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RESEARCH PAPERS

J. Heat Transfer. 1976;98(2):153-158. doi:10.1115/1.3450511.

A large inlet break Loss of Coolant Accident in a Pressurized Water Reactor (PWR) would cause the flow through the core to reverse within milliseconds. Currently approved methods of analysis conservatively assume that vapor blanketing of core heat transfer surfaces occurs upon this first reduction to zero flow. A coordinated experimental and analytical study has been conducted to determine when and where the vapor blanketing or Critical Heat Flux (CHF) conditions actually do develop in constant pressure rapid flow reversals. The results indicate that first occurrence of CHF is due not to low coolant velocities, but to flow stagnation in the channel interior with associated rapid channel voiding. Calculations indicate that good cooling should persist over large regions of the core for about 1 s longer than is currently assumed.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1976;98(2):159-165. doi:10.1115/1.3450512.

Using a recently developed method, measurements were obtained of local film thicknesses during transient voiding of a liquid-filled channel. The liquid film remaining on the channel walls was found to vary in thickness over a range of 0.015–0.15 times channel diameter. In a Lagrangian coordinate system, the film thickness at a fixed distance from the head of the void was found to increase with increasing void acceleration. In an Eulerian system, the film thickness at a fixed location on the channel wall was found to decrease with increasing acceleration, when measured at the same time after passage of the head of the void. In all cases, film thickness monotonically decreased with increasing distance from the head of the void. Complete film breakage (dryout) was not observed in these experiments. These experimental measurements of local film thicknesses during transient voiding conditions are pertinent to thermal analyses for reactor safety studies.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1976;98(2):166-172. doi:10.1115/1.3450513.

Experiments on film boiling of carbon dioxide were performed covering the range of pressures from the triple point to the critical point. Measurements were also made at supercritical pressures. Three different heating wire sizes were employed with diameters of 0.0508, 0.1, and 0.4 mm. The boiling curves, plotted in terms of heat flux and temperature difference, were found to be pressure dependent, with a more marked dependence for smaller diameter heating wires. The role of pressure level was exhibited in greater detail in a presentation in which the heat transfer coefficient is plotted against pressure at fixed values of heat flux. The most rapid variations of the heat transfer coefficient with pressure occur in the neighborhoods of the triple and critical points, with relatively gradual variations in evidence in the intermediate range of pressures. The curves of heat transfer coefficient versus pressure take on minimum values at the triple and critical points. Nusselt numbers evaluated from the experimental data agree satisfactorily with available predictive equations. Photographs of the vapor separation patterns revealed that with increasing pressure, the bubble columns which break away from the vapor film successively evolve into vapor columns and vapor sheets. As the critical pressure is approached, the height of the sheet diminishes.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1976;98(2):173-177. doi:10.1115/1.3450514.

Film boiling experiments were carried out in an aqueous-calcium sulfate solution. The experimental results indicate that scale formation on heating surfaces during evaporation of a calcium sulfate solution can be avoided under carefully controlled conditions. Experimental heat transfer results for both distilled water and aqueous calcium solutions compare very well with analytical predictions. In addition, for high heat fluxes, contact between liquid and heating surface was found to exist during stable film boiling in a quiescent, saturated or almost saturated liquid.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1976;98(2):178-181. doi:10.1115/1.3450515.

The heat transfer characteristics of an evaporating ethanol meniscus formed at the exit of a glass capillary tube were studied experimentally. The meniscus profile was photographed and was found to be a function of the evaporation rate and the initial hydrostatic head. The meniscus was found to be stable over a wide range of evaporation rates.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1976;98(2):182-188. doi:10.1115/1.3450516.

A useful solar-thermal converter requires effective control of heat losses from the hot absorber to the cooler surroundings. Based upon the theory and some experimental measurements it is shown that the spacing between the tilted hot solar absorber and successive glass covers should be in the range 4–8 cm to assure minimum gap conductance. Poor choice of spacing can significantly affect thermal conversion efficiency, particularly when the efficiency is low or when selective black absorbers are used. Recommended data for gap Nusselt number are presented as a function of the Rayleigh number for the high aspect ratios of interest in solar collector designs. It is also shown that a rectangular cell structure placed over a solar absorber is an effective device to suppress natural convection, if designed with the proper cell spacing d, height to spacing ratio L/d and width to spacing ratio W/d needed to give a cell Rayleigh number less than the critical value.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1976;98(2):189-193. doi:10.1115/1.3450517.

