Periodic heat conduction with relaxation time in cylindrical geometry

Steady-periodic heat conduction with relaxation time in an infinitely long hollow cylinder is considered. Four boundary value problems, with boundary conditions of the first and of the second kind, are solved analytically. The solution for a solid cylinder with a sinusoidally varying surface temperature is obtained as a special case of a solution found for the hollow cylinder. The effects of the relaxation time on the steady-periodic temperature field are analysed, in details, for a solid cylinder with a sinusoidally varying surface temperature and for a hollow cylinder with a sinusoidally varying heat flux at the inner surface and with a constant temperature at the outer surface. The results show that thermal resonances may occur and suggest that accurate measurements of the relaxation time could be obtained by means of experiments on steady-periodic heat conduction in cylindrical geometry. Received on 15 April 1997     

Determination of the thermal stress wave propagation in orthotropic hollow cylinder based on classical theory of thermoelasticity

The thermoelasticity problem in a thick-walled orthotropic hollow cylinder is solved analytically using finite Hankel transform and Laplace transform. Time-dependent thermal and mechanical boundary conditions are applied on the inner and the outer surfaces of the cylinder. For solving the energy equation, the temperature itself is considered as boundary condition to be applied on both the inner and the outer surfaces of the orthotropic cylinder. Two different cases are assumed for solving the equation of motion: traction–traction problem (tractions are prescribed on both the inner and the outer surfaces) and traction–displacement (traction is prescribed on the inner surface and displacement is prescribed on the outer surface of the hollow orthotropic cylinder). Due to considering uncoupled theory, after obtaining temperature distribution, the dynamical structural problem is solved and closed-form relations are derived for radial displacement, radial and hoop stress. As a case study, exponentially decaying temperature with respect to time is prescribed on the inner surface of the cylinder and the temperature of the outer surface is considered to be zero. Owing to solving dynamical problem, the stress wave propagation and its reflections were observed after plotting the results in both cases.     

On a stress function method of a thermoelastic problem expressed in cylindrical coordinates in a multiply-connected region exhibiting temperature-dependent material properties

Summary This paper is concerned with the formulation of a plane thermoelastic problem in a multiplyconnected region exhibiting temperature-dependent material properties in terms of a stress function by deriving the integral conditions necessary for the assurance of the single-valuedness of the rotation and displacements, i.e., new Michell's conditions and the finite difference representation of the resulting fundamental equations.The method of solution for the thermoelastic problem in the multiply-connected region is applied to a transient plane-strain thermal stress problem in a hollow circular cylinder having temperature-dependent material properties subjected to an asymmetrical heating by a high-temperature fluid on the inner surface of the cylinder.

---

Zur Methode der Spannungsfunktion bei thermoelastischen Problemen mit mehrfach zusammenhängendem Gebiet und temperaturabhängigen Materialeigenschaften

Übersicht In dieser Untersuchung wird ein thermoelastisches Problem mit mehrfach zusammenhängendem Gebiet und temperaturabhängigen Materialeigenschaften mit Hilfe einer Spannungsfunktion behandelt. Die Bedingungen für Eindeutigkeit von Rotation und Verschiebung werden hergeleitet. Die Grundgleichungen des Problems werden mit der Methode der finiten Differenzen gelöst.Als Anwendungsbeispiel wird ein hohler Kreiszylinder mit temperaturabhängigen Werkstoffeigenschaften betrachtet. Der Zylinder wird dabei durch eine Flüssigkeit mit hoher Temperatur in seinem Innern einer symmetrischen Erwärmung unterworfen.

     

Free-convection flow through an annular porous medium

This study addresses the Brinkman-extended Darcy model (Brinkman flow) of a laminar free-convective flow in an annular porous region. Closed form expressions for Velocity field, Temperature field, Skin-friction and Mass flow rate are given, under a thermal boundary condition of mixed kind at the outer surface of the inner cylinder while the inner surface of the outer cylinder is isothermal. The governing independent parameters are identified to be Darcy number (Da) and ratio of outer to inner radii (R). It is hoped that the study of such flows gives limiting conditions for developing flows and provides an analytical check on numerical solutions for more complex problems dealing with non-Darcian free-convection flow in an annular region.     

