Symmetric Temperature Distribution Research Articles

Ion drag and thermophoretic forces acting on free falling charged particles in an rf-driven complex plasma

Monodisperse plastic microspheres have been dropped through a long radio-frequency discharge column. The trajectories of the falling particles have been measured. It was observed that the particles are driven out of the plasma. From the trajectory analysis and plasma measurements the forces on the particles have been derived. Special attention has been paid to the thermophoresis and ion drag forces which are also considered to be responsible for the void formation in microgravity experiments. Two experimental situations have been considered here: first a plasma characterized by its natural symmetric electric potential and temperature distribution and second, a plasma with an asymmetric temperature and electric potential profile. For both cases a good agreement has been found between the measured “trajectory force” obtained from the particle trajectory analysis and the sum of the ion drag, thermophoretic and electric field force.

AN INTERFEROMETRIC INVESTIGATION OF NATURAL CONVECTION IN A PARTIALLY OPENED ENCLOSURE WITH A DISCRETE HEAT SOURCE

Natural convection in an enclosure with an opening in the right vertical wall and a heat source on the bottom surface was investigated using a holographic interferometric technique. In particular, emphasis was placed on the effects caused by changing the opening length, divider height, and heat source temperature. When the enclosure was partially opened, warm air from inside escaped from the upper part of the opening and was replaced by surrounding air, which flowed into the enclosure from the lower part of the opening. The flow rates of inflow and outflow through this opening increased with larger opening length, smaller divider height, and higher heater temperature. When the opening length was small, the opening did not significantly affect the upward flow of warm air from the heater, and resulted in a symmetrical temperature distribution. The divider prevented the development of upward flow from the heat source such that the temperature in the absence of a divider was generally higher than that for the longest divider. For cases with a large opening length, the upward flow was forced to move into the enclosure's left-hand side by the increased inflow. The effect of the divider height was not significant due to the increased flow rates through the increased opening length. The temperatures achieved with the longest divider were a little higher than those for the other cases due to the lower cold flow rate and the blocking of the cold air inflow by the longest divider.

A Study on the Characteristics of Natural Convection in a Partially Opened Enclosure with a Heat Source

Natural convection heat transfer in an enclosure with an opening in the right veritcal wall and a heat source at the bottom surface is investigated using a holographic interferometric technique. The effects of the opening length, divider length attached to the top wall, and heater temperature on the temperature distribution are examined. The opening length as well as the divider length greatly affects the degree of inflow and outflow of air. In the case of small opening length, the opening doesnt affect much the upward warm air flow resulting in the symmetric temperature distribution .The upward flow in hindered by the divider resulting in the decrease of heat transfer from the heater region to the upper region. The longest divider shows the highest temperature in the lower region of enclosure. In the case of large opening length, the inward cold flow moves the upward flow to the left direction. Among the cases of different divider length, the case of H(sub)d=0.25H shows the highest temperature in the lower region of enclosure.

Thermal stress in a trigonal crystal rod: Second corrected solution

The surface thermal stresses from an earlier article for a rectangular trigonal crystal rod with zero average stress on each lateral surface are developed into Fourier series and ordinary (T=0) stress solutions are added to attempt to zero the remaining surface stress. To first zero the surface tensile stress, these stresses are developed as sine series so the shear stresses must be developed as cosine series. This leads to stress “swapping” between surfaces as a residual shear stress remains. Another computer code like the one developed for the earlier article has been generated to add these correcting stresses to the original stresses. For a chosen symmetric temperature distribution, iteration of a process to correct the stresses has converged to nearly zero remaining stress on the lateral surfaces.

Tests of the geometrical description of blood vessels in a thermal model using counter-current geometries

We have developed a thermal model, for use in hyperthermia treatment planning, in which blood vessels are described as geometrical objects; 3D curves with associated diameters. For the calculation of the heat exchange with the tissue an analytic result is used. To arrive at this result some assumptions were made. One of these assumptions is a cylindrically symmetric temperature distribution. In this paper the behaviour of the model is examined for counter-current vessel geometries for which this assumption is not valid. Counter-current vessel pairs intersecting a circular tissue slice are tested. For these 2D geometries vessel spacing, tissue radius and resolution are varied, as well as the position of the vessel pair with respect to the discretized tissue grid. The simulation results are evaluated by comparison of the different heat flow rates with analytical predictions. The tests show that for a fixed vessel configuration the accuracy is not a simple decreasing function of the voxel dimensions, but is also sensitive to the position of the configuration with respect to the discretized tissue grid.