This paper presents new experimental measurements on free convective heat transfer rates through inclined air layers of high aspect ratio, heated from below. The Rayleigh number range covered is from subcritical to 105 ; the range of the angle of inclination, φ measured from the horizontal is: 0 < φ < ∼70 deg. Although it was anticipated that the results might be identical to the results for the horizontal layer if one replaced Ra by Ra cos φ, significant departures from this behavior were observed, particularly in the range 1708 < Ra cos φ < 104 , 30 deg ≤ φ < 60 deg. A recommended relationship giving the Nusselt number as a function of Ra cos φ and φ is reported. This relationship fits all data closely.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1976;98(2):194-201. doi:10.1115/1.3450518.

The effect of localized heating in rectangular channels was studied by solving the partial differential equations for the conservation of mass, momentum, and energy numerically using an unsteady state formulation and the alternating-direction-implicit method. The heating element was a long, horizontal, isothermal strip located in one, otherwise-insulated vertical wall. The opposing wall was maintained at a lower uniform temperature and the upper and lower surfaces were insulated or maintained at the lower temperature. Computations were carried out for Pr = 0.7, 0 ≤ Ra ≤ 105 , a complete range of heater widths and locations and a wide range of aspect ratios. Flow visualization studies and comparison with prior computed results for a limiting case confirm the validity of the computed values. The computed rates of heat transfer and circulation provide guidance for locating heaters or coolers.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1976;98(2):202-207. doi:10.1115/1.3450519.

An improved model and algorithm were developed for the numerical solution of three-dimensional, laminar natural convection in enclosures. Illustrative calculations were carried out for heating from below in a cubical box, a long channel with a square cross section and in the region between infinite, horizontal plates. The results are in good agreement with prior experimental and theoretical results. For the infinite flat plates the three-dimensional model correctly produces a two-dimensional solution. For the cube the solution produces different stable solutions depending on the initial conditions. A fluid-particle path is shown to be a good method of illustrating the three-dimensional motion. In the cube and in each cubical cell in the channel this streak-line was found to consist of a pair of double helices.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1976;98(2):208-212. doi:10.1115/1.3450520.

The laminar boundary layer equations for free convection over bodies of arbitrary shape (i.e., a three-term series expansion) and with arbitrary surface heat flux or surface temperature are solved in local Cartesian coordinates. Both two-dimensional bodies (e.g., horizontal cylinders) and axisymmetric bodies (e.g., spheres) with finite radii of curvature at their stagnation points are considered. A Blasius series expansion is applied to convert from partial to ordinary differential equations. An additional transformation removes the surface shape dependence and the surface heat flux or surface temperature dependence of the equations. A second-order-correct, finite-difference method is used to solve the resulting equations. Tables of results for low Prandtl numbers are presented, from which local Nusselt numbers can be computed.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1976;98(2):213-220. doi:10.1115/1.3450521.

Wet geothermal formations or reservoirs are of great current interest as a new energy source. Such formations have the potential for large quantities of energy at temperatures of interest for power production and other uses. In these reservoirs the ground water usually contains dissolved solids in such high concentration as to pose a serious disposal problem. For this reason and also to maintain the water table, in most cases, the water will be reinjected into the reservoir after the useful energy has been extracted. Efficient utilization of the potential of a given reservoir requires optimum location of costly producing and reinjection wells. Selection of well location must be based upon an understanding of the heat and mass flows within the reservoir. In this paper, we present some general considerations for physical modeling as well as the results obtained from a laboratory model having two wells to simulate a geothermal energy extraction loop.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1976;98(2):221-225. doi:10.1115/1.3450522.

This paper investigates the transient temperature distribution within packed beds after being subjected to single blow heating. Numerical solutions are derived for the fluid and solid temperatures that include the effect of forced convection heat transfer at the fluid-exit surface. An inlet-face heat transfer coefficient is specified that includes both the effect of small scale inlet-face convective heat transfer and heat conduction in the oncoming transpirant. The boundary conditions do not require fluid or solid temperatures to be specified at the bounding surfaces. Charts are presented for predicting the response times for packed bed heat exchangers and chemical reactors covering a wide range of parameters.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1976;98(2):226-231. doi:10.1115/1.3450523.