Axisymmetric circumferential internal crack problem of a thick-walled cylinder with inner and outer claddings

The elastostatic axisymmetric problem for a long thick-walled cylinder containing an axisymmetric circumferential internal crack with two claddings is considered. The claddings having different elastic properties than the hollow cylinder are assumed to be bonded to inner and outer wall of the hollow cylinder. The problem is formulated in terms of a singular integral equation of a well known type, the derivative of the crack surface displacement being the density function, using the standard transform technique. By using appropriate quadrature formulas, the integral equation is reduced to a system of linear algebraic equations. This system is solved numerically and the related stress-intensity factors are calculated for the cases of hollow cylinder with two claddings bonded to inner and outer wall of the cylinder, a cladding bonded to inner wall of the cylinder, a cladding bonded to outer wall of the cylinder and no cladding under axial tensile load. The influence of the geometrical configuration, the claddings and internal crack length on the stress-intensity factors is shown graphically.     

Multiple axial cracks in a coated hollow cylinder due to thermal shock

The transient thermal stress problem of an inner-surface-coated hollow cylinder with multiple pre-existing surface cracks contained in the coating is considered. The transient temperature, induced thermal stress, and the crack tip stress intensity factor (SIF) are calculated for the cylinder via finite element method (FEM), which is exposed to convective cooling from the inner surface. As an example, the material pair of a chromium coating and an underlying steel substrate 30CrNi2MoVA is particularly evaluated. Numerical results are obtained for the stress intensity factors as a function of normalized quantities such as time, crack length, convection severity, material constants and crack spacing.     

Analysis of entropy generation and thermal stability in a long hollow cylinder with asymmetry convective cooling

The inherent irreversibility and thermal stability in a long hollow cylinder with temperature-dependent internal heating and asymmetric convective cooling at both inner and outer surfaces is investigated. Analytical solution is obtained for the governing equation and the expressions for the temperature field, thermal stability criterion, volumetric entropy generation number, and irreversibility distribution ratio are presented. With certain combinations of the heat transfer parameters, entropy generation rates can be minimized.     

Non-Fourier heat conduction in a finite hollow cylinder with periodic surface heat flux

Analytical solution of the non-Fourier axisymmetric temperature field within a finite hollow cylinder exposed to a periodic boundary heat flux is investigated. The problem studied considering the Cattaneo–Vernotte (CV) constitutive heat flux relation. The material is assumed to be homogeneous and isotropic with temperature-independent thermal properties. The standard method of separation of variables is used for solving the problem with time-independent boundary conditions, and the Duhamel integral is used for applying the time dependency. The solution is applied for the special cases of harmonic uniform heat flux and an exponentially pulsed heat flux with Gaussian distribution in outer surface for modeling a laser pulse, and their respective non-Fourier thermal behavior is studied.     

Features of how surface waves form in a cylinder made of a hard material and filled with a fluid

The properties of harmonic surface waves in an elastic cylinder made of a rigid material and filled with a fluid are studied. The problem is solved using the dynamic equations of elasticity and the equations of motion of a perfect compressible fluid. It is shown that two surface (Stoneley and Rayleigh) waves exist in this waveguide system. The first normal wave generates a Stoneley wave on the inner surface of the cylinder. If the material is rigid, no normal wave exists to transform into a Rayleigh wave. The Rayleigh wave on the outer surface forms on certain sections of different dispersion curves. The kinematic and energy characteristics of surface waves are analyzed. As the wave number increases, the phase velocities of all normal waves, except the first one, tend to the sonic velocity in the fluid from above __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 9, pp. 48–62, September 2007.     

