bluuebunny/crossref_metadata_2025 huggingface dataset:
Liquid extraction in an agitated vessel
Authors: Overcashier R. H. , Kingsley H. A. , Olney R. B.
Published: June 2004

This investigation was undertaken to show how the efficiency of solute transfer between two immiscible liquids is influenced by the type, size, and submergence and rotational speed of the impeller and the degree of baffling, residence time, and phase ratio. The system water‐kerosene‐n‐butylamine solute was agitated in a continuous‐flow 14 3/4‐in. ‐diam. vessel using propellers, spiral turbines, and flat‐blade turbines from 4 to 10 in. in diameter. The feed streams were introduced at the wall at the bottom of the vessel and left at the top of the vessel.

On the basis of the power required for a given level of stage efficiency, the best agitator design is any impeller that has a diameter about 40% of the vessel diameter and is centered in the unbaffled vessel. Without baffles the impeller type and depth of submergence have little effect on performance. The power increase required by the addition of baffles is small at the highest stage efficiencies, especially with the larger radial‐flow impellers, but may be severalfold at efficiency levels of 70 to 90%. This presumably results from the lowered mass transfer driving force caused by the increase in end‐to‐end mixing due to wall baffles. Whether baffles have such a large adverse effect if the feed is introduced into the impeller rather than at the vessel wall is not fully established, but there is some evidence that baffling is also undesirable in this case. For baffled operation, impeller type and submergence do affect performance.

A correlation of stage efficiency is presented in terms of Reynolds number and power number. In addition, energy input per volume of total flow is correlated in terms of residence time and stage efficiency for one size of baffled propeller.

Spot samples taken from the vessel showed large, random‐concentration fluctuations out to 20 residence times and perhaps indefinitely. Reproducible results were obtained by taking time‐averaged samples.
Two‐phase flow of hydrogen in horizontal tubes
Authors: Rogers John D.
Published: June 2004

Semirigorous equations are developed for flow of flashing liquids in pipe lines. These relations are applied to the flow of hydrogen, and computed correlations are presented for the pressure drop and vapor fraction. The calculations have been carried out as functions of the parameters: diameter, 3/8 to 4 in.; mass rate per unit area, 0.0528 to 682 lb./(sq. ft.) (sec.); pressure, 14 to 30 lb./sq. in. abs.; vapor fraction, 0.005 to 0.65; and heat leak, equivalent to 0 to 0.0224 B.t.u./(sq. ft.) (sec.) for a 3/4‐in. line.
Phase separation and mass transfer in a liquid‐liquid cyclone
Authors: Simkin D. J. , Olney R. B.
Published: June 2004

Liquid‐liquid phase separation and mass transfer studies were made in a 4‐in.‐diam. cyclone of conventional construction. The cyclone was tested with oil‐water volume phase ratios ranging from values of 1/3 to 9/1 and for total flows up to 24 gal./min., although most variables were studied at a feed rate of 10 gal./min. Kerosene or a white oil (vis. 9 centipoises at 77°F.) was used as the oil phase. Valve or line premixing was used to disperse the feed. Valve pressure drops were in the range of 0.1 to 1.0 lb./sq.in., and inlet drop sizes, where determined, were about 1 mm. The optimum cyclone geometry (volume, diameter of inlet, overflow and underflow lines) and the optimum split (overflow/underflow) were determined in terms of a phase‐separation efficiencyEs.

At optimum geometry and split a number of mass transfer runs were made in which monobutylamine solute was transferred from the kerosene to the water phase. These runs indicated thatEsdecreased but mass transfer efficiency increased as the feed rate or pressure drop across the mixing valve was increased.
Agitation of non‐Newtonian fluids
Authors: Metzner A. B. , Otto R. E.
Published: June 2004

Since the shear rate of a non‐Newtonian fluid is of importance in fixing the rheological or viscometric behavior of such a material, the present study has been concerned with the development of a general relationship between impeller speed and the shear rate of the fluid. The resulting relationship was then used to interpret and correlate power‐consumption data on three non‐Newtonian fluids by use of a generalized form of the conventional power‐number–Reynolds‐number plot for Newtonians.

Flat‐bladed turbines from 2 to 8 in. in diameter were used exclusively. Tank diameters ranged from 6 to 22 in. and power inputs from 0.5 to 176 hp./1,000 gal. The study encompassed a 130‐fold range of Reynolds numbers in the laminar and transition regions. The results to date indicate that power requirements for the rapid mixing of non‐Newtonian fluids are much greater than for comparable Newtonian materials.
Calculated performance of a dissolved—gas‐drive reservoir by a phase‐behavior method
Authors: Brinkman F. H. , Weinaug C. F.
Published: June 2004

A phase‐behavior approach to the prediction of the performance characteristics of a dissolved‐gas–drive reservoir is unique in that the problem of choosing flash, differential, or composite‐solution gas‐oil ratios and formation‐volume factors has been circumvented. Data required are a compositional analysis of the reservoir fluid, the bubble point of this fluid, and the relative‐permeability curves for the reservoir rock.

