Ideal Thermal Contact Research Articles

D'Alembert's Solution in Thermoelasticity—Impact of a Rod Against a Heated Barrier: Part I. A Case of Uncoupled Strain and Temperature Fields

The problem of impact of a thermoelastic rod against a heated rigid barrier is considered, in so doing lateral surfaces and free end of the rod are heat insulated, while there is either free heat exchange between the rod and the rigid obstacle within contacting end or ideal thermal contact, as a particular case. The rod's thermoelastic behavior is described by the Green–Naghdi theory of thermoelasticity. D'Alembert's method, which is based on the analytical solution of equations of the hyperbolic type describing the dynamic behavior of the thermoelastic rod, is used as the method of solution. This solution involves four arbitrary functions which are determined from the initial and boundary conditions and are piecewise constant functions. The procedure developed enables one to analyze the influence of thermoelastic parameters on the values to be found, as well as to investigate numerically the longitudinal coordinate dependence of the desired functions at each fixed instant of the time beginning from the moment of the rod's collision with the barrier up to the moment of its rebound. The case of uncoupled stress and temperature fields is examined in the first part of the paper, while the case of coupling thermoelasticity is considered in detail in the companion paper. It has been shown that the possibility for generating the reflected thermal wave from the incident elastic wave at the free rod's end is unavailable in the case of the uncoupled strain and temperature fields, and that the rod's rebound may occur either at the moment of arrival at the contact place of the reflected elastic wave from the incident thermal wave or at the time when the reflected elastic wave from the incident elastic wave reaches the contact point.

Singular perturbation analysis of dynamic fields in a thermoelastic solid with a small surface-breaking crack

An asymptotic analysis is presented for a dynamic problem of a semi-infinite isotropic thermoelastic solid with a small surface breaking crack. The exterior surface of the solid is subjected to a series of short thermal pulses. The crack surface is traction free and an ideal thermal contact is assumed across the crack. The stress intensity factor is asymptotically evaluated as a function of the crack depth and time. The effect of a boundary layer associated with the diffusive term is identified. The theoretical model is supplied with numerical simulations.

Nonstationary Heat Conduction of Three-Dimensional Bodies with Uneven Inclusions

A study is made of the nonstationary heat conduction of a three-dimensional body with an uneven inclusion mated with the matrix by an ideal thermal contact. Using thermal potential determined and studied on uneven surfaces, the problem has been reduced to an unconditionally solvable system of integral equations. The results have been illustrated with an example of sudden heating of a body with a circular conic inclusion.

Thermoelements with side heat exchange

Thermoelements with side heat exchange are studied. These thermoelements differ from conventional thermoelements in the position of their arms: one pair of end sides is in ideal thermal and electrical contact, whereas the other pair is in isothermal contact with a thermostat; thermal flux is incident on one of the side faces, while the three other sides are adiabatically isolated from the environment. Thermoelectric power and efficiency under steady-state conditions are investigated. The results obtained are analyzed, and possible applications are suggested.

Solution of the Unsteady Heat-Conduction Equation for a System of Two Bounded Heterogeneous Cylinders with the Use of The Integral Transformations of Hankel and Laplace

Consideration has been given to the problem of uniform unsteady lateral heating of two bounded cylinders having dissimilar thermophysical characteristics and being in ideal thermal contact. The exact analytical solution for determination of a three‐dimensional temperature field in real space has been found with the use of the integral‐transformation method. The distinctive features of the solution obtained have been investigated and examples of specific calculations have been given.

Two‐Dimensional Stationary Temperature Field of a System of Bounded Inhomogeneous Cylinders which Are in Ideal Thermal Contact

The problem on uniform stationary lateral heating of two bounded cylindrical bodies with different thermophysical characteristics which are in ideal thermal contact within the region of contact has been considered. The exact analytical solution of this problem has been obtained and the conditions of energy balance have been investigated.

On the Question of Calculation of Temperature Fields in Piecewise-Homogeneous Orthotropic Media

Based on the theory of R-functions, we propose structures of a solution of the boundary-value problem of heat conduction in piecewise-homogeneous orthotropic media, satisfying the conditions of convective heat exchange on the boundary of an orthotropic body and the conditions of ideal thermal contact on the boundary between media. We present the results of a computational experiment confirming the correctness and computational fitness of the proposed structural models.

