bluuebunny/crossref_metadata_2025 huggingface dataset:
Heat transfer through a homogeneous isotropic turbulent field
Authors: Hanratty Thomas J.
Published: June 2004

Because of the large scale of the motion responsible for mixing in turbulent fields, turbulent transport processes differ from molecular transport processes in that the mixing depends on the previous history of the diffusing material and turbulent fields are generally nonhomogeneous.

The effect of the time dependency of the diffusion process is examined for the case of heat transfer from a hot wall to a cold wall through a turbulently flowing fluid. The fluid is assumed to have a uniform velocity and the turbulence is assumed to be homogeneous and isotropic. The calculations are carried out by assuming a distribution of heat sources along the hot wall and of heat sinks along the cold wall. G. I. Taylor's theory of turbulent diffusion for a homogeneous isotropic field is used to describe the properties of these sources and sinks. These calculations are compared with temperature profiles obtained as a solution to Fick's Law using a constant diffusion coefficient. A marked difference between the two sets of curves is obtained in the vicinity of the wall and in the beginning of the heat exchange section.

A calculated profile on the basis of an idealized model of heat transfer in channel flow is compared with actual measurements made by Page, Corcoran, Schlinger, and Sage (7) at a distance far enough downstream so that the temperature profile had reached a steady condition.
Catalytic hydrogenation of carbon monoxide and dioxide over steel
Authors: Smith Buford D. , White Robert R.
Published: June 2004

The hydrogenation of carbon monoxide and carbon dioxide on various steel catalysts was studied in the temperature range of 800° to 1,300°F. and at pressures from 5 to 30 atm. The feed gases (3.75 to 20 SCFH) were passed over a catalyst bed of 1/8‐in. steel balls supported in a brass‐lined reactor 0.81 in. in diam. The percentage of carbon oxides in the feed was 30% in the runs using a H2CO2 feed and varied from 15 to 38% in the runs with a H2CO feed. The effects of temperature, pressure, feed composition, space velocity, and mass velocity were studied. Carbon deposition did not affect the activity of the catalyst and could be removed readily.
Mass transfer in a wetted‐wall column: Turbulent flow
Authors: Schwarz W. H. , Hoelscher H. E.
Published: June 2004

The object of this study has been the measurement of concentration profiles of water vapor in a wetted‐wall column with fully developed turbulent pipe flow of air for several positions downstream of the inlet. The air Reynolds number was 25,000. The mathematical formulation of this problem involves the Navier‐Stokes equations and the mass transfer equation with a boundary condition of constant concentration at the wall. No attempt has been made toward an analytical solution of this problem, as the exact solution of the turbulence problem has not been developed. Instead, values of the mass and momentum transfer correlation,urh, andurux, have been computed as a function of the radius. The eddy diffusivity for momentum and mass and the local mass transfer rates are shown for engineering purposes.
Crystal‐size distribution in mixed suspensions
Authors: Saeman W. C.
Published: June 2004

Although vacuum crystallizers are used widely, crystal‐size–control methods have not been adequately analyzed. This paper supplies in part the deficiency of technical information on this problem. Industrial crystallizers may have inherent nucleation rates in excess of or below the seed‐crystal requirement for the desired product‐crystal size. This paper deals specifically with means of crystal‐size control by removal of excess nuclei from mixed circulating suspensions as encountered in vacuum crystallizers. It is shown that under certain conditions the cumulative size distribution in the suspension varies as the fourth power of the size. Therefore, it may also be shown that the key to effective size‐control procedures is the segregation time of nuclei in the fines‐removal system. Procedures based mainly on crystal‐size classification by hydraulic elutriation can hardly be effective unless they are also designed to meet the segregation‐time requirements.
Purity control in sodium‐cooled reactor systems
Authors: Bruggeman Warren H.
Published: June 2004

Recent advances in purity control in sodium systems are covered. Emphasis is placed on results from the prototype S.I.R. system as well as other unpublished data. Included are chemical and nuclear activation analyses of sodium, filtration data, and details and operation of cold traps and plugging indicators.
Process for fission‐product removal from uranium‐Bismuth reactor fuels by use of fused‐salt extraction
Authors: Dwyer O. E.
Published: June 2004

The liquid‐metal‐fuel reactor under development at the Brookhaven National Laboratory uses a fuel which is a solution of U233, Mg, and Zr in liquid bismuth. For a power breeder thermal reactor, high neutron economy is essential, and this calls for low concentrations of those fission products in the fuel which are high neutron capturers. Roughly 45% by weight of the fission products can be continuously removed from the fuel by salt extraction with alkali and alkaline‐earth fused‐salt mixtures. These fission products contain the highly “poisonous” rare earths. This paper will present a discussion of processdesign considerations and proposed flow sheets.
Liquid‐metal extraction for processing of spent fuel
Authors: Voigt A. F. , Daane A. H. , Dewell E. H. , Clark R. G. , Gonser J. E. , Haefling J. F. , Malaby K. L.
Published: June 2004