The paper describes an analytical and experimental study of the effects of fluid injection on heat transfer in laminar air flow over a long square cavity. The Reynolds number (based on cavity width) ranged in value from 10 to 1000. The injection (of air) at the cavity wall was varied in velocity from 0 to 5 percent of the main stream. The results indicate the greatest reduction in heat transfer to be occurring at the reattachment point. An expression is suggested for predicting the approximate reduction in heat-transfer rate from the entire cavity surface.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1976;98(2):232-239. doi:10.1115/1.3450524.

Thermal conductivity measurements were performed to determine the characteristics of hollow glass microspheres as an insulating material and as an opacifying agent for other insulations. The experiments were carried out with a radial flow heat transfer apparatus especially designed to suppress extraneous heat transfers, both internal and external to the heated section, and to provide uniform temperatures on the bounding surfaces. Three types of microsphere insulations were investigated, differing in bulk density and in the presence or absence of an aluminizing coating. The thermal conductivity of the microsphere insulations was found to be about one and a half times that of stagnant air over a wide temperature range. Additional experiments, involving the use of an opacifier (powdered silicon), demonstrated that radiative transfer has a minor effect on the thermal conductivity of microsphere insulations. This finding was corroborated by the fact that the high-temperature conductivity of the aluminized microspheres was not appreciably different from that of the uncoated microspheres. Another set of experiments was performed in which microsphere insulation was added to opacify silica aerogel, a fine powder insulation that is markedly affected by radiative transfer. The presence of the microspheres brought about reductions in conductivity of almost a factor of two at an optimum mixture ratio of the constituents. Furthermore, it was found that the conductivity of such a mixture was lower than that of either constituent, thereby illustrating their synergistic interaction.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1976;98(2):240-244. doi:10.1115/1.3450525.

An analysis is presented which extends the theoretical work of Weighardt and determines the adiabatic wall effectiveness of a turbulent boundary layer in a constant free-stream velocity flow heated or cooled by the discharge of a secondary fluid through a slot. A comparison of the analysis with the experimental results of Wieghardt is made and it is found that the streamwise decay in adiabatic wall effectiveness, except in the immediate region of the slot, may be explained by considering the thermal boundary layer growth within the hydrodynamic boundary layer.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1976;98(2):245-250. doi:10.1115/1.3450526.

Film injection from discrete holes in a three row staggered array with 5-dia spacing was studied for three hole angles: (1) normal, (2) slanted 30 deg to the surface in the direction of the mainstream, and (3) slanted 30 deg to the surface and 45 deg laterally to the mainstream. The ratio of the boundary layer thickness-to-hole diameter and the Reynolds number were typical of gas turbine film cooling applications. Results from two different injection locations are presented to show the effect of boundary layer thickness on film penetration and mixing. Detailed streaklines showing the turbulent motion of the injected air were obtained by photographing very small neutrally-buoyant helium filled “soap” bubbles which follow the flow field. Unlike smoke, which diffuses rapidly in the high turbulent mixing region associated with discrete hole blowing, the bubble streaklines passing downstream injection locations are clearly identifiable and can be traced back to their point of ejection.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1976;98(2):251-256. doi:10.1115/1.3450527.

Heat transfer coefficients for laminar flow of water and ethylene glycol in an electrically heated metal tube with two twisted-tape inserts were determined experimentally. The Nusselt number for fully developed flow was found to be a function of tape twist ratio, Reynolds number, and Prandtl number. These Nusselt numbers were as much as nine times the empty tube constant property values. The correlation of these data is in fair agreement with the only available analytical predictions. The friction factor is affected by tape twist only at high Reynolds numbers, in accordance with analytical predictions. The performance of these augmented tubes is compared with that of empty tubes under similar heating conditions.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1976;98(2):257-261. doi:10.1115/1.3450528.

Heat transfer characteristics for a laminar forced convection fully developed flow in an internally finned circular tube with axially uniform heat flux with peripherally uniform temperature are obtained using a finite element method. For a given fin geometry, the Nusselt number based on inside tube diameter was higher than that for a smooth tube. Also, it was found that for maximum heat transfer there exists an optimum fin number for a given fin configuration. The internal fins are of triangular shape.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1976;98(2):262-268. doi:10.1115/1.3450529.

