General equations for the computation of stress rates in solid and hollow cylinders subjected to transient temperature distributions are developed, based on the assumptions of an elastic, perfectly plastic material obeying the Tresca yield condition with Poisson ratio of one half. For most temperature distributions, it appears that these equations can be integrated only by numerical means. However, for one particular temperature distribution, equivalent to a phase transformation which occurs at a fixed temperature, it is found possible to integrate them analytically, and expressions for the transient and residual stresses are obtained in closed form. The latter results are compared with experiment and qualitative agreement noted.

In an earlier paper (1) an analysis was carried out to determine the stresses and deflection in an infinite strip plate undergoing large deflections when the plate was subjected to a combined normal loading and uniform temperature rise through the thickness, both of which were permitted to vary across the plate width. This paper extends the analysis and design charts to the case where the temperature distribution through the thickness of the plate may have any desired distribution. If the usual plate assumptions regarding plane sections remaining plane are valid, then the arbitrary temperature distribution can be represented completely by the average temperature and the first moment of the temperature about the plate middle surface, as far as the engineering stresses and deflections are concerned. The convenient nondimensional design charts cover equilibrium positions in the buckling as well as nonbuckling range and show maximum stress and central deflection as a function of pressure, average temperature, and temperature moment for cases of both clamped and simply supported edges.

When a floated gyroscope is subjected to a temperature distribution which is not symmetrical about a plane parallel to the gravitational force, convection currents tend to rotate the gimbal. The rebalance torque and the free drift rate due to thermal effects are first determined for the case of an exactly centered gimbal. It is then shown that moderate gimbal eccentricity has little influence on thermal drift, and, in fact, reduces thermal rebalance torque.

Formulas are obtained for the temperature and fin efficiency of a heat exchanger consisting of round tubes with square fins. Curves are presented for the fin efficiency as a function of tube radius, all other parameters remaining fixed, and also for the temperature distribution in one particular fin.

The problem to be considered is that of determining the flexural stresses which result from temperature differences T between corresponding points on the upper and lower faces of circular plates ( T = temperature at lower face minus temperature at upper face), when T is assumed to vary only with the distance from the center of the plate. This problem arises, for example, in the design of heated or cooled cylindrical processing tanks or vessels. In such cases, heat may be applied to the circular bottom of the vessel by a single concentric burner or heating element or by a ring of burners or elements, and the resulting temperature distribution will be approximately axisymmetric.

The paper treats the stress distribution in a metal tube which is subject to a very high radial temperature variation and pressure. The radial temperature distribution across the tube wall and the variations of the modulus of elasticity and the coefficient of thermal expansion are obtained from experimental data, and all these effects of temperature are taken into account in the calculations. The fundamental equations in the case of plane strain and plane stress can be formulated as the nonhomogeneous Whittaker differential equations. The corresponding solutions are obtained by the method of variation of parameters and in terms of Kummer series. An example is shown, and the stress distribution across the wall is given. For comparison, the stress distribution of the case of constant modulus of elasticity and coefficient of expansion is included.

Stresses and deformations in rectangular strips due to various longitudinal temperature distributions are presented in formulas, tables, and graphs. The results are important for slabs, plate assemblies, rectangular ducts, tube-sheet ligaments; they apply, in a more qualitative fashion, also to cylindrical bodies.

The temperature distribution in the wake of a heated sphere 0.5 in. diam was determined at a gross stream velocity of 30 fps. Measurements were carried out in a channel 0.70 in. in height and 12 in. in width. The surface temperature of the sphere and the energy dissipation from it were determined as a function of gross stream velocities between 10 and 90 fps. The temperature distribution in the wake was correlated on the basis of methods developed for cylinders and satisfactory agreement was obtained.

An incompressible, hot liquid in steady-state-flow condition is flowing through a long tube, transferring heat to the surrounding walls. The outer surface of the tube is kept at zero temperature. Temperature distribution and thermal stress in the tube are calculated.

Calendering (rolling) of plastics at high speeds produces blistering and peeling which are attributed to a combination of uneven temperature distribution, and effect of temperature on the physical properties of the material. In this paper the problem is examined by studying the calendering of a viscous liquid in some detail. It is shown that a thermal boundary-layer effect exists of such magnitude as to account for formation of blisters. An example is given using typical calendering dimensions and physical properties of a plastic, which yields a thermal boundary-layer thickness of the order of depth of the blisters as observed. These data furnish further qualitative confirmation to the physical argument.

For the past few years a program has been under way to obtain reliable data on the rate of heat transfer to air moving at supersonic speeds. The investigation was limited to air flowing at supersonic speeds in a round tube. The program was divided into two separate parts, the first for measurement of the adiabatic wall temperatures of a supersonic stream and the second for the heat-transfer rate. The first part of this program is described here. The details of three experimental test combinations used to measure the adiabatic wall temperature and local state of a supersonic stream of air are presented. The experimental data for forty runs, in the form of measured pressure and temperature distributions, are included. The range of diameter Reynolds number covered is from 0.15 × 10 5 to 5 × 10 5 . The length Reynolds number extends to 120 × 10 5 . The Mach number at the inlet to the round tube is about 2.6. The calculated quantities such as the local apparent friction coefficient, recovery factor, local Mach number, and so forth, are obtained from the simple one-dimensional flow model for which the properties of the stream are uniform at any cross section of the tube and boundary-layer effects are ignored. A subsequent paper deals with the calculation of these quantities when account is taken of the boundary-layer growth in the tube on the basis of a two-dimensional flow model.

By combining the results of an elementary thermodynamic analysis of the temperature distribution in the burned gases of a constant-volume bomb with an examination of the velocity relations at the flame front, it is possible to relate the “normal burning velocity” to the time rate of production of burned gases. Integration of this equation leads to an estimate of the time required for the combustion process.

This paper contains an exact closed solution for the temperature distribution in a preheated air jet when the flow is steady and laminar. Both the two-dimensional and the axially symmetrical cases have been treated. The solution is immediately applicable to other similar problems of diffusion.

In this paper the two-dimensional boundary-layer problem of the steady laminar flow of a perfect gas along a thin flat insulated plate has been solved for a wide range of gas velocities and properties. It is found that compressibility and Prandtl number do not introduce any new phenomena, but do alter the drag on the plate, the equilibrium temperature of the plate, and the velocity and temperature distribution through the boundary layer. The drag coefficient for the plate is given by Equation [24] together with Fig. 2. The temperature of the plate is given by Equation [27 a or b], and approximately by Equation [26] or by Figs. 3 or 4. Typical velocity and temperature distributions are given in Figs. 5 to 10, inclusive.

This work extends a previously reported investigation of the boundary-layer problem associated with the steady laminar flow of a perfect gas along a thin flat insulated plate. In the earlier study the viscosity was assumed constant and the distributions of velocity and temperature were obtained for a wide range of conditions. Part I of the present paper shows, for Prandtl number 0.733 (air) and Mach number of the undisturbed stream 2, the velocity and temperature distributions in the boundary layer under various assumed viscosity variations. Part II gives the distributions for various Prandtl numbers and Mach numbers, assuming the same viscosity functions as used by von Kármán and Tsien. Part III is devoted to a discussion of the method of interpretation of traverse tests of the efficiency and flow coefficients of nozzles or other passages. The results of Part I show that the variation of viscosity with temperature does not alter the equilibrium temperature of the plate, and hence the reading of a plate thermometer. This result is extended in Part II where it is shown that θ at the plate wall is equal to the same quantity when μ is taken constant to within 1 per cent in all cases studied. Furthermore, φU ′ at the plate wall does not vary greatly, so that the drag coefficient C D is equal to 1.28/(Re) 1/2 to within 5 per cent for most of the cases investigated. In Part III a passage efficiency as usually calculated is found to be subject to two errors, one of which reduces and the other of which increases the test result. The net effect is to cause the standard traverse test to give a conservative estimate of the efficiency. The flow coefficient as determined by traverse tests is somewhat higher than the correct one.