bluuebunny/crossref_metadata_2025 huggingface dataset:
Hypothetical standard states and the thermodynamics of high‐pressure phase equilibria
Authors: Prausnitz J. M.
Published: June 2004

Thermodynamic analysis of phase‐equilibrium data is necessary for testing such data, for extension to new conditions, and for purposes of correlation and prediction of phase‐equilibrium behavior. While such analysis is common for low‐pressure systems, it is rare for high‐pressure systems owing to difficulties encountered in the definition of standard states. For a gaseous solute in the liquid phase it is proposed that the standard state be taken as the hypothetical liquid at the temperature and total pressure of the solution. The properties of this standard state are specified by the temperature and total pressure and by the specific volume which the substance would have if it did not experience a phase change. This standard state is useful since it is not a function of the solution but only of the substance being considered. For a condensable component in the gas phase it is convenient for most purposes to define the standard state as the ideal gas at the temperature and total pressure of the solution, but to separate the effect of composition on the activity coefficient from that of pressure, it is proposed to define the standard state as the real hypothetical gas at the solution conditions. To illustrate these ideas, activity coefficients are computed for several high‐pressure systems, and it is shown how these activity coefficients may be used in the correlation, testing, and extension of high‐pressure phase‐equilibrium data.
Thermodynamic consistency of binary liquid‐vapor equilibrium data when one component is above its critical temperature
Authors: Adler S. B. , Friend Leo , Pigford R. L. , Rosselli G. M.
Published: June 2004

Methods are developed for testing binary system phase‐equilibrium data for thermodynamic consistency when the more volatile component is above its critical temperature. The isothermal case with varying pressure and the isobaric case with varying temperature are considered individually. The rigorous form of the Duhem equation is employed rather than the simplified one, which for binary systems is inconsistent with the phase rule. Although derived for the specific case given in the title, the relationships developed are applicable to all conditions of binary systems. Sample calculations illustrating the methods are included.
Heat or mass transfer in a fluid in laminar flow in a circular or flat conduit
Authors: Brown George Martin
Published: June 2004

Accurate solutions to the Graetz equation and to the similar equation for flow between two parallel plates are presented including the first ten or eleven eigenvalues and important derivatives. The first six eigenfunctions are also presented at intervals of 0.05 from y = 0 to y = 1.
Heat and mass transfer to decelerating finely atomized sprays
Authors: Manning W. P. , Gauvin W. H.
Published: June 2004

The rate of heat and mass transfer in the nozzle zone of water sprays produced by internal‐mixing pneumatic nozzles and hollow‐cone pressure nozzles was determined for both concurrent and crosscurrent drying air‐flow patterns. The Nusselt numbers for the evaporating drops were correlated by means of the equation proposed by Ranz and Marshall for stationary drops in a moving air flow. Methods of measuring the physical properties of the water‐air system were developed, and special attention was devoted to the determination of drop velocities and air humidity.
Velocity of large drops and bubbles in media of infinite or restricted extent
Authors: Harmathy Tibor Z.
Published: June 2004

A new theory gives a simple method of calculating the terminal velocity of fluid particles moving in media of either infinite or restricted extent.

Empirical and semiempirical formulas [Equations (27) and (30)] and a graph (Figure 6) over the interval 0 ≤ d/D ≤ 1.3 are shown to yield satisfactory results for gas or liquid particles moving in liquid media. In the case of liquid drops falling through gaseous media they give only a rough approximation.

Graphs showing the variation of the drag coefficient (Figure 1) and the shape (Figure 2) of fluid particles with the Eötvös number are given. A semiempirical equation for the terminal velocity of solid spheres in restricted media has also been developed [Equation (24)].
Point source turbulent diffusion in a pipe
Authors: Flint Duane L. , Kada Hisao , Hanratty Thomas J.
Published: June 2004

Turbulent diffusion from a small source located in the center of a 3‐in. pipe was studied. Hydrogen and carbon dioxide were mixed in air, and potassium chloride solution was mixed in water. Eddy diffusion coefficients calculated from the data are correlated by plotting (E)/(2aUc) vs. NRe. Differences from other data in the literature are discussed. The results could not be used for determining the form of the correlation coefficient because of inaccuracies in the measurements for small diffusion times.
Mass transfer in laminar—boundary‐layer flows with finite interfacial velocities
Authors: Acrivos Andreas
Published: June 2004