Plutonium and the fission products can be removed from irradiated uranium by liquidmetal extraction by use of another metal immiscible with uranium. Metals studied have been silver, cerium, and lanthanum. Plutonium removal by silver is high, by the rare‐earth metals moderate. In all cases volatile elements, including cesium, strontium, and barium, are removed. Rare earths are efficiently removed. Ruthenium and molybdenum are largely unaffected. Experiments with synthetic fuels corresponding to long burn‐up periods show improved removal of most elements. Repeated batch extractions indicate that a continuous process separating the fuel into uranium, plutonium, and fission‐product fractions could be developed.
Continuous dissolution of uranium‐aluminum reactor fuels
Authors: Boeglin A. F. , Buckham J. A. , Chajson L. , Lemon R. B. , Paige D. M. , Stoops C. E.
Published: June 2004

Extensive pilot plant studies of the continuous, mercury‐catalyzed nitric acid dissolution of uranium‐aluminum alloy materials similar to possible reactor fuel elements were carried out. Marked differences were observed in the dissolution rates of cast and wrought alloys. Optimum feed‐acid concentrations varied with the type of alloy. At constant acid feed conditions dissolving rates varied approximately with the cube root of catalyst concentration up to a limiting concentration. The metal dissolving rate was proportional to the 0.8 power of the nitric acid feed rate. A general empirical correlation was developed.
Diffusion of uranium through graphite
Authors: Loch L. D. , Gambino J. R. , Duckworth W. H.
Published: June 2004

Diffusion rates of uranium through graphite were determined in the temperature range of 3,000° to 4,350°F. The diffusion couples consisted of sintered UC2 disks in contact with graphite rods. The observations indicated two distinct types of uranium transport which could be associated with volume diffusion and with migration along pores respectively.

Volume diffusion was characterized by steep concentration gradients and shallow penetration. The diffusion coefficient Dv, in sq. cm./sec. between 3,300° and 4,250°F., is given by an equation. Above 4,250°F. incipient melting of the UC2 was evident and the diffusion coefficients were much higher than those given by the equation.

As an example of the penetration resulting from volume diffusion, calculations show that, after 1,000 hr. at 4,200°F. the uranium concentration at 0.1 cm. from the interface will be 1,000 mg./cc., compared with 10,000 mg./cc. for pure UC2.

Pore migration resulted in uranium penetration far beyond that arising from volume diffusion at equivalent temperatures and diffusion times. However, uranium concentrations were very small compared with those corresponding to volume diffusion. Pore migration is strongly temperature dependent.

To estimate the practical importance of pore migration, the uranium flow through a graphite wall at 3,000°F. was measured. With a wall thickness of 0.32 cm., the average flow per unit area was 0.015 mg./ (sq. cm.)/ (hr.) for a 40‐hr. test.
Light transmittance as a measure of interfacial area in liquid‐liquid dispersions
Authors: Trice Virgil G. , Rodger Walton A.
Published: June 2004

Interfacial area in liquid‐liquid systems has been measured photographically. Precision and accuracy of the method have been shown to be better than 10%. To avoid tedium of counting drops, a simple light probe of easily reproducible design has been developed to measure the light transmission through the dispersions formed. A correlation of light transmittance with interfacial area is presented and its usefulness and limitations are discussed.
Apparatus for visual study of corrosion by hot water
Authors: Grieser Daniel R. , Simons Eugene M.
Published: June 2004

The design and operation of a windowed autoclave suitable for studying corrosion of materials by pressurized hot water are described. The technique for taking time‐lapse motion pictures of a specimen from the instant of contact with the high‐temperature water until the corrosion is complete is explained, and a set of typical pictures is presented showing the progress of the attack. Pressure and temperature measurements provide a means for rough computation of corrosion rates, as is shown by the results of two tests of uranium specimens subjected to pressurized hot water.
Mechanism of heat transfer to liquid drops
Authors: McDowell R. V. , Myers J. E.
Published: June 2004

The purpose of this investigation was to study the process of heat transfer to a liquid drop rising through another liquid. In experimental runs various‐sized drops of S.A.E.‐10 lubricating oil, kerosene, and xylene were heated with water; also, water drops were heated with various organic liquids. Theoretical calculations of temperature change were made, various mechanisms of heat transfer being assumed. The temperature change predicted with each mechanism was compared with the experimental results and the controlling mechanism thus determined for each system studied.
Liquid‐side resistance in gas absorption
Authors: Vivian J. E. , Peaceman D. W.
Published: June 2004

The film theory of liquid‐side resistance to gas absorption, embodying the assumption of a thin stagnant liquid film adjacent to the interface in which steady state diffusion occurs, has long been open to question, particularly in packed columns. Higbie's penetration theory, believed to be more reasonable, pictures the liquid as flowing over a piece of packing for a very short period of time before being mixed as it flows to the next piece of packing. In the penetration model absorption occurs during a series of brief contacts, and unsteady state mass transfer conditions prevail in the liquid.

Several short glass‐wetted‐wall columns 1.9 to 4.3 cm. long were constructed to simulate the assumptions of the penetration theory. Because of the short length ripples were absent except when the gas rate was higher than ReG = 2,200. The desorption of carbon dioxide from water and of chlorine from dilute hydrochloric acid (0.16 to 0.18 N) was studied. The desorption rate of carbon dioxide was unaffected by gas velocity up to ReG of 2,200 and increased 1.1%/°C. over the temperature range of 22° to 31°C.
Fractionation of gas mixtures in a moving‐bed adsorber. I. Correlation of adsorber performance
Authors: Kapfer William H. , Malow Monroe , Happel John , Marsel Charles J.
Published: June 2004

The design and operation of a pilot‐scale‐moving bed adsorber to separate the various components of a gas mixture using activated carbon as the preferential adsorbent are described. A binary system, methane–acetylene, and a ternary system, methane–carbon dioxide–acetylene, were studied. The performance of the unit was analyzed by means of the transfer‐unit‐height (H.T.U.) concept based on the observed changes in gas composition during tower operation. For both the binary and ternary systems the transfer‐unit height was independent of feed‐gas composition but was found to vary linearly with the ratio of feed gas to carbon flow. The over‐all transfer‐unit‐height values based on either the gas or the adsorbed phase were observed to vary from 6.5 in. at 1.39 std. cu. ft./lb. carbon to 36.9 in. at 4.81 std. cu. ft./lb. carbon.
Fluidized‐bed heat transfer: A generalized dense‐phase correlation
Authors: Wen Chin‐yung , Leva Max
Published: June 2004

A fluidized‐bed heat transfer mechanism is proposed that assumes that the chief resistance to heat exchange between a confining wall and a fluidized bed is in the laminar film at the vessel boundary. Heat flow through the film is by conduction. As the solids‐particle velocity along the wall will modify film thickness, correlation of film coefficients in terms of particle velocities or the equivalent suggests itself. That heat transport from the boundary of the heating element to the fluidized core proceeds by way of turbulent solids mixing seems indicated by the considerable effect that the solids heat capacity appears to exert on over‐all coefficients.

The resulting correlation is examined critically in relation to pertinent literature data. The effect of fluidized‐bed parameters on heat transfer coefficients is considered, and applicability and limits of the correlation are ascertained.
Prediction of vapor‐liquid equilibrium data for binary Hydrocarbon mixtures at various total pressures
Authors: Lu Benjamin C.‐Y.
Published: June 2004

An empirical method is suggested which permits the prediction of vapor‐liquid equilibrium data for binary hydrocarbon mixtures at various total pressures on the basis of equilibrium data at one constant pressure. This method has been tested with the vapor‐liquid equilibrium data of six nonideal systems measured at twenty‐one different experimental conditions. The total pressure range varies from 50 mm. of mercury to 4 atm. In all cases the predicted results are in good agreement with the experimental data.
Study of bubbling performance in relation to distillation and absorption
Authors: Chu Ju Chin , Forgrieve John , Grosso Robert , Shah S. M. , Othmer Donald F.
Published: June 2004

One of the important factors affecting the efficiency of vapor‐liquid contacting operations is the relationship between available interfacial area and contact time.

Because of the difficulties in measuring these quantities, little information has heretofore been made available on them. Previous studies have been confined to extreme over‐simplifications of the turbulent type of contacting taking place in fractionation devices. The present investigation consisted of the determination of interfacial area and contact time for the formation of air bubbles submerged in water and aqueous solutions. The bubbles were produced at single vertical slots and rose through a flowing liquid. In order to complete the study on physical contacting, a companion study is concerned with vapor‐liquid behavior in the forth and entrainment zones. The experimental technique in this study involved taking high‐speed motion pictures of the bubbling action. Measurements of the area and volume of bubbles were made at intervals during the course of their growth, and values of total contact time and average interfacial area per unit volume of vapor are presented.

It was found that both the average interfacial area per unit volume of vapor a and the total contact time tm were primarily affected by the head of flowing liquid on the slot. Below slot submergence of approximately 2.5 in. of liquid, interfacial area was shown to decrease with increasing slot submergence and increasing slot area. Above 2.5 in. of liquid, interfacial area was a function of skirt clearance, liquid viscosity, and surface tension.

Total contact time was found to increase with increasing slot submergence and to decrease with increasing vapor rate and skirt clearance.

Through the use of an integrated mass transfer–rate equation, the terms a and tm can be used in conjunction with the appropriate mass transfer coefficient for predicting the point efficiencies on bubble‐cap plates.
Mass transfer at low pressures
Authors: Sherwood Thomas K. , Cooke Norman E.
Published: June 2004

Data are reported for the evaporation of spheres of naphthalene into air, helium, carbon dioxide, and Freon‐12, and of liquid diethyl adipate into air at pressures from 0.1 to 3,000μ Hg and at Reynolds numbers from 0 to 1.37. By use of suitable values of the surface‐evaporation coefficient and the assumption of additivity of surface evaporation and diffusional resistances, the data are well correlated. The results lend semiquantitative support to the theory of sublimation of crystals developed by Stranski.
Mass and heat transfer to single spheres and cylinders at low Reynolds numbers
Authors: Friedlander S. K.
Published: June 2004

Rates of mass and heat transfer to single spheres and cylinders at low Reynolds numbers are predicted from boundary‐layer theory. The velocity distributions which are assumed to exist are those derived from the linearized Navier‐Stokes equations by Tomotika and Aoi.

In the case of the sphere the Nusselt number is found to be a function only of the Peclet group when the Stokes streamline function is assumed to apply. Experimental data for mass and heat transfer to singel spheres fall 10 to 40% higher than predicted from the theory. Experimental data for heat and mass transfer to single cylinders at large NPe check the theory.

Curves are also plotted for the efficiency of removal of colloidal particles by combined direct interception and diffusion for both spheres and cylinders.
Spray—extraction‐tower studies
Authors: Johnson A. I. , Minard G. W. , Huang Chen‐Jung , Hansuld J. H. , McNamara V. M.
Published: June 2004

This paper describes further research on a 4‐in. I.D. by 8‐ft. spray tower of Elgin design. Previous work concerned limiting flow and holdup in this tower. Owing to its high capacity and low cost, the spray tower would have much greater commercial application in liquid‐liquid extraction if its conditions of transient operation could be predicted and if it could be operated to yield low Ht values. This research attempts to show that transient conditions can be predicted and that low Ht values for both mass and heat transfer can be realized near the limiting flow conditions.

Theroretical equations for rate of approach to steady state derived and tested for the systems ethylene dichloride–water–propionic acid and ethylene dichloride–water–acetic acid show that the approach depends on the ratio of the phase flow rates. This study is important for the prediction of start‐up time for industrial towers.

With the same systems the extraction capacity of the spray tower was investigated up to the condition of rejection. The results were correlated as KEa and Ht, OE vs. a function of the ratio of the phase flow rates. The dispersed‐phase flow rate was found to have primary significance.

The heat transfer rates between water as continuous phase and solvents of various denisties were correlated as Ht′ values plotted against a function of the ratio of the phase flow rates. The advantages of operation near rejection were demonstrated, and the effect of direction of heat transfer was found to be significant.
Studies of thermal conductivity of liquids: Part III
Authors: Sakiadis Byron C. , Coates Jesse
Published: June 2004

Values of thermal conductivity and temperature coefficients for thirty‐five pure organic liquids, in addition to those previously reported, obtained with a previously described apparatus (Part I), are presented. Values of thermal conductivity or temperature coefficients for twenty‐eight of these liquids have not been reported before. The experimentally determined maximum error is ±1.0%.

The two methods for predicting the thermal conductivity of liquids previously proposed (Parts I and II) are extended to cover the types of compounds studied in this investigation, in particular ring compounds.

The temperature coefficient of thermal conductivity was observed to decrease rapidly, approaching zero as the freezing point is approached. The existence of a transition temperature or region within the liquid state is shown and identified with the onset of molecular rotation.
Performance of packed columns. IV. Effect of gas properties, temperature, and pressure on gasphase mass transfer coefficients
Authors: Shulman H. L. , Margolis J. E.
Published: June 2004

To test the applicability, over a wide range of temperatures, pressures, and gas physical properties, of the mass transfer correlation presented earlier, 0.5‐in. naphthalene Berl saddles were vaporized into air, carbon dioxide, and Freon‐12 in a 4.0‐in. column. Temperatures from 15° to 73°C. and pressures from 0.26 to 1 atm. were covered.

The correlation was found to represent all the experimental data when the surface temperature of the naphthalene was used to evaluate the correct driving force.

This correlation, when combined with effective interfacial areas presented previously, makes it possible to estimate the volumetric mass transfer coefficeint,kGa, for any gas‐liquid‐solute system.
Equilibrium in the system Cu++–Na+–Dowex‐50
Authors: Rao H. C. Subba , David M. M.
Published: June 2004

Equilibrium isotherms are presented for the cation exchange of copper and sodium on Dowex‐50 resin in solutions from 0.01 to 4N in chloride content, and the equilibrium data are correlated on the basis of the Donnan equilibrium. Data are also given on the water content of the resin and the diffusible ions present in this water.
Reaction kinetic studies: Catalytic dehydrogenation of sec‐butyl alcohol to methyl ethyl ketone
Authors: Perona Joseph J. , Thodos George
Published: June 2004

Reaction kinetics for the catalytic dehydrogenation of sec‐butyl alcohol to methyl ethyl ketone has been investigated at atmospheric pressure and temperatures ranging from 650° to 750°F. in the presence of solid brass spheres, 1/8 in. in diameter. The nature of this catalyst permitted a direct evaluation of the surface involved in this reaction and allowed the definition of a surface‐feed ratio to be expressed as S/F in place of the conventional weightfeed ratio W/F commonly used in catalytic studies. Feed compositions ranged from secbutyl alcohol to mixtures containing high percentages of methyl ethyl ketone and hydrogen.

In these studies mass transfer effects were found to be significant and, for a proper representation of conditiated at the catalyst surface, must be taken into account. The effect of feed compositions on the initial rates of reaction showed that the rate‐controlling step was the desorption of hydrogen involving a single‐site mechanism.

In addition, the results of these studies have been used to produce values of height of reactor unit HRU which have been found to correlate with mass velocity and temperature. The HRU provides a simple means of calculating the depth of catalyst necessary to effect a designated conversion.
Hydraulics of wetted‐wall columns
Authors: Michalik E. R.
Published: June 2004

On the assumption of laminar Newtonian flow, flow profiles are developed for both the vertical plate and cylindrical column by use of classical equations. From the flow profiles the mass transport, vertical pressure gradient, and optimal design parameters are calculated. With the Reynolds‐number criterion used to ascertain the maximum nonturbulent velocity, minimal values for the plate distance and column radius can be calculated. An example is included for each case.
Approximate operational calculus in chemical engineering
Authors: Churchill Stuart W.
Published: June 2004

Approximations are suggested to extend the usefulness of operational calculus in solving boundary‐value problems of interest to the chemical engineer. General approximations are outlined and specific ones illustrated. The use of computing machines with operational calculus is also considered.
Measured plate efficiencies and values predicted from single‐phase studies
Authors: Rush F. E. , Stirba Clifford
Published: June 2004

Plate efficiencies measured on 18‐in.‐diam. sieve plates are reported for the acetic acid‐water system and for the methyl isobutyl ketone‐water system at atmospheric pressure. In the former system the major resistance to mass transfer is in the gas phase; liquid‐phase resistance to mass transfer is controlling in the latter. Efficiencies are also reported for the aniline‐nitrobenzene system (gas‐phase resistance controlling) at 5 mm. Hg absolute on 6‐in.‐diam. sieve plates. Pure gas‐ and liquid‐phase efficiencies for both plate designs were determined by the adiabatic humidification of air and the desorption of oxygen from water into air. Predicted values of plate efficiency for each of the binary systems studied were computed from the pure phase efficiencies according to the procedure outlined by Gerster et al. A comparison between measured and predicted efficiencies is presented as a guide for future research in this field.
Critical constants of the aromatic hydrocarbons
Authors: Thodos George
Published: June 2004

Following an approach similar to that presented for the aliphatic (6, 7) and naphthenic (8) hydrocarbons, methyl‐group contributions have been developed that now make possible the calculation of van der Waals' constants for aromatic hydrocarbons of considerable size and complexity. These constants are then utilized to calculate the critical temperatures, pressures, and volumes for these aromatic hydrocarbons.

In addition, simple relationships have been developed that permit the evaluation of both van der Waals' constants for the unsubstituted linearly fused aromatic hydrocarbons.

Comparisons of calculated critical constants with values presented in the literature for over twenty aromatic hydrocarbons produced average absolute deviations of 0.70% for the critical temperature and 2.14% for the critical pressure.
Diffusion coefficients in hydrocarbon systems: Methane in the liquid phase of the methane–n‐heptane system
Authors: Reamer H. H. , Sage B. H.
Published: June 2004

The production and refining of petroleum involve many processes in which conditions deviate markedly from equilibrium. For prediction of the behavior of such nonequilibrium systems, information concerning the molecular‐transport characteristics of the paraffin hydrocarbons is of practical interest.

Fick diffusion coefficients for methane were measured in the liquid phase of the methane–n‐heptane system at temperatures between 40° and 340°F. at pressures up to 3,500 lb./sq. in., but the pressure range was limited at the higher temperatures by approach to the critical state of this binary system.

The measurements obtained confirmed the fact that the Fick diffusion coefficients for methane decrease with an increase in the concentration of this component and increase rapidly with an increase in temperature for a constant composition. These data together with similar information for other binary paraffin hydrocarbon systems indicate that the Fick diffusion coefficients for methane decrease with an increase in the molecular weight of the less volatile component.
Thermal‐conductivity–reduced‐state correlation for the inert gases
Authors: Owens E. James , Thodos George
Published: June 2004

The fragmentary thermal‐conductivity data for argon available in the literature have been correlated by use of a residual thermal conductivityk–k* vs. density ρ relationship. This correlation produced a unique continuous curve which was found to be singularly independent of temperature and pressure for both gaseous‐ and liquid‐state data. From low‐pressure thermal‐conductivity valuesk* and the relationship given above, it is possible to determine thermal conductivities at any condition of temperature and pressure for which a corresponding density is available. This procedure was used to calculate reliable thermal conductivitieskfor high‐pressure regions where experimental data were lacking.

In a similar manner the critical thermal conductivitykcfor argon was established directly from the critical density and the quantityk*. Thekcvalue permitted the calculation of reduced thermal conductivitieskRand made possible the construction of an extensive reduced‐state chart. Although this correlation was developed mainly from data for argon, it was found to apply equally as well to the other inert gases as postulated from the theory of corresponding states.

A comparison of thermal conductivities calculated from the reduced‐state plot with over 200 experimental points produced an average deviation of 1.8% for all the inert gases. This chart was also found applicable to the diatomic gases and their mixtures but produced significant deviations for substances having more than two atoms per molecule.
Fluid friction in noncircular ducts
Authors: Walker J. E. , Whan G. A. , Rothfus R. R.
Published: June 2004

Pressure drop due to fluid friction has been measured in a smooth tube; in six smooth concentric annuli; and between smooth, parallel, flat plates. The data cover the viscous, transition, and lower turbulent ranges of flow. Friction factors are in agreement with theory in the viscous range and can be correlated uniquely in the fully turbulent range by means of a modified hydraulic radius concept. Limits of the transition region in annuli are functions of the ration of inner and outer radii. Correlations in the fully turbulent range permit friction factors for the noncircular ducts to be predicted within the uncertainty of smooth‐tube data. Such factors can be used for the prpose of correlating other variables as well as for direct calculation of pressure drop.
Vapor‐liquid equilibria and heat of mixing: n‐octane–ethylbenzene–cellosolve system
Authors: Murti P. S. , Van Winkle Matthew
Published: June 2004

Vapor‐liquid equilibria of the systems n–octane–Cellosolve, ethylbenzene‐Cellosolve, and n–octane–ethylbenzene‐Cellosolve were determined at 760 mm. Hg. The activity coefficient data of Yang and Van Winkle (23) for the system n–octane–ethylbenzene and the data of this work on other systems were expressed by Wohl's three‐suffix Margules equations. The ternary data are predicted satisfactorily from the binary constants and no noticeable ternary effects seem to exist for this ternary system.
Diffusion in a moving medium with time‐dependent boundaries
Authors: Forster H. Kurt
Published: June 2004

The problem of diffusion in a moving medium with given motion of the boundaries is considered. The method presented yields the analytical solution to any desired degree of accuracy provided that solutions for certain associated problems of diffusion in a medium at rest with boundaries at rest are known. The method is applied to the analysis of partial and approximate solutions previously presented for the one‐dimensional case of a spherical cavity in a liquid with radial boundary motion induced by evaporation.
Entrapment of gas in the spreading of a liquid over a rough surface
Authors: Bankoff S. G.
Published: June 2004

Conditions for the incomplete displacement of gas from the valley between two parallel ridges by a liquid‐drop front advancing over the ridges are calculated. The significant parameters are found to be the liquid density, surface tension, contact angle, and geometry of the ridges. The solution may be obtained analytically or, more conveniently, graphically. Surface roughnesses are divided into four classes, one of which can stably switch from liquid—to gas—fill, and another vice versa. This may account for some of the hysteresis effects reported in bubble nucleation. It is pointed out that surfaces consisting predominately of cavities are more likely to follow these considerations than grooved surfaces, owing to displacement of gas by advance of liquid along the grooves. An example important in boiling and cavitation theory is worked out, and qualitative agreement with the literature is shown.
Kinetic studies of carbonation reactions using radioactive tracers
Authors: Himmelblau D. M. , Babb A. L.
Published: June 2004

In this study a radioactive tracer technique was used to determine the kinetic reaction rate constants in the CO2NaHCO3Na2CO3H2O system at temperatures of 32, 50, and 68°F., and at various values of pH ranging from 5.6 to 7.6. By operating with this system at chemical equilibrium but at isotopic disequilibrium, it was possible to divorce the influence of the diffusion of CO2 into and out of the aqueous solution from the kinetic effects of the chemical reaction. Radioactive carbon‐14 in the form of CO2 was analyzed by means of the Bernstein‐Ballentine technique in order to measure the rates of reaction.

By this treatment, without using intricate equipment, reaction rate constants were computed from simple, integrated first‐order equations. Results showed that values for the forward rate constant of the reaction CO2 + H2O ⇌ HCO3− + H+ agreed well with the values published by previous investigators. On the other hand, the forward rate constants of the reaction CO2 + OH− ⇌ HCO3− were about 100 times as large as previously reported values. This difference is believed due to the complete elimination of any mass transfer effects in this study. In addition, values for the rate constants of the reverse reactions were measured for the first time, and the calculated values of the equilibrium constants for the two reactions agreed within 6% on the average with those given by Harned and Owen. The technique used, with its variations, is expected to have numerous applications in the study of the kinetics of heterogeneous systems.
Wall effect for the fall of single drops
Authors: Strom J. R. , Kintner R. C.
Published: June 2004

Measurements were made of the rate of fall of drops of five organic liquids through an aqueous phase contained in eight vertical cylinders of various diameters. Newton's equation for the wall proximity effect for rigid spheres or cylinders predicts values somewhat in excess of the observed. A correction factor equation with the more convenient equivalent spherical diameter is presented. Its use is limited to d/D ratios less than one half. The ultimate velocity of a drop of specific size in an infinite medium can be calculated from that measured in a small tube by multiplying the latter by the ratio of the tube cross‐sectional area to the area of the annular space between tube wall and drop.
Viscous flow in multiparticle systems: Slow motion of fluids relative to beds of spherical particles
Authors: Happel John
Published: June 2004

A mathematical treatment is developed on the basis that two concentric spheres can serve as the model for a random assemblage of spheres moving relative to a fluid. The inner sphere comprises one of the particles in the assemblage and the outer sphere consists of a fluid envelope with a “free surface.” The appropriate boundary conditions resulting from these assumptions enable a closed solution to be obtained satisfying the Stokes‐Navier equations omitting inertia terms. This solution enables rate of sedimentation or alternatively pressure drop to be predicted as a function of fractional void volume.