On the modeling of thermo-mechanical phase transformations in solids

The present paper represents an effort to model coupled thero-mechanical effects in the mcroscopic response of solids that arise from the occurrence of phase transformations. A Helmholtz free energy potential is constructed to describe the response of the thermoelastic material to be considered. Apart from some considerations pertaining to properties of the hypothetical material, the analysis is carried out in the context of a simple problem, idealized from an experiment, in which an annular cylinder is deformed to a state of radially symmetric, finite anti-plane shear in the presence of differing inner and outer surface temperatures. After constructing all radially symmetric weak solutions involving at most a single surface of discontinuity of strain or temperature gradient, we determine the implications for quasi-static motions of the second law of thermodynamics. In particular, the results concerning creep as predicted by the present model are in qualitative agreement with the results of the motivating experiment.     

Influence of thermally induced chemorheological changes on the torsion of elastomeric circular cylinders

When an elastomeric material is deformed and subjected to temperatures above some characteristic value T _cr (near 100^∘C for natural rubber), its macromolecular structure undergoes time and temperature-dependent chemical changes. The process continues until the temperature decreases below T _cr. Compared to the virgin material, the new material system has modified properties (reduced stiffness) and permanent set on removal of the applied load.A new constitutive theory is used to study the influence of the changes of macromolecular structure on the torsion of an initially homogenous elastomeric cylinder. The cylinder is held at its initial length and given a fixed twist while at a temperature below T _cr. The twist is then held fixed and the temperature of the outer radial surface is increased above T _cr for a period of time and then returned to its original value. Assuming radial heat conduction, each material element undergoes a different chemical change. After enough time has elapsed such that the temperature field is again uniform and at its initial value, the cylinder properties are now inhomogeneous. Expressions for the time variation of the twisting moment and axial force are determined, and related to assumptions about material properties. Assuming the elastomeric networks to act as Mooney-Rivlin materials, expressions are developed for the permanent twist on release of torque, residual stress, and the new torsional stiffness in terms of the kinetics of the chemical changes.     

Transient thermal elastic fracture of a piezoelectric cylinder specimen

A finite piezoelectric cylinder with an embedded penny-shaped crack is investigated for a thermal shock load on the outer surface of the cylinder. The theory of linear electro-elasticity is applied to solve the transient temperature field and the associated thermal stresses and electrical displacements without crack. These thermal stresses and electrical displacements are added to the surfaces of the crack to form an electromechanical coupling and mixed mode boundary-value problem. The electrically permeable crack face boundary condition assumption is used, and the thermal stress intensity factor and electrical displacement intensity factor at the crack border are evaluated. The thermal shock resistance of the piezoelectric cylinder is evaluated for the analysis of piezoelectric material failure in practical engineering applications.     

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…     

Unsteady numerical simulation of double diffusive convection heat transfer in a pulsating horizontal heating annulus

A numerical study is conducted on time-dependent double-diffusive natural convection heat transfer in a horizontal annulus. The inner cylinder is heated with sinusoidally-varying temperature while the outer cylinder is maintained at a cold constant temperature. The numerical procedure used in the present work is based on the Galerkin weighted residual method of finite-element formulation by incorporating a non-uniform mesh size. Comparisons with previous studies are performed and the results show excellent agreement. In addition, the effects of pertinent dimensionless parameters such as the thermal Rayleigh number, Buoyancy ratio, Lewis number, and the amplitude of the thermal forcing on the flow and heat transfer characteristics are considered in the present study. Furthermore, the amplitude and frequency of the heated inner cylinder is found to cause significant augmentation in heat transfer rate. The predictions of the temporal variation of Nusselt and Sherwood numbers are obtained and discussed.     

