Steady Temperature Gradient Research Articles

Adaptation of the impedance tube technique for the measurement of combustion process admittances

This paper describes the development and application of the impedance tube technique in the measurement of localized combustion process admittances. The latter are needed for combustor stability analyses. The experimental set-up consists of a tube with the combustion process to be investigated at one end and an acoustic driver at the other end. The latter is used to excite a standing wave in the tube whose structure depends upon its interaction with the combustion process. The needed combustion process admittance is determined from acoustic pressure measurements taken at several locations along the tube. The paper discusses the theoretical foundation of the experiment and the developed data reduction procedure which accounts for the presence of steady state temperature gradient, mean flow gradient and gas-phase losses in the tube. Results showing the applicability of the developed experimental technique are provided.

Experiments on convective layer formation and merging in a differentially heated slot

This work describes experiments in which a stably stratified salt solution is subjected to steady lateral temperature gradients. The criteria for the onset of layered convection are observed to agree with previously published stability analysis. Convective layers formed in this way are found to be statically unstable; they always merge two into one to form a new system. This process continues until the density jump at the solute interface between layers is larger than the density deficit produced by the side wall heating/cooling. The eventual stable system develops into well-mixed convective layers separated by sharp solute interfaces. The conditions for any subsequent layer intermixing and its effect on the lateral heat transfer across the slot, are also described.

Steady heat transfer to a thin infinite disk with a cut-out opening

A method is proposed which allows one to find the steady temperature gradient at the rim of a round opening cut out in an infinite nonuniform disk from the given temperature of the rim without a preliminary determination of the temperature field.

Transport and Deposition of Metals in Sodium-Stainless Steel Systems, (V) An Experiment on Thermal Diffusion of Zinc, Antimony and Cesium in Liquid Sodium

Thermal diffusion constants were determined over a temperature range of 400°–700°C in liquid sodium alloyed with trace amounts of zinc, antimony or cesium. Purified sodium containing a radioisotope of one of the three solute metals was filled by suction in a capillary made of stainless steel. The capillary was then carefully seal-welded to prevent the sodium from oxidation; the sealed capillary was placed along the core of a heat conductor rod; a steady linear temperature gradient was produced along its length by heating its head and cooling its foot. After a predetermined period of this thermal diffusion run, the capillary was quickly chilled to solidify the sodium and sectioned into pieces. The specific radioactivity observed in the sodium in the sectioned piece were plotted in log-log scale against the absolute temperature prevailing in the piece during the thermal diffusion run, and the thermal diffusion constant was obtained from the inclination of the straight lines drawn through the plots. All thre...

Analysis of the transfer function governing crystal growth in the Czochralski process

A transfer function relating the crystal radius to the heater power is derived assuming small deviations from the steady state growth conditions. The derivation is based on the conditions of heat balance in the zone near the growth interface. The transfer function is expressed in terms of the physical constants of the material being grown together with values of the steady state temperature gradients in the crystal and the melt, which can be measured experimentally. It is shown that the dynamics of heat transfer in the interface zone represent a significant lag in the overall transfer function. The results also provide a means of estimating the effect of changes in the growth conditions on the dynamic response and of comparing the behaviour of different materials.

Strength-deformation considerations of a reactor core support structure

A method is presented for the strength-deformation solution of a typical nuclear reactor core support structure. The structure under consideration consists of two axisymmetric multiregion plates, located one above the other, and interconnected by concentric rings of tubes. This main body of the structure is supported at the outer circumference or at some intermediate radius by circular cylindrical shells. Loading of the structure may be twofold: static transverse pressure on the plane of the plates or the shell walls, and steady state temperature gradients, both along the radius and across the plates, their individual regions and the separate shells. Plates with perforations of triangular configuration may also be included in the list of region properties to be considered. Solution to this composite structure problem is obtained by mathematical superposition of elementary thin plate, circular cylindrical shell, and ordinary beam problems. This is accomplished by the matrix inversion procedure to solve the resulting simultaneous equations. Analytical results are presented in the form of a matrix, giving the expressions for the coefficients in terms of the design variables. The proposed analytical method is also incorporated into a computer program. This program thus makes the stress-deflection solution of the composite support structure readily available to the designer.