Asymptotic expressions are presented in this paper for the mass transfer Nusselt number in both forced‐ and free‐convection laminar‐boundary‐layer flows with large interfacial velocities directed toward the surface. The analysis is valid for arbitrary surface geometries and includes transfer in a variable properties fluid. It is shown, in addition, how these asymptotic formulas may be used in conjunction with the Nusselt number for zero interfacial velocities to estimate the rate of mass transfer for the intermediate regions.
Liquid viscosities above the normal boiling point for methane, ethane, propane, and n‐butane
Authors: Swift G. W. , Lohrenz John , Kurata Fred
Published: June 2004

Viscosities, obtained with a falling‐cylinder viscometer, are presented for liquid methane, ethane, and propane from their normal boiling points to their critical points and for n‐butane from its normal boiling point to 100°C. The data of this study are compared with those of other investigators.

The experimental viscosities of this study are correlated within ± 5% over the reduced‐temperature range from 0.65 to 0.95 by means of a modified Smith‐Brown correlation. The Grunberg‐Nissan equation for estimating the critical viscosity was tested with the experimentally determined critical viscosities of this study and was found satisfactory.
The viscosity of liquid mixtures
Authors: McAllister R. A.
Published: June 2004

The theory of viscosity of liquid mixtures presented here is based on Eyring's theory of absolute reaction rates. The most important conclusions drawn are that for liquids the free energies of activation for viscosity are additive on a number fraction or mole fraction basis and that interactions of like and unlike molecules must be considered. Methanol‐toluene, benzene‐toluene, and cyclohexane‐heptane systems were analyzed with a three‐body model and found to fit within the accuracy of the experimental data. Acetone‐water mixtures fit a four‐body interaction much better. Indications are that to describe acetone‐water mixtures well would require consideration of seven‐ or eight‐body interactions.
Flow patterns and mixing rates in agitated vessels
Authors: Norwood K. W. , Metzner A. B.
Published: June 2004

Mixing rates in agitated vessels are predicted through measurement of the flow patterns which determine them. These measurements suggest the use of a model that assumes that nearly all the mixing occurs in a small “perfectly mixed” region near the impeller, with flow throughout the remainder of the tank serving primarily to bring the fluid into this region of the impeller.

On the basis of this model, equations were developed for relating volumetric flow rates, hence the mixing rates, to the operating variables. While the theory could be checked directly only to Reynolds numbers of slightly over 600 (owing to limitations of the experimental technique employed in this part of the mixing‐rate studies), the volumetric flow rates could be measured from Reynolds numbers of 36 to 1.7 × 104. The times required for completion of an acid‐base neutralization (terminal mixing) were also measured from Reynolds numbers of 1.6 to 1.8 × 105.

Flat‐blade, dimensionally similar turbines with diameters of 2, 4, and 6 in. were used. Tank diameters ranged from 5.76 to 15.5 in. The baffle width equaled one tenth of the tank diameter in all runs. All the data were for Newtonian fluid systems, but the extension of this work to non‐Newtonian materials is discussed briefly.
Transient response study of gas flowing through irrigated packing
Authors: Demaria Francesco , White Robert R.
Published: June 2004

The transient response of a gas phase as it flows through an irrigated packed column can be interpreted as a distribution of time spent by the elements of gas as they flow through the bed.

A step function in helium concentration was introduced in the entering air stream of a column packed with Raschig rings, and the outlet concentration was recorded with time. Water was used as the liquid phase. Size of Raschig rings, depth of bed, water and gas flow rates were the main variables investigated.

The response curve for the gas reveals an increasing departure from uniform flow of the gas stream as liquid and gas rates are increased to flooding. The first and second moments of the time distribution give directly the porosity and the axial dispersion of the gas. These quantities have been found to be mainly dependent on liquid flow rates. The skewness which characterizes the weight that the various gas elements have on the dispersion about the average residence time has been found to give a convenient measurement of the uniformity of gas flow through the bed.
Mass transfer in semifluidized beds for solid‐liquid system
Authors: Fan Liang‐Tseng , Yang Yung‐Chia , Wen Chin‐Yung
Published: June 2004

A new fluid‐solid contacting technique known as Semifluidization has been studied. Mass transfer data were obtained for a benzoic acid–water system, and correlations in terms of mass transfer factors and over‐all void fractions (for both packed and fluidized sections) are presented. Previous mass transfer correlations for fixed and fluidized beds are critically evaluated with respect to the limitation and applicability and are discussed in relation to semifluidized‐bed mass transfer correlations.
Detonation characteristics of hydrogen‐oxygen mixtures at high initial pressures
Authors: Gealer Roy L. , Churchill Stuart W.
Published: June 2004