Reactor fuel elements generally consist of rod bundles with the coolant flowing axially through the bundles in the space between the rods. Heat transfer calculations form an important part in the design of such elements, which can only be carried out if information of the velocity field is available. A one-equation statistical model of turbulence is applied to compute the detailed description of velocity field (axial and secondary flows) and the wall shear stress distribution of steady, fully developed turbulent flows with incompressible, temperature-independent fluid, flowing through triangular arrays of rods with different aspect ratios (P/D ). Also experimental measurements of the distributions of the axial velocity, turbulence kinetic energy, and Reynolds stresses were performed using a laser Doppler anemometer (LDA), operating in a “fringe” mode with forward scattering, in a simulated interior subchannel of a triangular rod array with P/D = 1.123 and L/D H = 77. From the experimental results, a new mixing length distribution is proposed. Comparisons between the analytical results and the results of this experiment as well as other experimental data available in the literature are presented. The results are in good agreement.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1976;98(2):269-275. doi:10.1115/1.3450530.

The governing equations of thermal ignition are analyzed for porous solid fuel, such as coal, of various two-dimensional and axisymmetric geometries by the Laplace asymptotic method. Mass diffusion of the gaseous oxidant through the porous fuel is included. The nonlinear partial differential equations of energy and mass balances in time-space coordinates containing the Arrhenius volumic chemical reaction terms are analyzed. By employing the Laplace asymptotic technique and by invoking a certain limit theorem, the governing equations are reduced to a first order ordinary differential equation governing the fuel surface temperature, which is readily solved numerically. Detailed discussion of the effects of the various governing parameters on ignition is presented. Because of the basically closed-form nature of the solutions obtained, many general and fundamental aspects of the ignition criteria hitherto unknown are found.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1976;98(2):276-283. doi:10.1115/1.3450531.

Measurements of mean axial velocity, and the corresponding normal stress are reported for the isothermal flow of air and for a combusting mixture of natural gas in an axisymmetric furnace enclosure with a coaxial burner. Temperature and wall heat flux measurements were also obtained for the combusting flow. The swirl number of the flow was 0.5. The measurements are compared with the results of a calculation procedure incorporating a two equation turbulence model and a one step reaction model. The combustion model allowed fuel and oxygen to coexist at the same place but not at the same time. The comparison indicates that the calculation procedure qualitatively represents the measurements but that quantitative differences exist. The argument is sufficiently close, however, to justify the use of the method for some design purposes.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1976;98(2):284-291. doi:10.1115/1.3450532.

The human body was modeled by a finite difference numerical procedure to determine the effect of simulating the sweating rate by different analytical models. Six different models were used in which the hypothalamus, muscle, average skin, and local skin temperatures were used as the controlling parameters for the rate of local sweating. These different models were tested by comparing their predictions of local temperatures for an exercising man with measured values. The computer program was then used to compute the thermal response of a man subjected to microwave irradiation of the entire body and the head only. Transient head and body temperatures and sweating rates were computed and compared with the temperature changes due to an equivalent exercise level. Significant differences in the results found by using the different sweat models point out the need for further work in determining accurate analytical descriptions of this major mode of body heat loss.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1976;98(2):292-296. doi:10.1115/1.3450533.

The effects of thermal insult on living tissue have been studied by direct microscopic observation of the circulatory system’s response to a controlled trauma regimen. An experimental apparatus has been developed which utilizes a unique high and low temperature stage in conjunction with a precision thermal control system to examine the injury process in the microcirculation of the golden hamster cheek pouch. Unique features of this experimental apparatus are: (1) continuous monitoring of the injury processes at the cellular level, (2) capability for quantitative assay of thermal injury, (3) precise control over the thermal parameters that govern injury, (4) versatility in isolating the effects of these individual parameters. The important thermal parameters monitored using this experimental procedure are the time rates of change of temperature during burning and cooling, the maximum temperature reached, and the length of time the tissue was held at this temperature. With this type of experimental apparatus any portion of the burn protocol, such as the maximum temperature reached during burning, may be varied while holding all other parameters constant. It is well documented that the microvascular bed is a primary site for manifestation of burn wound injury. Burn injury occurs as a consequence of rate dependent physiochemical processes, and, therefore, develops over a finite period of time subsequent to trauma. The experimental technique is designed to determine the gross response of the microvascular system to burn trauma. Initial investigations on burn injury have demonstrated a direct dependency of the extent of damage upon both the maximum temperature attained and the duration of exposure. The minimum temperature required to produce stasis within 20 s after completion of the burn in 95 ±5 percent of the microcirculation decreased exponentially with burn duration between the extremes of 85°C for 1 s exposure and 60°C for 100 s exposure.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1976;98(2):297-302. doi:10.1115/1.3450534.