A study of three-dimensional natural convection in high-pressure mercury lamps—III. Arc centering by magnetic field

The present work constitutes the third part of a series of work with the goal of developing a three-dimensional computational model to help understand the various physical mechanisms involved in high-pressure discharge arcs. The effect of an externally applied magnetic field on the convection and temperature characteristics is studied in the present effort. The classic experiment of Kenty is first simulated. It is found that the magnetic field can induce a downward velocity to the hot gas core to offset the buoyancy-induced nonuniformity in the temperature field. Separate pairs of contra-rotating recirculating eddies resulting from the magnetic and buoyancy effects can be identified. Qualitative as well as quantitative agreements between Kenty's experiment and the present prediction are observed. The feasibility of applying the magnetic control to optimize the operation of the modern discharge lamp is then investigated. The model reveals that convection strengthens if either the pressure inside the arc-tube or the magnitude of the magnetic field increases. Furthermore, with the same geometry, the required strength of the magnetic field to center the hot core and maintain a symmetric temperature distribution is linearly proportional to the arc-tube pressure. This finding yields a very useful method for optimizing the discharge lamp design.

Detecting phase transformations in electrically conductive materials by means of thermoelectric anomalies

A number of techniques are available to detect the transformation of the body-centred cubic phase (ferrite) to the face-centred cubic phase (austenite), and vice versa, in steels. These methods require the use of sophisticated measuring techniques. It was discovered that the electric potential generated at a dissimilar metal junction (the thermoelectric potential) is sensitive to the phase composition of the two metals forming the dissimilar junction. Using a simple electrical circuit it was possible to utilize this principle to detect phase transformations in a high chromium steel specimen during heat treatment. This is an elegant and novel technique to detect phase transformations in all cases where a temperature gradient exists across a specimen. A symmetrical temperature distribution along the length of specimen is not necessary for the success of this method.

Effect of thermally induced stresses on the rapid-thermal oxidation of silicon

During rapid-thermal processing (RTP), radiative losses from the edge of silicon wafers which are heated by uniform irradiation create a radial temperature gradient. This temperature gradient induces a stress distribution which is compressive at the center and tensile towards the edge of the wafer. This thermally induced stress affects oxidation kinetics during the rapid-thermal oxidation (RTO) of silicon. The tensile stress enhances the oxidation towards the edge of the wafer, which is opposite to the effect of the radial temperature gradient. For a radially symmetric temperature distribution, the resolved stress and its effect on oxidation are largest along specific crystal directions, namely, the slip directions on slip planes. The stress effect on oxidation is largest at low temperatures and for short times. The temperature dependence relates to the magnitude of the temperature gradient and yield strength of silicon at different temperatures. As the oxidation proceeds, the influence of the thermally induced stress on RTO kinetics diminishes as the effects of the intrinsic stress and the viscous properties of the oxide increase. These observations have implications for RTP temperature measurement and RTO process uniformity.

Thermoelastic Solutions for a Finite Substrate With an Electronic Device

Sneddon and Lockett obtained a fairly general solution to the steady-state thermoelastic problem for the thick plate (Sneddon and Lockett, 1960). In particular, they have obtained the exact solutions for axially symmetrical temperature distributions on the upper surface of the thick plate. In this note, their exact solution will be applied to an electronic problem, namely, a chip on a substrate with finite thickness. Emphasis is placed on the generation of dimensionless charts for the temperature, displacement, and stress distributions in the substrates. These charts are not only useful for designing substrates but also can be used to verify finite element analysis procedures.

