Heat Flow Conditions Research Articles

Characterization of shape and heat flow in melt-grown crystals by an affective seed radius

The shape of the liquid-solid interface of crystals grown from the melt by heat removal through a seed in fixed position can be described by an ellipsoid of rotation, having a linear eccentricity equal to the seed radius R. This statement is derived from the equation of heat flow and proper boundary conditions. This prediction is tested experimentally by growing KCl crystals and observing their shapes. The measured linear eccentricity R * = √ (a 2 - b 2) ( a = crystal radius, b = crystal length), is in general not equal to R. R * is interpreted as an effective seed radius characterizing the heat flow conditions of the system. R * was found to be independent of the actual seed radius R for KCl crystals grown in air and increases linearly with the crystal radius. Here the convection of the gas ambient acts as effective seed. Its radius R * approaches R if the crystals are grown at pressures below 50 Torr.

The solution of the dendrite problem for the edgewise growth of a platelet

The dendritic steady-state growth of a platelet into its pure undercooled melt has been solved using a self-consistent method. The method requires solution of the shape of the dendrite that simultaneously satisfies the required heat flow and temperature variations over the dendrite surface. To find this shape, a Taylor expansion in terms of geometric constants is carried out around the dendrite tip for a given assumed tip radius and velocity. The melt undercooling is a derived quantity. It is necessary to carry out expansions of the heat flow and thermal boundary conditions to fourth order in order to specify the first geometric shape factor which shows departure from a parabola. The geometric constants are found to be multi-valued, and are interpreted to mean that the original assumption of steady-state is probably generally invalid. This then may be the fundamental origin of dendritic branching. The range of validity of these conclusions is briefly discussed.

Approximate Theory of Thermal Stress Resistance of Brittle Ceramics Involving Creep

The effect of stress relaxation by creep on the thermal stress fracture of brittle ceramics at high temperature under conditions of quasi‐static heat flow is discussed. It is shown that, to a good approximation, thermal stress relaxation rates can be calculated on the basis of creep rates which correspond to the minimum temperature of the ceramic workpiece. For materials exhibiting linear stress‐creep rate dependence, expressions for the relaxation time and maximum temperature difference or heat flux to which ceramic bodies can be subjected are derived in terms of the material variables affecting thermal stress fracture and stress relaxation by creep. A numerical example shows that high‐temperature creep can materially affect the thermal stress behavior of brittle ceramics. Appropriate thermal stress parameters are proposed to form the basis of proper material selection for high‐temperature environments involving thermal stress and stress relaxation by creep. Conditions for which thermal stress calculations should be based on an elastic or viscoelastic analysis are outlined.

Temperature Effect on Formations During Jet Perforating

Abstract An investigation into the thermal reactions during jet perforating has been conducted over a period of years. Theoretical considerations have been investigated and correlated to experimental laboratory tests. The tests have been conducted under a variety of simulated well conditions and into sandstone, limestone, and dolomite cores. Various well fluids were used in the tests. Jet charges contained in steel guns and self-contained or directly exposed jet charges were both used in this investigation. Introduction For almost a decade now jet perforating has been used in well completions. With the introduction of this radically different tool, misconceptions as to its method of penetration arose. In some instances it was thought that the jet stream itself burned its way through the casing, cement and into the formation. This, of course, was a misconception. Numerous surface tests have indicated no burning action. The mechanics of penetration of a formation or target is altogether a different subject and is not covered in this paper. A direct mathematical explanation of the thermal aspects of jet perforating, especially the heat transfer relations, is very complicated. It is probably for this reason that very little work has been done on this problem. With the ever increasing use of jet perforating, the question of what happens to the formation during perforating is of interest to the petroleum industry. Theoretical Considerations The nature of an explosion or decomposition of a high explosive is a complex phenomena and entails unusual heat flow conditions. Actual well conditions present many variables that vastly complicate the calculations by having multiple explosions occurring with the jet charges cased in various materials in both dry and in fluid filled holes. These extremely complex conditions result in laboratory measuring methods as a practical approach to temperature reactions. Types of Jet Perforators A conventional jet perforating carrier has a number of ports or holes in a hollow steel tube with a jet charge arranged to shoot through each port. At the time of firing, all charges in a gun are detonated, resulting in an explosion in each jet charge.

Analytical Approaches to Local Oscillator Stabilization

The behavior of local oscillator tubes and associated circuit elements under the complex conditions of heat flow can be treated analytically. By means of such an analytical treatment, local oscillators at frequencies up to and beyond 1000 mc may be stabilized methodically with conventional temperature-sensitive elements. The resultant frequency stability is generally satisfactory for most practical purposes.

The Determination of Transient Temperatures and Heat Transfer at a Gas-Metal Interface Applied to a 40-mm Gun Barrel

The problem of measuring very rapidly changing temperature and heat transfer at a gas-solid interface is becoming of increasing importance. This paper presents a method of doing this under the conditions of unidirectional heat flow in a semi-infinite solid. Temperatures are measured very near the metal surface by means of a special type of thermocouple. Equations are derived in which resulting thermocouple measurements are used to calculate the heat transfer through the surface. The method is illustrated by application to a 40-mm gun barrel. Experimental temperature records from four thermocouples installed along the barrel are shown. The ballistic heat transfer a t these locations is determined from these records. The experimental temperature curves are also compared with theoretical results.

On the theory of the propagation of sound in he ii

The considerations of a previous publication on the same subject, based on the two-fluid model, are generalized to the case that the relaxation time for the transformation of the two fluids into each other may not be regarded as infinitely small and that pressure has a noticeable influence on their equilibrium ratio. It is shown that under these circumstances a damping of first sound results in addition to that due to viscosity. From the experimentally determined attenuation it follows that the relaxation time near the γ-point must be either less than about 10−12 s or greater than about 10−4 s. The theory of the temperature jump at a material boundary for stationary heat flow is discussed on the same basis.

熱源による熱傅導理論(第1報)

In this research, heat conduction is limited to physical systemes governed by linear differential equations. Generalizing the conception of heat source, the author proposes a general solution of unsteady heat flow due to the heat sources which change the distribution, shape and place of growing heat energy such as chemical change, radioactivity, Joule's heat of electric current etc. Main solutions are shown in equations (P-1) to (P-7).Specializing equations (P-1) and (P-7), the general solutions of heat flow corresponding to all welding conditions of heat flow in simple form solid are derived.But the above-mentioned limit is doubtful in such high temperature phenomenon as welding, there-fore their effects should be investigated in the future.

An Electrical Geometrical Analogue for Complex Heat Flow

Abstract Through the medium of the resistance concept, the general similarity of “contour maps” for heat flow and electrical flow may be visualized. The electrical analogy permits ready study of simple and complex heat-flow conditions which, because of distorted temperature conditions, would defy orthodox mathematical or graphical analysis. Internal-temperature lines (isotherms) obtained by relatively simple equipment with a geometrical type of analyzer are shown for one complex case of flow conditions.

A GRAPHICAL METHOD OF CALCULATING HEAT LOSS THROUGH FURNACE WALLS*

AbstractWhen a wide range of temperatures is considered, difficulty is encountered in accurately representing the thermal conductivity of any material, the temperature‐conductivity function of which is not a straight‐line relation. This difficulty can be obviated by use of the “true” conductivity function as defined herein.The use of the “true” conductivity function confers the additional advantage that it makes possible a graphical method for the calculation of heat transmission through compound structures, under conditions of equilibrium heat flow. Though this is still a trial‐and‐error process, from the theoretical viewpoint it is more sound and from the practical angle more easily usable than the arithmetical method generally employed heretofore. The new method is illustrated by the solution of a typical problem.

Quenching: a Mathematical Study of Various Hypotheses on Rapid Cooling

Mathematical Study of the Temperature Changes in a Hot Body after Quenching, Assuming Various Conditions of Heat Flow from the Surface.\char22{}(1) Assuming no thermal resistance at the surface, theoretical cooling curves for a steel ball and a steel plate are computed (Fig. 1). (2) Assuming constant thermal resistance, the general equation is derived for the case of a cylinder of finite length (Eq. 17). (3) Assuming a vapor layer which conducts the heat to a liquid layer at rest, the general solutions for the temperatures at the surface of a large body (Eq. 41) and of a plate (Fig. 5) are obtained. (4) Assuming that the heat after passing through the vapor layer is carried away by convection at a uniform rate, the equation and curves are obtained for the case of a plate (Eq. 58; Fig. 6).

The Problem of Aeroplane-Engine Design

Abstract The aeronautical engine is emerging from the stage of invention to the stage of design, and this paper suggests steps to be taken towards the satisfactory solution of the problem. It resolves the engine into a light, high-tensioned steel structure, consisting of seamless tubing and forged or welded steel parts, possibly formed in drop-forge dies. To this steel stress structure are added certain members, such as the piston, exhaust valve and guide, designed primarily for heat-flow conditions and not for stresses; and certain closing members, such as the ports for the intake and exhaust, which can be very properly cast in aluminum, and the water jacket; and the oil crankcase closure, which can be made of any material desired.

Photographic and microscopic section: Twenty-second stated meeting, April 4th. Dr. Henry Leffmann in the chair. Present, 48 members and visitors

Catalytic powders with fine microstructures can be produced from a rapidly solidified gas atomized Al–Ni alloy. The solidification microstructure of the droplets is closely linked with heat flow conditions. Thus, the heat transfer conditions between the gas and droplet are essential to microstructural evolution. In this study, a phase field model for simulating single and multiple dendrite growth in a binary Al–Ni alloy was constructed and the microstructural evolutions occurring during a gas atomization process were evaluated. Temporal variations in the heat transfer coefficient and the boundary heat flux were taken into account. The results revealed that the heat transfer coefficient of the atomized droplet in flight is correlated with the droplet size and the relative velocity between the droplet and the atomizing gas. During the simulation, the competition between boundary heat flux extraction and latent heat release from phase transition causes a recalescence process in thermal history, thereby affecting the gradient temperature distribution and, consequently, the dendrite morphology. Dendrite growth under the effects of the heat transfer coefficient is restrained continuously because of the decreasing amount of extraction. The computational results confirmed the fine homogeneous microstructure and low microsegregation levels of gas atomized powders.