An estimation of thermophysical properties of layered materials by the laser-flash method

An investigation of two-layered and three-layered systems by the flash method has been carried out. Because of the behaviour of the material analysed, the theory considers two-layered and three-layered composites with the ideal thermal contact described by zero thermal contact resistance. The data reduction algorithm is introduced and results are given of an estimation of the thermal diffusivity of alumina (aluminium oxide, Al 2 O 3 ) on copper/alumina layers. An estimation of the thermal diffusivity of one layer requires, besides the knowledge of other relevant properties (density, heat capacity, and thickness of components), knowledge of the thermal diffusivity of the remaining layer(s). The way the error in the known thermal diffusivity influences the error in the unknown thermal diffusivity estimation is analysed. The proposed approach, which indicates error propagation and estimates the accuracy limits, is applied to a two-layered system.

Adaptive correction of dynamic temperature measurements to improve estimation of thermophysical properties

The influence of sensor dynamics on the estimation of thermophysical properties of materials in transient heat conduction experiments is investigated. The temperature measured by the sensor (subminiature sheathed thermocouple) is corrected by identifying, in the same experiment, as well as the thermophysical properties of the material, also the unknown coefficients appearing in the dynamic model of the sensor itself. This approach provides an auto-adaptive temperature correction which can be used to improve the accuracy of the estimated thermophysical properties and to give quantitative information on the behaviour of the sensor in a dynamic regime. Different kinds of sensor - material coupling are investigated and compared: ideal thermal contact; presence of a thin air gap with or without the application of a heat sink compound at the measurement junction. Several results are presented, both from numerical simulations and true experiments at atmospheric pressure. Moreover, first results concerning the dynamic behaviour of the thermocouple inserted in a porous insulating material below atmospheric pressure are also presented. Among the different dynamic models utilised for characterising the transient thermal behaviour of the sensor, the first-order differential system with constant coefficients is relatively simple to implement, efficient, stable, and recommended.

Three-dimensional thermoelasticity problems for nonuniformly heated laminar transversally isotropic plates

Three-dimensional heat-conduction and thermoelasticity boundary-value problems are considered for laminar transversally isotropic rectilinear plates under the action of a nonuniform temperature field. Both ideal and nonideal thermal and mechanical contact conditions at the interfaces are fulfilled. Cases where the roots of the basic characteristic equation are different and include duplicate values are discussed for transversally isotropic bodies (rectangular anisotropy). In the numerical calculation of thermoelastic deformation for a two-layer plate, a sinusoidal face temperature is specified. Characteristic thermomechanical effects are discovered.

The plane contact problem of steady thermoelasticity taking heat generation into account

The plane steady contact problem of thermoelasticity when there is heat generation from friction, which arises when an infinite cylindrical punch moves over the surface of an elastic half-space along its generatrix, is considered. It is assumed that heat exchange between the free boundary of the half-space and the surrounding medium obeys Newton's law, while the condition for ideal thermal contact exists in the region in which the solids interact. The problem is reduced to a system of three integral equations in the heat fluxes and temperature. The effect of the thermal and mechanical properties of the cylinder and the half-space on the main contact characteristics is investigated numerically.

Thermoelastic state of a two-component hollow cylinder with edge radial cracks

Stationary two-dimensional axisymmetric problems of thermal conductivity and thermoelasticity for a hollow two-component cylinder with cracks are studied by the method of singular integral equations. The cross section of the cylinder has the form of a circular concentric ring with a layer of another material that also has the form of a concentric ring and contains edge radial cracks. The surfaces of the cylinder are free of stresses. Thermal processes on these surfaces are characterized by temperature conditions of the third kind. Conditions of ideal thermal and mechanical contact are satisfied on the interface of the two media. A numerical solution is obtained for the case where the inner and outer cylindrical surfaces are kept at different constant temperatures. Stress intensity factors near the tip of one or two edge cracks were found for various values of thermal and mechanical characteristics of the cylinder.