Bethe lattice spin glass: The effects of a ferromagnetic bias and external fields. I. Bifurcation analysis

We present a rigorous analysis of the ±J Ising spin-glass model on the Bethe lattice with fixed uncorrelated boundary conditions. Phase diagrams are derived as a function of temperature vs. concentration of ferromagnetic bonds and, for a symmetric distribution of bonds, external field vs. temperature. In this part we characterize the bulk ordered phases using bifurcation theory: we prove the existence of a distribution of single-site magnetizations far inside the lattice which is stable with respect to changes in the boundary conditions.

Bethe lattice spin glass: The effects of a ferromagnetic bias and external fields. II. Magnetized spin-glass phase and the de Almeida-Thouless line

In this and the companion paper, we analyze the ±J Ising spin-glass model on the Bethe lattice with fixed uncorrelated boundary conditions. Phase diagrams are derived as a function of temperature vs. concentration of ferromagnetic bonds and, for a symmetric distribution of bonds, external field vs. temperature. In this part we characterize magnetized spin-glass (MSG) phases by divergence of an appropriate susceptibility: at zero field this signals the existence of an intermediate MSG phase; at nonzero field, this is used to identify the de Almeida-Thouless line.

Thermohydraulic Investigations of Decay Heat Removal Systems by Natural Convection for Liquid-Metal Fast Breeder Reactors

To examine the function of the safety-related SNR-2 decay heat removal concept, natural convection experiments were performed in two- and three-dimensional water models, scaled 1:20, under conditions of symmetric and nonsymmetric loads of the immersed coolers installed in the upper plenum at 180-deg positions with respect to each other. The temperature and velocity distributions were measured and the flow patterns recorded for different configurations of the instrumented plug.For symmetric load conditions, symmetric temperature and flow distributions were measured in two- and three-dimensional models. Nonsymmetric load conditions produce remarkable temperature differences between the two separated plenums of the two-dimensional model if fluid circulation is suppressed by a closed plug. An open plug allows fluid to pass through and shows lower temperature differences. In contrast, in the three-dimensional experiment, azimuthal fluid flow inside the plenum prevails even with the plug closed, and identical temperature distributions are measured. The calculations using the COMMIX-1B code are generally in good agreement with the measurements.

Thermal stresses in a transversely isotropic elastic solid weakened by an external circular crack

This paper examines the problem of the steady state thermoelastic behaviour of an external circular crack located in a transversely isotropic elastic medium. The surfaces of the crack are subjected to a symmetric temperature distribution. The mathematical analysis of the problem is approached via a Hankel transform development of the governing equations. Numerical results presented in the paper illustrate the manner in which the thermoelastic stress intensity factors are governed by the elastic and thermal properties of the transversely isotropic elastic solid.

POINT SOURCE OF HEAT IN AN ELASTOPLASTIC MEDIUM

Abstract An infinite elastoplastic medium (Tresca's criterion) is loaded with a spherically symmetrical time-dependent temperature distribution. The thermal expansion induced by changes in temperature can lead to the generation of plastic zones. It is shown that relatively simple formulas can be used to calculate the boundaries of the plastic zones for any temperature distribution. The cases of increasing and decreasing plastic zones are considered. These formulas are applied to the case of a constant point source of heat acting during a finite or infinite interval of time.

Transient thermal stresses in a bonded composite hollow circular cylinder under symmetrical temperature distribution

Abstract A general treatise for the transient thermal stress problem of a composite circular cylinder made by bonding is described under a symmetrical temperature distribution. Analysis is developed by stress function method by the aid of Laplace transforms. Numerical examples are illustrated for the hollow composite cylinder with several radius-ratios made by the different materials due to transient heating at the internal surface by liquid.

熱パルスによる低風速の測定

A pulsed-wire anemometer was developed for low velocity air flow down to 0.2m/s, which consists of a pulsed heating wire and two sensor wires, both being set down-stream. The current of the pulsed wire is electronically controlled so that a tracer of heated air has a spatially symmetric temperature distribution particularly around the maximum-temperature point when observed from the moving coordinate system. The velocity is detected from the time delay given by the maximum temperatures between the two sensor wires. This method is considered as a developed form of the pulsed-wire method originally informed by Bauer et al. or a developed form of the stationary heated-Wake metnhod by Kovasznay et al.Application of Bauer's method to the low velocity flow faces the difficulties caused by the variation of temperature distribution in the heated tracer due to the thermal diffusion, the error in detecting the moving tracer with a varying temperature distribution at the two separated-fixed points, and the time delay of detecting due to the heat capacity of the sensor. These difficulties were solved by the use of controlled heating current and the detection of the maximum, temperatures by two sensors.The waveform of the heating current pulse was theoretically and numerically analyzed in order to obtain heated tracer air With a symmetric temperature distribution at and above half the maximum temperature. Experimental investigation was made in the air flow using a wind tunnel of which the cross section is 70×140mm. The velocity investigated by this method ranges from 0.2m/s to 1.2m/s. Compared with the differential pulsed-wire method by Bradbury et al., the proposed method was shown to extend the measurement capability in the low velocity range.

Note on a paper by Mehta and Chaudhry

Mehta and Chaudhry [1] have dealt with the problem of determining the thermoelastic stresses in a rotating circular solid cylinder with axially symmetric temperature distribution, according to the finite deformation theory. In this note, it is shown that their paper is in error. After the error is corrected, their problem reduces to the corresponding one in isothermal elasticity, whose solution is well known.

Transient Thermal Stresses in Elasto-Plastic Discs

A thin circular disc of elastic-perfectly plastic material, subjected to an axially symmetric transient temperature distribution, is treated analytically. All material parameters are assumed to be independent of the temperature. Poisson's ratio is taken to be one-half. The Tresca yield condition with associated flow rule is employed.The temperature distribution is that which appears when the outer rim surface of the disc receives a rapid temperature increase and it is solved approximately by the collocation method.The analysis shows that under certain circumstances, plastic deformation will occur in a moving annular region. This region starts to develop at the exterior surface and moves inward, while changing its width. After a certain finite time its width shrinks to zero. Except for a residual constant state of strain, the strain field is then again elastic.An application to the method of separating the ring and the shaft in a shrink-fit is carried out numerically. The residual stresses in the ring are calculated.

Thermoelastic stresses in rotation of a circular cylinder in finite deformation theory

Using finite deformation theory, the thermoelastic stresses produced in a right circular cylinder rotating about its axis with constant angular velocity, under axially symmetric temperature distribution, have been evaluated. The effect of temperature distribution on the angular velocity consistent with the deformation Produced has been determined for a neo-Hookean type of material.

Experimental measurements of self-heating in the explosive decomposition of diethyl peroxide

A detailed investigation of the role of self-heating in the spontaneous ignition of gaseous diethyl peroxide has been made. Special emphasis has been given to quantitative aspects and, in particular, to the direct measurement of the temperature in the reacting gas. Entry times for reactants are accurately controlled by an electromagnetic valve. Temperature-position profiles are mapped from the moment of admission to within milliseconds of explosion. The results establish beyond doubt the thermal character of this explosion and also afford new information about the limitations of the generally accepted standard techniques. In sub-critical conditions around 190°C, a symmetrical (parabolic) temperature distribution is established within 0.2 sec after entry. Within the limits of experimental error, the shape and size of the profiles are in full agreement with the predictions of thermal explosion theory. The profile gradually decays as the peroxide is consumed. In super-critical conditions, accurate temperature profiles are more difficult to obtain, since the temperature increases very swiftly towards the onset of ignition; this necessitates very strict control of the initial conditions. The temperature profiles are again found to be parabolic, even at the very instant of explosion. The effect of inert diluents on the critical conditions for ignition have been examined in terms of the measured thermal conductivities of the mixtures. Qualitatively, there is the expected correlation between critical pressure and thermal conductivity, but the quantitative predictions are not exact. By systematically studying the temperature effects accompanying the entry of a wide variety (twenty) of inert gases, their origins have been identified. They arise from dynamic heating, inescapable on rapid entry to an evacuated vessel, and potentially of considerable size (over 200°C). These effects can be reduced in intensity but not altogether avoided and there can be little doubt that many previous investigations of pressure-temperature limits have suffered from them.