Numerical and analytical simulation of peristaltic flows of generalized Oldroyd‐B fluids

In this paper, we study the peristaltic flows of generalized Oldroyd‐B fluids through the gap between concentric uniform tubes under the assumption of large wavelength and low Reynolds number approximations. The inner tube is rigid and the outer tube has a sinusoidal wave travelling down its wall. Homotopy perturbation and variational iteration methods are used for solution of the problem. The obtained solution is then used to discuss various interesting features of peristalsis. The effects of relaxation time, retardation time and radii of the tubes on pressure rise and friction forces (per wavelength on the inner and outer tubes) are discussed with illustrations. It is found that pressure rise diminishes with increase in relaxation time or the ratio of radii of inner and outer tubes. It increases with increasing retardation time. The effects of both time parameters on friction forces have the opposite behavior to that of pressure rise. Copyright © 2010 John Wiley & Sons, Ltd.     

QUALITATIVE ANALYSIS OF DYNAMICAL BEHAVIOR FOR AN IMPERFECT INCOMPRESSIBLE NEO-HOOKEAN SPHERICAL SHELL

IntroductionIn applications, it is commonly considered that the phenomena of cavity formation,growth and run-through of adjacent cavities occur in materials as precursors to failure. Thesephenomena are mainly due to instability of materials. On the other …     

Water surface wave radiation generated by multiple cylinders oscillating with identical frequency

ＩｎｔｒｏｄｕｃｔｉｏｎＡｆｕｎｄａｍｅｎｔａｌｓｕｂｊｅｃｔｉｎｔｈｅｓｔｕｄｙｏｆｉｎｔｅｒａｃｔｉｏｎｂｅｔｗｅｅｎｗａｖｅｓａｎｄｂｏｄｙｉｓｔｏｓｏｌｖｅｔｈｅｔｗｏ＿ｄｉｍｅｎｓｉｏｎａｌｒａｄｉａｔｉｏｎｐｒｏｂｌｅｍｇｅｎｅｒａｔｅｄｂｙｃｙｌｉｎｄｅｒｓｏｓｃｉｌｌａｔｉｎｇｉｎｏｒｂｅｌｏｗｔｈｅｆｒｅｅｗａｔｅｒｓｕｒｆａｃｅ,ｗｈｉｃｈｈａｓａｔｔｒａｃｔｅｄｗｉｄｅａｔｔｅｎｔｉｏｎ．ＥｖｅｒｓｉｎｃｅＵｒｓｅｌｌｐｕｂｌｉｓｈｅｄｔｈｅｐａｐｅｒ［１］ｉｎｖｏｌｖｉｎ…     

Thermally induced vibration and stability of laminated composite plates with temperature-dependent properties

This paper presents a study on the buckling and vibration of initially stressed composite plates with temperature-dependent material properties in thermal environments. The initial stress is taken to be a combination of a pure bending stress and an axial stress. The temperature distribution in the plate is assumed to be uniform and linear in the transverse direction. The governing equations including the transverse shear deformation effects are established using the variational method. The effects of various parameters on the buckling and vibration behaviors of laminated plates with respective temperature-dependent and temperature-independent material properties are investigated. The buckling load and natural frequency are sensitive to the thermal stresses and initial stresses. Numerical results reveal that temperature-dependent material properties should be considered in the buckling and vibration analysis for laminated plates under thermal conditions.     

功能梯度压电材料圆环位移和电势边值问题的精确解

圆环形的压电材料器件在智能结构中得到了广泛的应用。本文推导了横观各向同性功能梯度压电材料圆环在内、外边界上给定位移和电势情况下的一般解。极化方向在圆环的半径方向,材料常数的梯度方向也设定在半径方向,并可表示为半径r的幂,本构关系为线性。然后推导了压电圆环外壁固定、接地,内壁沿垂向有一微小位移、电势分别为余弦分布和均匀分布的问题的精确解,并计算了该问题在这两种电势情况下产生的无量纲形式的径向和环向位移、电势、应力及电位移沿径向分布的数值结果。计算中考虑了不同的材料梯度,以及内壁的位移与电势的不同比例。