Gas‐oil ratios and formation‐volume factors were calculated under conditions duplicating the performance of the reservoir. A comparison was then made between these results and those obtained by calculations involving a differential, a flash, and a composite process. A vital factor in the solution of the problem is the accuracy of the calculated equilibrium constant. Agreement within 3% was obtained when a calculated differential formation‐volume curve was compared with an experimentally determined curve.
Heat transfer in the critical region
Authors: Bringer R. P. , Smith J. M.
Published: June 2004

Heat transfer coefficients were measured experimentally for carbon dioxide in turbulent flow in an 0.18‐in. I.D. pipe. The pressure was 1,200 lb./sq. in. abs. and the bulk temperature varied from 70° to 120°F. In this critical region the coefficients between fluid and tube wall ranged from 300 to 2,600 B.t.u./(hr.)(sq. ft./°F.) over a Reynolds number interval of 30,000 to 300,000.

Existing empirical and semitheoretical correlations were found inadequate in this region, where the thermal conductivity, viscosity, density, and specific heat are all varying rapidly and nonuniformly with temperature. A method of integrating the heat and momentum transfer equations with variable physical properties, recently proposed by Deissler, was applied to the experimental data and found to fit well. The application required extensive calculations, which were carried out with an Electrodata digital computer.

A simplified procedure was proposed for estimating heat transfer coefficients in the critical region by using a semitheoretical equation developed for zero heat flow. Simple rules were suggested for estimating the temperature at which to evaluate the physical properties when this equation is applied to the realt case of finite heat transfer. The method worked well when compared with the computed heat transfer coefficients of Deissler for supercritical wate but showed about 30% deviation when compared with the carbon dioxide results. This discrepancy is believed due to the fact that the carbon dioxide was very close to the critical point (reduced pressure = 1.1) but the water was somewhat further removed (reduced pressure = 1.6).
Viscosity of suspensions of spherical and other isodimensional particles in liquids
Authors: Ting Andrew Pusheng , Luebbers Ralph H.
Published: June 2004

The viscosity of a suspension is related to the properties of the suspending liquid and the suspended particles by measuring the viscosity of suspensions made up of closely sized materials such as glass spheres, plastic Zeolite spheres, blasting sand, and salt cubes in a wide range of concentrations in liquids of varying properties made up of castor oil, tetrabromoethane and carbon tetrachloride, or corn syrup and water. The measurements were made under carefully controlled conditions by means of a Brookfield viscometer, and the reproducibility of results was demonstrated by repetitive runs.

Equations are derived to describe the viscosities of these various suspensions in terms of the viscosity and density of the suspending liquid and of the shape, size distribution, density, and concentration of solid particles. The range of concentration covered is from infinite dilution to near infinite viscosity.

The results obtained can best be explained by postulating nonuniform distribution of particles in a suspension in a network of tetrahedral and simple cubical packings.
Dynamics of liquid agitation in the absence of an air‐liquid interface
Authors: Laity David S. , Treybal Robert E.
Published: June 2004

The dynamics of agitating single‐ and two‐phase liquid mixtures in the absence of an air‐liquid interface was compared with that of similar systems with an interface. Two geometrically similar cylindrical vessels, 12 and 18 in. in diameter respectively, were used, each fitted with a similar six‐bladed, disk‐turbine impeller.

New general correlation curves of power number with Reynolds number are presented which show that elimination of the air‐liquid interface makes it possible to attain dynamic similarity in scale‐up in unbaffled vessels but makes little difference in baffled vessels.
Vapor‐liquid equilibria of Benzene–n‐hexane and benzene‐cyclohexane systems
Authors: Rao V. N. Kumarkrishna , Swami D. R. , Rao M. Narasinga
Published: June 2004

Vapor‐liquid equilibria of two binary systems, benzene–n‐hexane and benzene‐cyclohexane, were measured at pressures from 4 to 18 atm. The three‐constant Redlich‐Kister equation was found satisfactory for correlation.

With the benzene‐n‐hexane system no azeotrope occurred; with the benzene‐cyclohexane system an azeotrope appeared, and the mole fraction of cyclohexane in it diminished with increase in pressure. Lack of correction for fugacity in the vapor phase introduced a maximum error of 4% in activity coefficients at highest pressure.
Diffusion in three‐component gas mixtures
Authors: Toor H. L.
Published: June 2004

A solution to the Stefan‐Maxwell diffusion equations for equimolal countercurrent diffusion in a three‐component gas mixture is obtained which is similar in form to Gilliland's equation for diffusion of two gases through a third inert gas. The important features of both types of diffusion are investigated and the conditions under which the following phenomena occur are determined: (1) diffusion barrier (the rate of diffusion of a component is zero even though its concentration gradient is not zero); (2) osmotic diffusion (the rate of diffusion of a component is not zero even though its concentration gradient is zero); (3) reverse diffusion (a component diffuses against the gradient of its concentration).

A generalized driving force which describes these phenomena is introduced, and approximate equations are developed which give the individual rates of diffusion directly.
Simplified flow calculations for tubes and parallel plates
Authors: Rothfus R. R. , Archer D. H. , Klimas I. C. , Sikchi K. G.
Published: June 2004

The effective correlations of turbulent velocities and friction losses for tubes and parallel plates recently published have been analyzed further in order to simplify their use and to extend the range of Reynolds number.