The influence of impact velocity and ice specimen geometry on the charge transfer associated with temperature gradients in ice

AbstractWhen pure uniform ice specimens of different temperatures are brought into gentle contact for times ranging from 10−3 to 5.10−2 sec and are then separated, the charge transfer is a maximum for a contact time of about 7.5 × 10−3 sec and is in agreement with the equations of Latham and Mason (1961a). With ice of higher conductivity the maximum charge transfer occurs after smaller contact times.For impact velocities less than about 7.5 cm sec−1 the charge transfer is in agreement with the theory but above this value the charge transfer increases linearly with impact velocity. The charge transfer is also enhanced, by as much as an order of magnitude, if the ice specimens are tapered. A tentative conclusion to be drawn from these experiments is that the value of 5 × 10−4 e.s.u., measured by Reynolds, Brook and Gourley (1957) for the charge transfer per collision between an ice crystal and a warmer artificial hailstone, which is sufficient to generate charge at a rate required by a tenable theory of thunderstorm electrification, may be explicable in terms of the temperature‐gradient effect.When steady temperature gradients are applied to uniform specimens of pure ice the potentials developed across the ice are unaffected by the pressure to which the ice is subjected. The application of steady temperature gradients to tapered ice specimens produces potentials which are up to an order of magnitude greater than predicted theoretically.

Transient Stresses in Nonhomogeneous Viscoelastic (Maxwell) Materials

This paper determines the transient-stress distribution, due to imposed strain rates, which exists in bars made of a linear nonhomogeneous viscoelastic (Maxwell) material. The cases of constant and exponentially decreasing strain-rate histories are solved. The particular nonhomogeneity is an exponential variation of the fluidity in the thickness coordinate. I t is shown that this fluidity variation can be the result of a steady linear temperature gradient. One-dimensional strength of materials assumptions are made for the problems of axial extension and bending. I t is further assumed that all of the initial stresses due to heating have vanished prior to load application. I t is found in the case of constant strain rate that the stress distribution approaches the configuration associated with a purely viscous material after one relaxation time of the cold face. In addition, an approximate solution to the problem of constant load is given in Appendix A.

Electric charge transfer associated with temperature gradients in ice

The development of electric potentials in ice crystals under the influence of temperature gradients is investigated both theoretically and experimentally. The maintenance of a steady temperature gradient across a piece of ice is accompanied by concentration gradients of H + and OH - ions; because of the much greater mobility of H + ions, these diffuse more rapidly into the colder part of the ice and, in the steady state, a potential difference is set up across the ice crystal, the colder end being positive. A theory of this effect predicts a surface density of charge on the ends of the ice of σ = 5 x 10 -5 (d T /d x ) e. s. u. cm -2 and a potential difference across a uniform specimen of about 2Δ T mV, where Δ T is the temperature difference across the ends. These values are quite well confirmed by a series of experiments on specimens of highly purified ice. When two pieces of ice of initially different temperatures are brought into temporary contact and separated, the warmer acquires a negative charge and the colder an equal positive charge. The theory indicates that a maximum charge transfer of 3 x 10 -3 Δ T , e. s. u. cm -2 should occur with a contact time of about 0.01 s and that it should thereafter decline as the two pieces of ice become more nearly equal in temperature. The theoretical value for the charge developed for a contact time of ~ 0.01 s is well confirmed by experiments which also show that very little charge separation occurs if the contact period exceeds ½ s. Experiments in which the ice was contaminated with carbon dioxide, hydrofluoric acid, and sodium chloride in concentrations of up to 50 times that normally present in rain water, showed that the electrification was not greatly influenced by these impurities. These phenomena are thought to be of basic importance in the generation of electric charge in thunderstorms, this aspect being developed in the following paper.