Generalized dynamic problem of thermoelasticity for infinite two-layer rods

The method of influence functions is applied to determine the structure of the generalized nonstationary temperature field in infinite two-layer rods with ideal thermal contact along the joining line. The influence functions are constructed using the time-domain Laplace transform. Generalized dynamic displacement and stress fields are constructed by the operational method.

Calculation of the time required by a Gifford-McMohan microrefrigerator to go into normal operation

One of the basic parameters of microrefrigerators (MR) working on the Gifford-McMohan cycle is the time required to go into normal operation. We have developed a method of calculation of the starting characteristics of a two-stage MR working on this cycle. As in [1-3], our procedure is based on the energy balance method. Assumptions made in this case were as follows: temperature distribution along length of liner and displacer is linear at each instant; all elements in liner and displacer of the corresponding stage have identical temperature in the saem section; there is ideal thermal contact between cooling head and cooled object. Processes of cooling of masses in the MR were assumed to be quasi-steady at each instant. Time required by the second stage to attain the set cryostatically controlled temperature is taken as the time to go into normal operation. The dependence of specific heat of materials used in MR designs on temperature is represented as polynomials [4].

Thermoelastic state of an isotropic medium containing an anisotropic ellipsoidal inclusion, for ideal mechanical and thermal contact

Thermoelastic state of an isotropic medium containing an anisotropic ellipsoidal inclusion, for ideal mechanical and thermal contact

Charge carrier sorting over energy in semiconductors by means of phonon diffusion

A study is made of anomalous temperature fields which occur in finite semiconductor specimens. These fields are created by charge carrier sorting over energy due to mutual electron-phonon entrainment at arbitrary rates of electron and phonon energy relaxation at the boundaries. Expressions are found for entrainment levels which depend on specimen dimensions, cooling length, and electron and phonon energy relaxation rates at the boundaries, which when exceeded cause the electron temperature differential between the boundaries to exceed the temperature differential between the heater T1 and cooler T2, producing an initiating phonon flux, while for scattering on deformation acoustical phonons these differentials have opposite algebraic sign. In the case where the electrons are thermally insulated, while the phonons have ideal thermal contact with heater and cooler, for total entrainment the electron temperature differential produced by charge carrier sorting over energy due to phonon entrainment is an order of magnitude higher than T1-T2, and produces the major contribution to thermo-emf in sufficiently short specimens.

The temperature, heat flux, and growth kinetics for a metal crust on a refractory

The assumptions of ideal thermal contact and semiinfinite refractory lining have been used in an analytic solution for the crust kinetics. That solution has an advantage over a numerical one in that it enables one to analyze the effects of the various physical factors. The solution has been obtained in terms of dimensionless variables, particularly as a function of the unique dimensionless parameter, which enables one to evaluate crustal development for any physical conditions. Further improvement to the solution can be obtained by incorporating the nonideal refractory-liquid contact.

Simultaneous DSC-TG up to 1700 K

A DSC-TG-sample carrier up to 1700 K employs plate-type thermocouples as heat flux sensors. Flat bottomed sample pans ensure an almost ideal thermal contact with these sensors, resulting in high sensitivity and peak resolution. Its performance was tested with standard materials and some polymeric samples. The construction of the sample carrier permits quantitative determinations of specific heat at high temperatures. Results are shown with sapphire, aluminium oxide, graphite and glass samples.

Wärmeleitfähigkeitsmessungen mit dem Plattengerät: Einfluβ der Schutzringbreite auf die Meβunsicherheit

The temperature field in circular and square plate test specimens is calculated and thereby the error from the heat exchange at the outer edge of the guard ring derived for single and double plate devices under conditions of isothermal hot and cold plates and ideal thermal contact. The error is shown to be proportional to the reduced temperature difference (difference between the mean specimen and the ambient temperatures divided by the difference between the hot and cold plate temperatures) and the margin of error, therefore, can be optimally reduced by an appropriate adjustment in the ambient temperature. Experiments on an extruder foam confirm the results of the analytical calculations. Diagrams and tables which are developed on the basis of the above derived relationships, make possible estimation of margin of error for different measuring arrangements for plate devices of usual sizes.