Working diagrams have been developed from which turbulent friction losses and local velocities for tubes and parallel plates can be calculated without interpolation or trial‐and‐error procedures. Tentative values of parallel‐plate friction factors and average‐to‐maximum velocity ratios in the transition region are also included, and new experimental values of the velocity ratio in smooth tubes are reported. The working diagrams permit more rapid, accurate, and consistent calculations of fluid behavior to be made over a wider range of operating conditions than was previously possible.
Effect of wall roughness on convective heat transfer in commercial pipes
Authors: Smith J. W. , Epstein Norman
Published: June 2004

Heat transfer and friction measurements were made for air flow through a smooth copper pipe and six other commercial pipes, with a ratio of diameter to equivalent sand roughness varying from 640 to 64. The Reynolds number range was 10,000 to 80,000. Though some increase in heat transfer coefficients with roughness was found, the heat transmission per unit power loss always decreased.

The momentum–heat‐transfer anlogies of Reynolds and Colburn are shown to be inadequate for handling the experimental data. Those of Prandtl and Taylor, von Kármán, and Pinkel fail to show a required Reynolds number dependence ofjhwhen friction factor has become independent of Reynolds number for a rough pipe. Martinelli's equation shows such dependence and, even in approximate form, gives good prediction of the experimental results.
Volumetric and phase behavior in the hydrogen–n‐hexane system
Authors: Nichols W. B. , Reamer H. H. , Sage B. H.
Published: June 2004

In spite of the importance of hydrogenation procesing operations in the refining of petroleum there are only limited experimental volumetric and phase equilibrium data concerning mixtures of hydrocarbons and hydrogen. An investigation of the volumetiric and phase behavior of the hydrogen–n‐hexane system was therefore undertaken.

The experimental study involved measurements of the specific volume of four mixtures of hydrogen and n‐hexane at eight temperatures between 40° and 460°F. for pressures up to 10,000 lb./sq. in In addition, the composition of the gas phase in heterogeneous mixtures was determined at six temperatures within the interval mentioned above for pressures as high as 10,000 lb./sq. in.

Little about this system was found to be qualitatively unusual except that the critical pressure exceeded 10,000 lb/sq. in. at all temperatures below 340°F. As would be expected, the dew‐point gas was rather lean in n‐hexane for temperatures below 220°F. and at pressures above 100 times the vapor pressure of n‐hexane throughout the pressure range covered by this study.
Some remarks on longitudinal mixing or diffusion in fixed beds
Authors: Aris Rutherford , Amundson Neal R.
Published: June 2004

It has been shown both theoretically and experimentally that the radial Peclet number in a packed bed approaches about 11. If it is assumed that the interstitial volume of the bed forms mixing cells, then a comparison of the solutions obtained from the mixing and turbulent diffusive mechanisms shows that the axial Peclet number for agreement of the two must be about 2, as a limiting case for high Reynolds numbers. This is substantiated by experiment.
Fluidization and sedimentation of spherical particles
Authors: Hanratty Thomas J. , Bandukwala Abdemannan
Published: June 2004

Data are presented in support of an expression describing the relation between the sedimenting velocity or the fluidizing velocity and the fraction voids. This expression which contains no empirical constants may be obtained by considering a particle in a fluid having the average properties of the suspension. Stokes's law is used to calculate the force on the particle, and an equation derived by Vand is used to describe the viscosity of the suspension. The equation based on this model is valid for particle Reynolds numbers less than 0.07. The model may be used as an approximation of bed behavior at higher Reynolds numbers by application of a correction to Stokes's law.
Nusselt values for estimating turbulent liquid metal heat transfer in noncircular ducts
Authors: Hartnett James P. , Irvine Thomas F.
Published: June 2004

A simple expression for estimating the turbulent forced‐convection heat transfer performance of liquid metals flowing through noncircular ducts is presented. This equation requires the knowledge of the slug Nusselt number evaluated for the specific geometry and for the pertinent boundary conditions. Such Nusselt values are presented herein for a number of technically important geometries. One check on the heat transfer prediction given by Equation (4) is in the case of an annular duct with constant heat flow through the outer wall with the inner wall insulated, for which experimental data exist. The prediction agrees within 20% with the experimental data.

Several possible boundary conditions that may exist in noncircular cross sections are throughly discussed, and it is hoped that as a result this paper may serve to clarify some of the confusion existing in the literature.
Surface tension of acetone‐water solutions up to their normal boiling points
Authors: Howard Katherine S. , McAllister R. A.
Published: June 2004

The surface tensions against air of acetone‐water solutions have been measured over the entire composition range from 20°C. to generally within 1° to 10°C. of the normal boiling points. The capillary‐height method was employed and the results are thought to be accurate to better than ±0.5%.
Drying of sand on a hot surface
Authors: Ludt R. W.
Published: June 2004

Constant layer moisture at the hot surface is found to exist during the constant‐rate period of drying of sand on a hot surface in still air. It accounts not only for the constantrate period of drying itself but also largely for the length of the period.