The characteristics of thermal diffusion

When a gas mixture is contained in a vessel in which a steady temperature gradient is maintained, a concentration gradient is in general set up, whose amount is determined by the logarithm of the temperature ratio, and by k T , the thermal diffusion ratio; the general theory of non-uniform gases gives successive approximations to k T , and the first of these, [k T ]1, is accurate within a few per cent. The paper discusses the dependence of [k T ]1 on ( a ) the ratio of the molecular masses; ( b ) their concentration ratio ( c 1 or c 2 ); ( c ) the two ratios of the molecular diameters, inferred from the coefficient of viscosity, to their joint diameter, inferred from the coefficient of diffusion; and ( d ) three parameters depending on the mode of interaction between the unlike molecules. When this interaction is according to the inverse-power law, the three parameters ( d ) are all expressible in terms of the mutual force index, and [k T ]1, is a function of five independent variables. The general nature of its dependence on these variables is discussed, with particular reference to the end values (for c 1 or c 2 zero) of the thermal diffusion factor α, given by k T / c 1 c 2 ;these end values involve fewer variables (less by two) than the general values, and their functional character can be represented graphically. It is shown that k T may be zero not only when c 1 or c 2 is zero, but also for at most one intermediate mixture ratio. Formulae for [k T ]1 appropriate to various special cases are also given.

The temperature and humidity relations of the cockroach (Blatta orientalis)

1. An apparatus is described in which a steady temperature gradient can be maintained and in which conditions of temperature and humidity can be accurately measured. 2. The preferred temperature range (indifference zone) of normal adult male Blatta orientalis in this apparatus is 20–29 ° C. 3. The indifference zone is not altered by changes in the humidity of the air. 4. Specimens desiccated to 70% of their original weight show a much lower preferred temperature, namely 12–23 ° C. 5. This is interpreted as a reaction to a gradient of saturation deficiency, an avoiding reaction against air of higher evaporating power.

The Thermal and Electrical Conductivity of Fused Quartz as a Function of Temperature

Thermal conductivity of fused quartz.---The thermal conductivity as a function of the temperature has been determined for clear fused quartz by the radial flow method from 235\ifmmode^\circ\else\textdegree\fi{}K to 1225\ifmmode^\circ\else\textdegree\fi{}K. The specimen was in the form of a hollow cylinder closed hemispherically at one end. Energy to maintain a steady temperature gradient was supplied by means of an electrically heated filament mounted axially inside the specimen. Thermal contact with the specimen was made with mercury inside and outside at the lower temperatures and with the tin-lead eutectic at the higher temperatures. Inside and outside temperatures were obtained with thermocouples. A guard ring scheme was used to prevent heat loss or gain at the open end of the cylinder and correction was made for the heat flow through the hemispherical end cap. The results may be represented by the linear equation: $K=3.83\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}T+0.00163$. An abrupt change in the thermal conductivity was noted in the vicinity of 1140\ifmmode^\circ\else\textdegree\fi{}K which is attributed to heat treatment i.e. annealing or partial crystallization.Electrical conductivity of fused quartz.---An attempt was made to measure the specific electrical resistance as a function of the temperature by the same method at the same time. The results were not conclusive because of the small number of data taken but there is every reason to believe that the method would be entirely successful for the determination of both quantities. The specific resistance was measured for a small piece of the original specimen. C. C. Bidwell's modification of K\onigsberger's formula was verified i.e. $\ensuremath{\rho}=A\ensuremath{\epsilon}(\frac{Q}{\mathrm{RT}}+a\mathrm{T})$ $\ensuremath{\rho}=\mathrm{A}{\ensuremath{\epsilon}}^{(\frac{Q}{\mathrm{Rt}}+aT)}$. The results indicate the presence of both electrolytic and delectiric polarization. Certain peculiarities in the polarization were noted at about 1140\ifmmode^\circ\else\textdegree\fi{}K as well as a general change in the resistance-temperature curve due to heat treatment. The interpolated results are as follows: