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RESEARCH PAPERS

J. Heat Transfer. 1967;89(2):121-130. doi:10.1115/1.3614330.

Fundamental concepts pertaining to the solution of heat conduction problems by probability methods (Monte Carlo methods) are devised and techniques of application are developed. It is demonstrated that probability methods can be applied over the entire range of heat conduction problems. These include both steady state and transient situations in bodies of arbitrary shape with arbitrary boundary conditions (including derivative conditions) and with volume heat sources. Problems involving nonlinear boundary conditions (e.g., combined convection and radiation) and moving boundaries (change of phase) are also accommodated by probability methods. All of these various situations are treated in the paper. Numerous computational experiments are carried out, many of which provide results for physical problems not heretofore solved in the literature. A new concept, the floating random walk, is introduced and this provides the flexibility needed to accommodate such a wide range of problems.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1967;89(2):132-138. doi:10.1115/1.3614335.

Theoretical predictions of radiant transfer through long passages are shown to be quite sensitive to directional variation of radiation characteristics and to polarization of the radiation. With use of the Fresnel relations for specular reflection to find the amount and state of polarization of radiation reflected by dielectric and metallic walls, values of transmittance are calculated and tabulated for long passages of square and infinite slot cross sections with lengths of up to 30 times the lateral distance between walls. Differences in answers by factors up to 14 are shown to result from neglect of directional variation, polarization, and phase change in the reflection process. A simple, approximate analytical relation is presented to permit transmittance and integrated transmittance obtained for isothermal passage walls to be used to calculate transfer in passages with adiabatic or refractory walls.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1967;89(2):139-145. doi:10.1115/1.3614336.

The nonsimilar boundary-layer flow and heat transfer of a cone rotating in a forced-flow field are investigated. Numerical solutions are shown for a half-cone angle of 53.5 deg with parameters (vw /ue )2 ranging from 0 to 20, and with Prandtl numbers from 0.2 to 10. With a half-cone angle of 90 deg (so that one has a rotating disk), the degenerate problem is solved in the same manner.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1967;89(2):146-152. doi:10.1115/1.3614337.

Where rapid heating is encountered, as in a prompt-burst nuclear reactor, a thermocouple with a rapid time-response is necessary to monitor the temperature of the specimen in question. Because all thermocouples have some mass, they cannot have an infinitely fast response. However, an intrinsic-type thermocouple has less thermal inertia than the usual welded-bead type. Thus it is a natural choice for the measurement of transient surface temperatures of conducting solids. In this report an analytical expression is obtained for the transient response of an intrinsic thermocouple. In support of the analysis, experimental data are presented which were obtained by means of a capacitor bank pulse-heating technique. It is concluded that thermocouple wires of small diameter and low thermal conductivity respond the fastest. As an example, a 1-mil constantan wire on a copper substrate produces 95 percent of the steady-state emf in 3 μsec.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1967;89(2):155-162. doi:10.1115/1.3614342.

An analytical study of the temperature distribution along thin fins with temperature-dependent thermal properties and internal heat generation is presented. The analysis utilizes a recently published bounding procedure which yields analytical and continuous bounding functions for the temperature distribution. Several numerical examples are considered. Tabular and graphical results are given. The effects of variable thermal properties and internal heat generation are also shown.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1967;89(2):163-167. doi:10.1115/1.3614343.

Experimental data are presented for local heat transfer rates near the entrance to a flat duct in which there is an abrupt symmetrical enlargement in flow cross section. Two enlargement area ratios are considered, and Reynolds numbers, based on duct hydraulic diameter, varied from 70,000 to 205,000. It is found that such a flow is characterized by a long stall on one side and a short stall on the other. Maximum heat transfer occurs in both cases at the point of reattachment, followed by a decay toward the values for fully developed duct flow. Empirical equations are given for the Nusselt number at the reattachment point, correlated as functions of duct Reynolds number and enlargement ratio.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1967;89(2):169-175. doi:10.1115/1.3614346.

Experimental data indicating some effects of free-stream turbulence intensity on time-average boundary-layer velocity profiles and on heat transfer from a constant-temperature flat plate with a favorable pressure gradient are presented for local Reynolds numbers ranging from 4 × 104 to 4 × 105 and for free-stream turbulence intensities from 0.4 to 8.3 percent. It is concluded that, for the range of variables covered by the experiments: (a) The effect of free-stream turbulence intensity on heat transfer through the laminar boundary layer with a zero pressure gradient is negligible; (b) for a given Reynolds number, the local Nusselt number increases with increasing free-stream turbulence intensity when a pressure gradient is present, the boundary-layer profiles for these conditions changing with a variation in free-stream turbulence intensity; and (c) no increase in Nusselt number with increase in free-stream turbulence intensity occurs for turbulent boundary layers with a favorable pressure gradient.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1967;89(2):177-184. doi:10.1115/1.3614349.

This investigation concerns the application of a flow visualization technique to obtain a quantitative and qualitative description of the secondary flow associated with a slowly oscillating disk. Included in the description is a systematic study of the flow behavior as a function of the Reynolds number. The three-dimensional character of the flow is verified and the development of a toroidal vortex both above and below the oscillating disk is illustrated. The experiments are performed in a vessel similar in design to a typical oscillating body viscometer. The effect of the Reynolds number on the damping rate of the disk is investigated. The influence of natural convective flows on the magnitude and reproducibility of the damping rate is obtained. The development of a secondary flow in the form of a toroidal vortex for both the rotating disk and rotating sphere is also illustrated.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1967;89(2):185-193. doi:10.1115/1.3614351.

An analysis has been made to determine the heat transfer and friction characteristics in a two-phase (gas-liquid) flow over a circular cylinder. It is demonstrated that the resulting two-layer flow problem can be formulated exactly within the framework of laminar boundary layer theory. Two cases are studied; (1) For the parameter E greater or equal to 0.1 and the drop trajectories straight and, (2) For E less or equal to 0.1 and for any drop trajectory. Solutions obtained in power series include the local liquid-film thickness, velocity and temperature profiles, skin friction and Nusselt number. Numerical results disclose a significant increase in both heat transfer rate and skin friction over those of a pure gas flow. The theoretical prediction compares favorably with experimental results of Acrivos, et al. [1].

Commentary by Dr. Valentin Fuster

DISCUSSIONS

TECHNICAL BRIEFS

J. Heat Transfer. 1967;89(2):195-196. doi:10.1115/1.3614354.
Abstract
Commentary by Dr. Valentin Fuster

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