Temperature of the air‐surface interface usually has minor effects on the rate of vaporization because equilibrium between vapor and the bed is not established during periods of rapid vaporization.

Numerical relationships have not been established.
Catalyzed gas‐liquid reactions in trickling‐bed reactors
Authors: Babcock B. D. , Mejdell Glør T. , Hougen O. A.
Published: June 2004

Kinetic studies were made in a differential flow reactor of the hydogenation of α‐methyl‐styrene with the liquid trickling over a bed of catalyst pellets countercurrent to a stream of hydrogen. The catalysts consisted of palladium, platinum, rhodium, ruthenium, and nickel supported on the external surfaces of aluminal pellets.

With palladium at pressures above 3 atm. the apparent rate‐controlling step was a surface reaction between dissociated hydrogen and α‐methylstyrene both adsorbed on different type of active sites. Below 3 atm. pressure the reactants competed for similar active sites. With platinum the apparent rate‐controlling step was a surface reaction between dissociated hydrogen and α‐methylstyrene on similar active sites. Rhodium and nickel catalyzed the polymerization α‐methylstyrene together with slow hydrogenation. Ruthenium had negligible activity for catalyzing the hydrogenation under the moderate conditions used in this work.

In all cases mass transfer resistances were negligible.
Prediction of cake‐washing results with continuous filtration equipment
Authors: Choudhury A. P. R. , Dahlstrom D. A.
Published: June 2004

This paper proposes a theory of filter‐cake washing on continous filtration equipment based upon the assumption that mixing of the strong liquor and wash fluid is controlling. The theory can be conventiently applied to experimental filtration leaf tests for determining wash efficiency and is easily extrapolated to full‐scale results with the normally experienced uneven cake thickness and wash‐fluid distribution taken into account.

To obtain the necessary wash‐fluid volume for proper soluble removal, a correlation method of wash time as a function of wash ratio with parameters of cake‐formation time has been derived from commonly accepted filtration theory. Experimental and plant data indicate a close agreement with the theory, and the method can be employed to predict filtration rate as a function of wash ratio. A typical illustration has been given to determine filtration requirements for recovering soluble uranium after leaching of the ore by continuous filtration. Washing rate was proved to be conrolling, and this design based only on cake‐formation rate would yield insufficient wash ratios and excessive soluble uranium loss. Final filter and flow‐sheet design must be based on uranium recovery which can be predicted by the proposed methods.
Axial mixing in pipes
Authors: Tichacek L. J. , Barkelew C. H. , Baron Thomas
Published: June 2004

The problem of axial mixing in straight pipes is analyzed by a modification of G. I. Taylor's analysis. The treatment presented here includes the effect of both Schmidt and Reynolds numbers throughout the turbulent‐flow range. All applicable data on flow of gases and liquids are found to confirm the validity of the method.

The analysis indicates that axial mixing increases rapidly as the flow approaches the laminar region, especially for liquids, and that pipe roughness causes a relatively small increase in axial mixing. Turbulent eddy diffusion in the axial direction has a negligible effect.

The results of the analysis are applicable to those systems wherein the kinematic viscosity of the flowing mixture does not vary greatly from one region to another and in which the concentration region of interest is spread out along a sufficient length of pipe. These limitations are broad enough to permit most practical problems to be treated by the method.
Reaction of porous solids
Authors: Petersen E. E.
Published: June 2004

A method is presented for the analysis of a reaction between a porous solid and a gaseous reactant where the kinetic expression is linear in the concentration and where appreciable concentration gradients are established in the pore system as a result of diffusive transport rate. Two cases are treated mathematically: a single cylindrical pore initially of uniform diameter and a porous solid initially containing uniform cylindrical pores with random intersections. The mathematical solutions to the latter case are used to interpret the experimental results reported in the literature on the gasification of graphite rods with carbon dioxide. Values of the computed effective diffusivity are an order of magnitude smaller than the bulk diffusivity at the same temperature and pressure.
Vapor‐liquid—equilibrium data for the ternary system cyclohexane‐heptane‐toluene
Authors: Myers H. S.
Published: June 2004

Previous papers have reported equilibrium data for the binary systems cyclohexaneheptane, heptane‐toluene, and cyclohexane‐toluene. This present study gives similar data for the ternary system cyclohexane‐heptane‐toluene and compares the activity coefficients with those predicted from the three limiting binaries.

The ternary activity coefficients fall well in line between the limiting‐binary data. Distribution is about as would be predicted by the ternary Margules equations. As an approximation, if the coefficients are plotted as a function of the aromatic concentration only, without consideration of the ratio of naphthenes to paraffins, reasonably good correlation is observed.
Heats of vaporization of hydrogen‐bonded substances
Authors: Bondi A. , Simkin Donald J.
Published: June 2004

A new method is proposed for the calculation of the heat of vaporization of hydroxylated compounds to an accuracy of about ±0.5 kcal./mole from no more data than the molecular structure and a boiling point. The older methods, by comparison, achieved an accuracy of about ±1 kcal./mole with a far greater computational effort, since they required the (usually hypothetical) critical temperature and critical pressure in addition to a boiling point.