The general concept of the mean diameter of the disperse phase of an aerosol system, first introduced by Mugele and Evans in 1951, has proven to be a very useful one. In this concept, the proper mean diameter, x p,q , is characterized by a single pair of indices, p and q, which are dependent on the actual type of aerosol system under consideration. This paper re-examines the validity of this concept of mean diameter in heat and mass transfer aerosol systems. The concept is found to be applicable only under a very narrow range of conditions. Attention is then given to a more general definition of a mean diameter, applicable to aerosol heat or mass exchangers. Analyses of these devices shows that the more general mean diameter is a function of the capacity rate ratio, R, and effectiveness of the heat exchanger, ε. Solutions to the governing equations have permitted the mean diameter to be presented graphically as a function of these variables. These solutions are given for two types of particle size distributions, the Rosin-Rammler and the log-probability, and for both parallel-flow and counter-flow heat exchangers. The solutions are, however, restricted to cases where the resistance to heat or mass transfer lies exclusively in the continuous phase.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1976;98(2):303-307. doi:10.1115/1.3450537.

A numerical investigation of an unsteady laminar forced convection from a circular cylinder is presented. The Navier-Stokes equations and the energy equation for an unsteady incompressible fluid flow are solved by the finite difference method. The results are obtained at Reynolds numbers 100 and 200. The temperature field around the cylinder is obtained throughout the region of computation and is shown by isotherms at different times. The variations of the local Nusselt number around the cylinder at different times are computed and shown by graphs. The mean Nusselt number and the Strouhal number are also calculated. The computed results are compared with the other available experimental and theoretical results and are found to be in good agreement with them.

Commentary by Dr. Valentin Fuster

ERRATA

Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J. Heat Transfer. 1976;98(2):308-309. doi:10.1115/1.3450538.
Abstract
Topics: Cylinders
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1976;98(2):310-311. doi:10.1115/1.3450539.

An asymptotically exact expression for radiation heat transfer through planar media is obtained at large optical depth for an exponential band model.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1976;98(2):311-313. doi:10.1115/1.3450540.
Abstract
Topics: Shapes
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1976;98(2):313-315. doi:10.1115/1.3450541.
Abstract
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1976;98(2):315-318. doi:10.1115/1.3450542.
Abstract
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1976;98(2):321-322. doi:10.1115/1.3450544.
Abstract
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1976;98(2):322-324. doi:10.1115/1.3450545.

The problem of combined free and forced convection in an inclined circular tube with uniform peripheral temperature and axial heat flux has been studied experimentally. For fixed Pr and Ra, experimental data showing the effect of tube inclination and Reynolds number on temperature and axial velocity profiles are reported and found to agree qualitatively with the theoretical predictions [7]. Also shown is the variation of Nusselt number with inclination angle for Ra Re = 30,000. No optimum angle for maximum Nusselt number was found.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1976;98(2):324-326. doi:10.1115/1.3450546.
Abstract
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1976;98(2):326-329. doi:10.1115/1.3450547.
Abstract
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1976;98(2):329-330. doi:10.1115/1.3450548.

An analytic expression for the temperature rise produced by a heat-generating layer in contact with a large body is obtained by the Laplace transform method. The solution is used to study the temperature distribution in thin film nichrome resistors under transient conditions.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1976;98(2):331-332. doi:10.1115/1.3450549.
Commentary by Dr. Valentin Fuster
J. Heat Transfer. 1976;98(2):332-334. doi:10.1115/1.3450550.

Noncircular duct hot patch data, extensively referred to in the literature, have been found to be in error. When these data are corrected and compared with predictions of hot patch dryout using the most recent form of the Tong F factor, it is found that physically unintelligible results are obtained. It is not clear whether the Tong F factor, the method of predicting the equivalent uniform dryout flux, or the method of reducing the hot patch dryout data is at fault.

Topics: Ducts , Errors
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster

DISCUSSIONS

Commentary by Dr. Valentin Fuster

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