Comparison of the theory is made with other relationships and data reported in the literature. Of special interest is its close agreement with the well known Carman‐Kozeny equation which has been widely used to correlate data on packed beds as well as sedimenting and fluidized systems of particles. This is remarkable in view of the fact that the force on each particle in a packed bed can be up to several hundred times that exerted on a single particle in an undistrubed medium.
Heterogeneous phase equilibria of the methane—hydrogen sulfide system
Authors: Kohn James P. , Kurata Fred
Published: June 2004

The experimental apparatus and procedures which were developed for the determination of the heterogeneous phase behavior of the methane‐hydrogen sulfide system have been described in a previous paper (2). The apparatus and procedures were tested and employed at temperatures in the range of —300 to 300°F. and at pressures up to 2000 1b./sq. in. abs. The vapor‐liquid, vapor‐solid, liquid‐vapor‐solid, liquid‐liquid‐vapor and liquid‐liquid‐solid phase border curves were determined for six mixtures of methane and hydrogen sulfide. The phase compositions were determined at selected points along the three‐phase univariant equilibrium lines. An invariant point (quadruple point) was found which involves the equilibrium of two liquid phases, a vapor phase, and a solid phase. These data are presented on P‐T and T‐X diagrams.

The data contribute to the understanding of phase behavior of light hydrocarbons containing hydrogen sulfide.
Viscosity: Reduced‐state correlation for the inert gases
Authors: Shimotake Hiroshi , Thodos George
Published: June 2004

A reduced‐state viscosity correlation has been constructed from the available data of the inert gases. For the development of this correlation, the fragmentary experimental data for argon were utilized along the lines proposed for thermal conductivities by Owens and Thodos (21) in order to determine the effect of pressure on viscosity. In addition, the only available low‐pressure viscosity data for neon and helium have been incorporated in this correlation to produce for the first time the effect of subatmospheric pressures. This correlation covers the range of pressures included betweenPR= 40 andPR= 0.015 × 10−4and extends up to temperatures ofTR= 100. It has been found that the effect of subatmospheric pressures on viscosity does not become significant above pressures of 1 mm. of mercury. However, at lower pressures, viscosity is found to decrease rapidly, particularly in the regions below absolute pressures of 0.01 mm. of mercury.

Viscosities calculated with the reduced state correlation produce an average over‐all deviation of 0.93% for neon, argon, krypton, and xenon. In these comparisons the available viscosity data for the gaseous and liquid states of these substances have been included. Deviations of the same order of magnitude are produced for helium in the gaseous state; however, these deviations become excessive for viscosities of helium in the liquid state.

The application of the final reduced state correlation has been extended to a number of diatomic and polyatomic gases and found to apply well to the diatomic gases only.
Drop formation in liquid‐liquid systems from single nozzles
Authors: Null Harold R. , Johnson Homer F.
Published: June 2004

Interfacial area is an important variable in mass transfer operations. In liquid‐liquid extraction systems, where interfacial area comprises drop surfaces, the area can be computed if drop sizes are known. This work presents a new correlation which predicts volumes of drops formed from single nozzles to within 20% throughout the range of nozzle flow rates for which uniform drop sizes are obtained.
Combined laminar free‐ and forced‐convection heat transfer in external flows
Authors: Acrivos Andreas
Published: June 2004

A method is presented for calculating the shear stress and the rate of heat transfer in external flows for combined laminar forced and free convection. The parameterGr/Re2is of fundamental importance in such problems. Numerical results are reported for the heating and cooling of upward flow past a vertical flat for three Prandtl numbers. It is found that the transition from forced to free convection is gradual, especially at high Prandtl numbers. The inflence of free convection on the separation point is also examined.
Some properties of the poisson distribution
Authors: Said A. S.
Published: June 2004

This paper lists various properties of the Poisson distribution and related functions which can be derived from elementary principles without reference to theories of probability or statistics. They are intended for use by persons who may have to deal with Poisson distributed variables but not from a satistical point of view. Limit values and sums of the Poisson distribution, the sums of related functions, and different relations between its sums and integrals are given.