The method is here applied to aliphatic and aromatic alcohols, to ether‐alcohols (e.g., the cellosolves), and to alcohols conaining keto or aldehyde groups (e.g., salicylaldehyde) and supersedes previous correlations covering the heats of vaporization of these compounds. The method can also be used to assess the quality of vapor‐pressure data of the compounds covered by it.

The method is based on the assumption that the heat of vaporization consists of two terms, the dispersion energy and the hydrogen‐bond increment (close but not equal to the hydrogen‐bond strength). The first term is calculated from a knowledge of the heat of vaporization of the equistructural hydrocarbon, now easily available from the Tables of A.P.I. Research Project 44. The hydrogen‐bond term is calculated from a set of rules given in the report.

The application of the increment method of this report to other properties and other functional groups is the subject of a continuing investigation.
Viscous flow in multiparticle systems: Motion of spheres and a fluid in a cylindrical tube
Authors: Happel John , Brenner Howard
Published: June 2004

An approximate theory for the behavior of multiparticle systems suspended in a viscous fluid is developed, based on a rigorous treatment for the case of a single sphere occupying any position in a cylindrical tube. The results obtained include estimates of the effect of some of the parameters involved on the particle velocities and spatial distribution of particles in very dilute sedimenting and fluidized beds as well as on the pressure drop resulting from passage of fluid. The conclusions presented are in agreement with such experimental data as are available and suggest a basis for more exact treatment of these systems.
Hydroextraction: Flow in submerged cakes
Authors: Storrow J. Anderson
Published: June 2004

Flow equations have been proposed for hydroextractor cakes wherein the pores are filled with moving liquid. These equations have been confirmed for the effect of each variable by use of different experimental techniques. The critical wetting rate has provided the most informative steady state, in which the cake is fed with liquid to maintain the inner surface of the liquid at radius rL coincident with that of the cake at radius rc. Transient techniques have also been used wither with a probe to time the movement of a liquid level between two radii less than rc, or with a photoelectric detector to observe the coincidence of rL = rc. The tests have proved the validity of the hydrodynamic assumptions involved in the equations and have provided both precise methods for research and practical methods for industrial purposes.
Radiant heat exchange in a gas‐filled enclosure: Allowance for nonuniformity of gas temperature
Authors: Hottel H. C. , Cohen E. S.
Published: June 2004

A method is presented for predicting the effect of allowance for radiation exchange on the distribution of temperature and heat transfer within a furnace chamber. The system is divided into surface zones and gas zones, the number being dependent on the desired accuracy of the result. Direct‐exchange factors are available for gas‐gas, gas‐surface, and surface‐surface zone interchange. From these factors one can determine the net exchange factor for any zone pair, making due allowance for interaction with all other zones. The resultant factors are then fed into a set of energy balances, one on each zone, which by simultaneous solution permit a determination of the space distribution of gas and surface temperatures and the distribution of heat flux over the surfaces.
Heat transfer between fluidized‐solids beds and boundary surfaces—correlation of data
Authors: Wender Leonard , Cooper George T.
Published: June 2004

A broad empirical study of nine independent sets of data on fluidized‐bed heat transfer is presented, with correlation of the data in two groups. A wide range of the many variables is covered, and some data on commercial units are included. Data for external (i.e., walls of the fluidizing vessel) and internal (i.e., tubes in the bed) heat transfer surfaces are correlated graphically. The correlations indicate the importance of heat transport by the mobile particles and of unsteady state conduction in the gas.
Distribution of eddy viscosity and mixing length in smooth tubes
Authors: Rothfus R. R. , Archer D. H. , Sikchi K. G.
Published: June 2004

Profiles of eddy viscosity and Prandtl mixing length in fluids flowing steadily and isothermally in smooth tubes have been calculated from the velocity data of several investigators for Reynolds numbers between 1.2 × 103and 3.2 × 106. In the transition range unusually high values of eddy viscosity and mixing length are obtained in some portions of the stream. In the fully turbulent range the effect of Reynolds number is small and the mixing length tends toward zero at the center of the tube. The parameters for turbulent flow between parallel plates have been correlated through the concept of an equivalent tube. The results are of importance in designing equipment for heat and mass transfer and mixing.
Convective heat transfer from hightemperature air inside a tube
Authors: Zellnik Herbert E. , Churchill Stuart W.
Published: June 2004

Local rates of convective heat transfer from air at high temperature to a cold wall were measured in the inlet region of a circular tube. Air entered the tube with a flat velocity and temperature profile at temperatures from 480° to 2,000°F. and flow rates corresponding to Reynolds numbers from 4,500 to 22,500. The inner surface of the 1.0‐in. I.D. tube was maintained at approximately 100°F. by water cooling. Local rates of heat transfer were determined at 1.5, 4, 7, and 10 tube diameters from the entrance by measuring the radial temperature profile in thermally isolated, annular sections of the tube wall.

