Problems in the Theory of Nonstationary Heat Conduction by the Method of Summation‐Integral Equations

The laws governing the development of spatial nonstationary temperature fields in a bounded cylinder and a halfspace where one of the end surfaces of the cylinder touches the surface of the halfspace in a circular region are determined. A solution of a mixed axisymmetric nonstationary problem of heat conduction is obtained in the region of Laplace transforms. In solution of this problem, there appear summationintegral equations with the parameter of the integral Laplace transform (Lparameter) and the parameter of the finite integral Hankel transform (Hparameter).     

Two-dimensional dynamic analysis of thermal stresses in a finite-length FG thick hollow cylinder subjected to thermal shock loading using an analytical method

This work is aiming to present an analytical method to study the dynamic behavior of thermoelastic stresses in a finite-length functionally graded (FG) thick hollow cylinder under thermal shock loading. The thermo-mechanical properties are assumed to vary continuously through the radial direction as a nonlinear power function. Using Laplace transform and series solution, the thermoelastic Navier equations in displacement form are solved analytically. The solution of the displacement field in the FG cylinder is obtained in the Laplace domain. Also, the fast Laplace inverse transform method (FLIT) is employed to transfer the results from Laplace domain to time domain. The effects of thermal shock loading on the dynamic characteristics of the FG thick hollow cylinder are studied in various points across the thickness of cylinder for various grading patterns of FGMs. A good agreement can be seen in the comparison of the obtained results based on the presented analytical method with published data.     

Dissipative heating of a hollow viscoelastic cylinder subjected to the action of normal loads moving along its surface with constant angular velocity

We consider a two-dimensional quasistatic problem of the stress-strain state and dissipative heating of a hollow circular viscoelastic cylinder subjected to the action of two, normal diametrically opposite loads moving along the surface of the cylinder with constant angular velocity. It is assumed that the physicomechanical properties of the material are independent of temperature. In this case, the combined problem of thermoviscoelasticity splits into two linear problems: the problem of the stress-strain state of the cylinder without axial symmetry and the axisymmetric problem of heat conduction with temperature averaged over a cycle and a known heat source. The exact solutions of these problems are obtained. The influence of both the coefficient of heat transfer on the inner boundary of the cylinder and the sizes of the cylinder on the temperature of dissipative heating are investigated. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 2, pp. 67–73, March–April, 1999.     

A problem in generalized magneto-thermoelasticity for an infinitely long annular cylinder

The problem of an infinitely long annular cylinder whose inner and outer surfaces are subjected to known surrounding temperatures and are traction-free is considered in the presence of an axial uniform magnetic field. The problem is in the context of generalized magneto-thermoelasticity theory with one relaxation time. The Laplace transform with respect to time is used. A numerical method based on a Fourier-series expansion is used for the inversion process. Numerical computations for the temperature, displacement and stress distributions as well as for the induced magnetic and electric fields are carried out and represented graphically.     

Magnetothermoelastic transient response of a multilayered hollow cylinder subjected to magnetic and vapor fields

Summary This paper deals with one-dimensional axisymmetric quasi-static coupled magnetothermoelastic problems subjected to magnetic and vapor fields. Laplace transform and finite difference methods are used to analyze the problems. Using the Laplace transform with respect to time, the general solutions of the governing equations are obtained in the transform domain. The solution is obtained by using the matrix similarity transformation and inverse Laplace transform. We obtain solutions for the temperature and thermal deformation distributions for a transient and steady state. It is demonstrated that the computational procedures established in this paper are capable of solving the generalized magnetothermoelasticity problem of a hollow cylinder with nonhomogeneous layers.     

The temperature field of an infinite solid containing a cylindrical channel with a thermally thin surface coating

The Laplace method of integral transformation is used to find an analytical solution of the problem of unsteady-state heat conduction for an infinite isotropic solid containing a cylindrical channel with a thermally thin surface coating filled with a high-temperature gas.     

Thermal stresses in a viscoelastic trimaterial

A general solution for a three dissimilar sandwiched medium subjected to a point heat source and a three-phase composite cylinder subjected to a remote uniform heat flow is presented in this work. The solutions to the heat conduction and thermoelastic problems are derived based on the method of analytic continuation associated with the alternation technique. A rapidly convergent series solution for both the temperature and the stress field, which is expressed in terms of an explicit general term of the corresponding homogeneous potential, is obtained in an elegant form. The hereditary integral in conjunction with the Kelvin–Maxwell model is applied to simulate the thermoviscoelastic properties while a thermorheologically simple material is considered. Based on the correspondence principle, the Laplace transformed thermoviscoelastic solution is directly determined from the corresponding thermoelastic one. The real-time solution can then be solved numerically by taking inverse Laplace transform. Two typical examples concerning interfacial stresses for plane-layered media and circularly cylindrical-layered media are discussed in detail.     

New implementation of MLBIE method for heat conduction analysis in functionally graded materials

The meshless local boundary integral equation (MLBIE) method with an efficient technique to deal with the time variable are presented in this article to analyze the transient heat conduction in continuously nonhomogeneous functionally graded materials (FGMs). In space, the method is based on the local boundary integral equations and the moving least squares (MLS) approximation of the temperature and heat flux. In time, again the MLS approximates the equivalent Volterra integral equation derived from the heat conduction problem. It means that, the MLS is used for approximation in both time and space domains, and we avoid using the finite difference discretization or Laplace transform methods to overcome the time variable. Finally the method leads to a single generalized Sylvester equation rather than some (many) linear systems of equations. The method is computationally attractive, which is shown in couple of numerical examples for a finite strip and a hollow cylinder with an exponential spatial variation of material parameters.     

Nonsteady heat transfer from a cylinder with injection

The problem of nonsteady heat transfer from a cylinder in the presence of radial injection is analyzed. The heat flux at the surface of the cylinder is found from the assigned variation in the surface temperature by the method of [1].Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 34, No. 5, pp. 923–927, May, 1978.     

Hyperbolic Heat Conduction in a Functionally Graded Hollow Sphere

Non-Fourier hyperbolic heat conduction in a heterogeneous sphere is investigated in this article. Except for the thermal relaxation time, which is assumed to be constant, all other material properties vary continuously within the sphere in the radial direction following a power law. Boundary conditions of the sphere are assumed to be spherically symmetric, leading to a one-dimensional heat conduction problem. The problem is solved analytically in the Laplace domain, and the final results in the time domain are obtained using numerical inversion of the Laplace transform. The transient responses of temperature and heat flux are investigated for different non-homogeneity parameters and normalized thermal relaxation constants. The current results for the specific case of a homogeneous sphere are validated by results available in the literature.