Differential and difference equations which lead to solutions in the form of a Poisson distribution are discussed. The general elution equation is derived by setting up the differential‐difference equation for plate n in a chromatographic column and showing that the Poisson distribution is a solution to this equation. The complete solution is then obtained by applying the boundary conditions of the process.
A reactor‐design equation based on a proposed distributed boundary‐layer thickness
Authors: Hoelscher H. E.
Published: June 2004

An empirical equation is developed which seems applicable to the general problem of fixed‐bed catalytic design and relates the reaction rate (in a differential reactor) or conversion (through an integral reactor) to the surface reaction rate, the flow rate through the bed, and the physical properties of the system. The development is based on the assumption that there exists a film of stagnant fluid surrounding each catalyst particle, through which mass is transferred only by molecular motion, and that the thickness of this film varies throughout the bed from zero to some upper limit in a manner which is described by a distribution function. The equation involves two empirical constants: the multiplying constant and the exponent in the usual jd‐factor‐Reynolds‐number relationship.

The application of this equation is illustrated. It appears to provide a basis for evaluation of the contribution of diffusional steps in the over‐all mechanism and to provide a means for predicting an expected conversion rate at any flow rate through the bed, provided only that the surface (chemical) reaction rate is known at the operating temperature. It also appears possible to calculate values of the surface‐reaction‐rate constant and the temperature coefficient from data taken from a reactor operating in the diffusion‐controlled range.
Drainage of packed beds in gravitational and centrifugal‐force fields
Authors: Nenniger Emile , Storrow J. Anderson
Published: June 2004

The basic differential equations are developed for the prediction of saturation‐time curves for the drainage of packed beds in either gravitational or centrifugal fields. The only mathematical solution existing at present, a series solution, is provided for these equations. A film drainage function is included to describe the movement of liquid along the surface of the particles when the main liquid level has passed through the pores of the bed. This method of analysis has been used successfully to predict the drainage of packed beds in a 9‐in.–diameter hydroextractor. The important value of capillary suction head is best found from ancillary tests with Haines apparatus, but the value can be found with reasonable accuracy from the change in drainage rate as the liquid surface enters the upper surface of the packed bed. When these two rates are available, the permeability can also be found, and all the major variables are obtained from the drainage test on either the hydroextractor cake or the packed bed under gravity drainage.
Heat transfer in forced convection with internal heat generation
Authors: Toor H. L.
Published: June 2004

A solution to the problem of heat transfer with simultaneous heat generation in viscous tubular flow is presented. The temperature profiles and heat transfer coefficients which are obtained apply to compressible as well as incompressible Newtonian and power‐law non‐Newtonian fluids with constant physical properties and to systems in which the heat generation is an arbitrary function of radius. An example of heat transfer with frictional heat generation in a non‐Newtonian fluid is also presented, and the solution to the problem in which a fluid enters a tube in laminar flow with an arbitrary temperature profile is given, with a consideration of a first approximation to the case of heat transfer in a turbulent fluid in which heat is being generated.
Generalized correlation for loading in packed towers with countercurrent gas‐liquid flow
Authors: Howkins J. E. , Davidson J. F.
Published: June 2004

Experiments in which a liquid film runs over a vertical string of spheres surrounded by a concentric tube through which air is blown upward have shown that loading in a packed tower is due to the formation of standing waves on the liquid film. In the ball‐and‐tube system a wave is formed just below the equator of each ball, owing to the pressure gradient within the air stream as it accelerates through the narrowing gap between the ball and the tube. Interfacial shear and surface tension are of secondary importance. The similarity between the characteristics of the ball‐and‐tube system and those of the randomly packed tower suggests that loading in the latter system is also due to wave formation. With this concept of loading, a correlation has been dérived.
Shape factors for conductive heat flow
Authors: Smith Julian C. , Lind John E. , Lermond David S.
Published: June 2004

Application of shape factors to problems of conductive heat flow eliminates the need for lengthy calculations by numerical approximation methods. Shape factors for several systems, determined bvy electrical analogues, are given in the accompanying article.
Critical temperatures and pressures of hydrocarbons
Authors: Forman J. Charles , Thodos George
Published: June 2004

A method has been developed for the calculation of van der Waals' constants both a and b for hydrocarbons usually encountered, including the aliphatic, naphthenic, and aromatic types. With these constants critical temperatures and pressures can be calculated directly.

Methods recently made available (12, 13, 14, 15) allow the calculation of these constants through the use of substitution values involving the replacement of hydrogen atoms by methyl groups in a definitely prescribed pattern. In this study van der Waals' constants are directly calculated from a consideration only of the molecular structure of the hydrocarbon. This approach has become possible through the assignment of group contributions to different types of carbon atoms, which can be combined in any manner to produce the van der Waals' constants representative of the molecular structure of the hydrocarbon.
Heat transfer to a liquid fluidized bed
Authors: Lemlich Robert , Caldas Isidoro
Published: June 2004

An experimental study of the rate of heat transfer from the retaining wall to a fluidized bed of solids was carried out for liquid water and glass spheres. The independent variables included mass velocity, particle size, bulk temperature, and wall temperature. Significant increases in heat transfer were observed, owing to the presence of the suspended solids, even to the extent of tripling the coefficient. For each of several particle sizes, the coefficient passed through a maximum corresponding to a particular mass velocity. The behavior of the bed at velocities below and above those for maximum coefficient was studied and categorized. Tentative correlations for both regions are offered.