The local rate data for all gas temperatures are well represented by previous correlations for small temperature differences if the gas properties are evaluated at the bulk temperature rather than at the film temperature. The data agree well with the data of previous investigators wherever the experimental ranges overlap.
A graphical method for solution of freezing problems
Authors: Longwell P. A.
Published: June 2004

Problems in heat conduction involving a moving boundary are encountered in the freezing of liquids and in other situations. Such problems are difficult to solve, and exact solutions are almost unknown. A graphical method for obtaining numerical solutions to problems of this type which can be described in terms of one space coordinate is derived and is demonstrated in two examples involving the freezing of liquids. The method, which does not require specialized knowledge or equipment, takes into account both sensible heats and latent heat.
Film boiling from vertical tubes
Authors: Hsu Y. Y. , Westwater J. W.
Published: June 2004

Heat transfer measurements were made with vertical stainless steel bayonet tubes, 3/8 to 3/4 in. O.D., with lengths from 2.6 to 6.5 in. The heat source was steam. The boiling film ΔT ranged from 154° to 314°F. for three organic liquids and from 547° to 788°F. for nitrogen, all at 1 atm. No forced convection was used. Benzene, carbon tetrachloride, and nitrogen on the longer tubes had h values two or three times greater than predicted by the Bromley equation; however, the Reynolds numbers were found to exceed 2,000. Nitrogen on the 2.6‐in. length obeyed the equation; the Reynolds numbers were less than 2,000, the flow was proved by photography to be turbulent and the h values were much higher than predicted for viscous flow. A correlation is given which fits all the data except for methanol. It shows that a vertical orientation is superior to the horizontal for liquids boiling outside tubes.
Heat and momentum transfer in the flow of gases through packed beds
Authors: Glaser Marvin B. , Thodos George
Published: June 2004

Heat and momentum transfer studies have been made for the flow of gases through fixed beds consisting of randomly packed, solid metallic particles. The experimental technique employed in these studies made possible for the first time the procurement of gas‐film heat transfer data under steady state conditions and in the absence of mass transfer effects. Electric current passed through the metallic particles of the bed created within the particles a steady generation of heat, which was continuously removed by gases flowing through the bed. Several direct temperature measurements of both gases and solids within the bed made possible the direct calculation of the heat transfer coefficient for the gas film to produce the Colburn heat transfer factor jh, which has been found to correlate with the modified Reynolds number, Reh = √ ApG/[µ(1 – ∈)φ]. The shape factor φ was established in these studies for cubes and cylinders and was found to be identical to their respective sphericities.

Pressure‐drop measurements produced a friction factor fk of the Blake type, which yielded separate curves for each shape when correlated with the modified Reynolds number Rem. No simple relationship was found to exist between the heat transfer and friction factors. A single correlation of the pressure‐drop data was obtained for the modulus fkoφn when correlated with a Reynolds number of the type Rem = √ ApG/[µ(1 – ∈)]. The exponent n varies with the particle shape.

Experimental runs have been carried out for 3/16, 1/4, 5/16‐in. spheres, 1/4 and 3/8‐in. cubes, and regular cylinders using hydrogen and carbon dioxide to extend the range of molecular weights beyond that of air, used for the majority of these runs. A particle‐size, column‐diameter effect was found to exist for both heat and momentum transfer. This effect becomes significant in the low Reynolds region.
Fluid‐particle heat transfer in packed beds
Authors: Baumeister Ernest B. , Bennett C. O.
Published: June 2004

Steady state heat transfer experiments were carried out in a 4‐in. I.D. transite tube packed with 3/8‐, 1/4‐, and 5/32‐in. steel spheres. Heat was generated in the pellets by means of a high‐frequency induction coil surrounding the test section. Average heat transfer coefficients between the bed of spheres and a stream of air passing through the bed were calculated for Reynolds numbers of from 200 to 10,400. To ensure the reproducibility of the data, the bed was repacked six times for each pellet size.

A study of the effect of the tube‐to‐pellet‐diameter ratio indicates that this effect is large for low values of the ratio, but much smaller for higher ratios. The results are presented both graphically and in terms of empirical equations. The analogies among heat, mass, and momentum transfer are discussed, and it was found that no simple relation between the heat transfer coefficient and the friction factor exists for packed beds with a gas as the fluid.

An attempt is made to predict the heat transfer rates for packed beds from heat transfer data for single spheres and from pressure‐drop measurements for the packed bed; however, the rates predicted from the pressure‐drop measurements are somewhat lower than the experimental results.
Local boiling coefficients on a horizontal tube
Authors: Lance R. P. , Myers J. E.
Published: June 2004

Local boiling heat transfer coefficients were experimentally determined for nucleate boiling around the outer circumference of horizontal copper tubing. The tubes used were of 16 B.W.G. hard‐temper copper with outside diameters of 1 1/4 and 2 in; the liquids boiled were methanol andn‐hexane. The maximum peripheral variation occurred with the 1 1/4‐in. tube in methanol where an over‐all ΔTof 30.2°F. gave local outside coefficients varying between 249 and 548 B.t.u./(hr.)(sq. ft.)(°F.). The minimum variation was found to occur in the same system, in which an over‐all ΔTof 72.3°F. gave coefficients varying between 856 and 910 B.t.u./(hr.)(sq. ft.)(F.°). The results, plotted in polar coordinates, showed a cardioid configuration for methanol with the maximum coefficients occurring at the bottom of the tube. Then‐hexane results had the general shape of horizontal ellipses with maximum coefficients occurring at the sides of the tube.
Rates of flow through microporous solids
Authors: Gilliland E. R. , Baddour R. F. , Russell J. L.
Published: June 2004

Rates of flow of pure gases, both those with no adsorption and those with appreciable adsorption, were studied as a function of pressure level, pressure drop, and temperature for flow through 1/2‐in.‐diameter cylindrical plugs of activated carbon and of unsintered Vycor glass. Adsorption isotherms for the pure gases on Vycor glass were measured over the range of variables covered in the flow studies. A few measurements were made for bulk liquid flowing through a Vycor plug.

Permeabilities, which are proportional to the rate of flow per unit of pressure drop, were satisfactorily correlated for hydrogen, helium, argon, and nitrogen by employing existing gas‐phase flow theory. Permeabilities considerably larger than the values predicted from the nonadsorbed gas correlation, sometimes more than seventeen times as large, were observed for ethylene, propylene, and isobutane flowing through a Vycor plug. For the hydrocarbon‐Vycor systems, permeabilities for vapor flow are as much as sixty times larger than for bulk liquid flow.

The unusual flow phenomena for the hydrocarbon‐Vycor systems are attributed to a rapid transport in the adsorbed layer. The total transport is treated as being the sum of gas‐phase and adsorbed‐layer flow. An equation describing adsorbed‐layer movement is derived by utilizing a force balance together with thermodynamic principles. The resulting equation has just one empirical constant, and its use requires adsorption‐isotherm data. It correlates very well the surface flow rates for the major range of the variables covered in this investigation. Rate measurements were made for adsorbed‐layer concentrations ranging from about one tenth of a monolayer up through the capillary condensation region. Deviations in the one constant form of the equation are observed below one tenth of a monolayer. The available literature data on flow in adsorbed layers are reasonably well correlated by the same equation.
Mass transfer from a soluble solid sphere
Authors: Garner F. H. , Suckling R. D.
Published: June 2004

Mass transfer from 3/8‐ and 1/2‐in.–diameter spheres of adipic acid and from 3/8‐, 1/2‐, 5/8‐ and 3/4‐in.‐diameter spheres of benzoic acid into a controlled stream of water passing in laminar flow through a 3‐in.‐diameter pipe is found to be correlated by the single equaton NSh = 2 + 0.95 NRe0.5 NSc0.33 for sphere Reynolds numbers between 100 and 700. The limitations on the application of this equation, due to mass transfer by natural convection, are discussed. Correlations are also obtained for transfer from separate regions of the sphere surface.

Skin–friction‐drag coefficients for single fixed spheres have been calculated from reported pressure distributions for Reynolds numbers between 100 and 1,000.

Good agreement is obtained between the mass transfer j factor and other reported values for heat transfer, but comparison with the calculated frictional forces indicates that the equality proposed by Colburn (3) does not hold, because the distributions of the mass transfer and the skin friction over the surface differ.
Calculation of the diffusion coefficient of dilute gases and of the self‐diffusion coefficient of dense gases
Authors: Slattery John C. , Bird R. Byron
Published: June 2004

A corresponding‐states correlation of low‐density binary‐ and self‐diffusion coefficients is presented. The equations are simple to use, are sufficiently accurate for most calculations, and correlate those data used in their derivation somewhat better than calculations based on the Lennard‐Jones potential if potential parameters have to be estimated from the critical properties. The Enskog kinetic theory of dense gases is used in modified form to obtain an expression for the high‐density diffusion coefficient for isotopic mixtures in terms of the viscosity and compressibility of the gas. Generalized viscosity and compressibility charts are then used to construct a graph for predicting a reduced self‐diffusion coefficient as a function of reduced temperatureTr=T/Tcand reduced pressurepr=p/pc. The effect of the pressure on the Schmidt number, Sc = μ/ρ𝒟, is also discussed. Finally the extension of this chart to nonisotopic mixtures is considered.
The role of porosity in filtration part 3: Variable‐pressure—variable‐rate filtration
Authors: Tiller F. M.
Published: June 2004

Virtually all filtration literature has been concerned with constant rate or constant pressure with greater emphasis on the latter. In contrast to these types of operations, industrial filtrations involving centrifugal pumps are accomplished under variable‐pressure—variable‐rate conditions. In spite of its importance virtually no work has been reported in connection with variable‐rate—variable‐pressure filtration. Formulas developed for constant pressure and constant‐rate filtration are not in general applicable to operations effected by centrifugal pumps. Methods solving variable‐pressure—variable‐rate filtration problems are presented.

A method of determining average filtration resistance as a function of compressive pressure under variable‐pressure—variable‐rate conditions is discussed, and formulas for determining point filtration resistance from data for average resistances are presented.
Prediction of resistance in constant‐pressure cake filtration
Authors: Kottwitz F. A. , Boylan D. R.
Published: June 2004

Methods of predicting resistance in constant‐pressure cake filtration have been classified into three groups, (1) basic particle and cake properties, (2) permeability tests, and (3) small‐scale filtration tests. Methods 2 and 3 involve the concept of specific filtration resistance, a property characteristic of each unit mass of deposited cake, and these methods were extensively investigated in the laboratory. Specific resistances for three chemical slurries were determined by laboratory filtrations and filter‐ and compression‐permeability tests. Results of these investigations showed that specific filtration resistance could be predicted from compression‐permeability test data.

Filtration tests made on commercial‐scale equipment operating on pearl cornstarch illustrated the correlation between predicted and actual specific resistance values, the resistance predicted from compression‐permeability test data agreeing very well with the actual resistance of the prefilt.
Momentum and mass transfer by eddy diffusioin in a wetted‐wall channel
Authors: Dhanak A. M.
Published: June 2004

The role of eddy diffusion of mass (water vapor) and momentum was investigated in a specially devised wetted‐wall channel in which the rippling of the liquid film was eliminated. The experimental measurements of the turbulent exchange coefficients for mass and momentum transport were carried out in a fully developed turbulent flow of air within the range of Reynolds numbers of 8,00 to 160,000. A correlation with Reynollds number revealed an approximately linear relationship of the eddy diffusivties to Reynolds number revealed an approximately linear relationship of the eddy diffusivities to Reynolds number [Equation (4)]. From the hot‐wire measurements it was found that within the main protion of the turbulent core eddy diffusivities remained fairly constant.
Heat transfer in film condensation
Authors: Baer Eric , McKelvey James M.
Published: June 2004

In this theoretical analysis of heat transfer in film condensation the total vapor‐side resistance to heat transfer is obtained by adding the resistance to conduction through the condensate film to the resistance due to the condensation process at the vapor‐liquid interface.

The analysis shows that under ordinary conditions conduction in the condensate film is controlling, provided the condensation coefficient is greater than about 0.10. However, under conditions of low total pressure, low heat flux, or low condensation coefficient, the resistances of both processes must be considered.

Experiments carried out on the condensation of methanol are in good agreement with the theory. Furthermore, values of the condensation coefficient for methanol are reported which show that small quantities of air will greatly reduce its magnitude. This is offered as an explantion of the commonly observed phenomenon of reduction of heat transfer rates when noncondensable gases enter a system.
Gas absorption accompanied by a liquid‐phase chemical reaction
Authors: Gilliland E. R. , Baddour R. F. , Brian P. L. T.
Published: June 2004

The rate of absorption of chlorine from chlorine‐nitrogen mixtures into solutions of ferrous chloride in 0.203 N aqueous hydrochloric acid was studied in a short wetted‐wall column. Dimensional analysis and the film and penetration theories were used to infer, from the absorption rate data, that the chemical reaction between chlorine and the ferrous ion is second order. The absorption‐rate results for experiments with a dilute gas phase agreed with theoretical predictions for absorption accompanied by a second order reaction with a reaction rate constant of 188 liters/(g. mole) (sec.). The results for experiments with pure chlorine gas deviated from the rest of the results, and they did not agree with the theoretical equations. It was shown that the assumption of a three‐step mechanism for the chemical reaction, including the formation of a complex ion and the decompositon of this complex ion, explains, at least qualitatively, the deviations observed for the pure chlorine gas runs.
Correlation of local velocities in tubes, annuli, and parallel plates
Authors: Rothfus R. R. , Walker J. E. , Whan G. A.
Published: June 2004

A consistent method is presented for predicting local velocities in smooth tubes, concentric annuli, and parallel plates. Consideration is limited to the steady, isothermal, fully turbulent flow of constant‐density fluids. Experimental data show the proposed correlation to be indepdent of Reynolds number and radius ratio. Intermediate quantities, calculated from friction data, permit local velocities to be determined over a wide range of operating conditions.
Discharge coefficients through perforated plates at reynolds numbers of 400 to 3,000
Authors: Smith P. L. , Van Winkle Matthew
Published: June 2004

The correlation of Kolodzie and Van Winkle (3) for predicting dry plate orifice coefficients through perforated plates originally covering a Reynolds number range of 2000 to 20,000 has been extended to apply to Reynolds numbers as low as 400. The correlation applies to column diameters ranging from 3 to 15 in.
Phase relations of binary systems that form azeotropes: I. The ammonia–n‐Butane system
Authors: Kay Webster B. , Fisch Herbert A.
Published: June 2004

Binary systems that form azeotropes in the critical region of the system show a wide variation in their phase behavior. As part of an investigation of the factors responsible for this variation, the P‐V‐T‐x relations of the ammonia‐n‐butane system were determined at the liquid‐vapor phase boundaries from near room temperature to the highest temperature and pressure at which the liquid and vapor coexist. Ammonia and n‐butane form an azeotrope whose composition varies from 81.7 mole % ammonia at 300 1b./sq. in. to 86.3 mole % at 1295 1b./sq. in. The critical locus possesses a minimum temperature point similar to other binary systems that form azeotropes in the critical region. The experimental results support the hypothesis that binary systems that form azetropes exhibit a characteristic pattern of P‐T‐x relations in the critical region that is distinctively different from systems that do not form azeotropes.