Detonation velocities of hydrogen‐oxygen mixtures were measured for initial pressures from 14.4 to 1,000 lb./sq. in. abs. and compositions from 40 to 80 mole % molecular hydrogen. Detonation and impact characteristics were computed for essentially the same range of conditions by the use of the elementary theory of detonation. Equilibrium compositions of hydrogen‐oxygen mixtures at pressures from 10 to 2,000 atm. and temperatures from 3,000 to 5,000°K. were included in the computations and have been filed with the American Documentation Institute. The effect of nonideal thermodynamic properties on the computed detonation velocities was considered.
A photographic study of pool boiling in the region of the critical heat flux
Authors: Cole Robert
Published: June 2004

A photographic study was made to investigate the boiling phenomena in the neighborhood of the critical heat flux. The system consisted of an electrically heated zirconium ribbon, insulated on its underface, suspended in a pool of water at its saturation temperature. Measurements of bubble diameters, bubble positions relative to the heating surface, local bubble frequencies, and contact angles at known times intervals were obtained from the film. Results indicate that at high heat fluxes the primary forces acting on a bubble leaving the surface are the buoyancy and drag forces. A dimensionless relationship is developed relating bubble velocity, bubble diameter, and contact angle at breakoff. Drag coefficients for freely rising vapor bubbles a saturated liquid are found to be representable by the usual drag coefficient‐Reynolds number curves for solid bodies. Jakob's plot of bubble frequency vs. bubble diameter at breakoff is extended to high heat‐flux values, and a relationship proposed by Deissler at the critical heat flux is found to yield reasonable agreement with the experimental data.
Studies on axial effective thermal conductivities in packed beds
Authors: Yagi Sakae , Kunii Daizo , Wakao Noriaki
Published: June 2004

The axial effective thermal conductivities of packed beds were determined by measuring the axial temperature gradients at steady state, the heat being conducted in the direction opposite to that of air. The present experiments were carried out with the beds of glass beads, metallic balls, broken pieces of limestone, and Raschig rings, taken in separate experiments.

It was found that the axial effective thermal conductivity increases more with the increase of air flow than it does in the case of radial conductivity. The axial effective thermal conductivity coincides with the radial conductivity when NRe → 0.
An experimentally verified theoretical study of the falling cylinder viscometer
Authors: Lohrenz John , Swift G. W. , Kurata Fred
Published: June 2004

A theoretical analysis was made for laminar fluid flow in the annulus of a falling cylinder viscometer. A viscometer calibration constant was defined from the results of this analysis. This constant was expressed in terms of only the physical dimensions of the viscometer. The volues lidity of the theory was demonstrated by the agreement between predicted and experimental values of the viscometer constant.

Methods of representing calibration data were compared. Temperature and pressure effects on the viscometer constants were related to the mechanical properties of the viscometer materials.

The results of this investigation showed that the practical design of falling cyclinder viscometers is possible.
The role of porosity in filtration: IV. Constant pressure filtration
Authors: Tiller F. M. , Cooper H. R.
Published: June 2004

Certain assumptions which have previously served as a basis for the conventional equations employed in constant pressure filtration are shown to be in error. It is demonstrated that the specific filtration resistance, the ratio of the mass of wet to mass of dry cake, and the rate of flow, q = dv/dθ, are not constant as has been assumed. In an example it is shown that q undergoes an eightfold variation as the liquid flows from the cake surface through to the medium.

Since the product αq appears in the basic differential equation, incorrect values of q lead to errors in the calculated values of α arising from experimental data. The errors are significant when thick slurries are employed.

New partial differential equations are presented for flow through compressible media in which q varies with cake thickness. Modifications of the conventional constant pressure equations are presented.
A study of hydrates in the methane‐propylene‐water system
Authors: Otto Frederick D. , Robinson Donald B.
Published: June 2004

Experimental data are presented to show the points of incipient hydrate formation in the methane‐propylene‐water system. The addition of 1.4% propylene to methane lowered the equilibrium pressure 400 lb./sq. in. at 50°F. The locus of the four‐phase equilibrium consisting of hydrate, vapor, water‐rich liquid, and hydrocarbon‐rich liquid was determined. This was terminated by the appearance of a critical condition at 1,370 lb./sq. in. abs. and 69.3°F., where the vapor phase contained 34.8% propylene on a dry basis. Below this pressure the hydrate, vapor, water‐rich liquid equilibrium does not exist for solutions containing more than about 25% propylene. Solid‐vapor equilibrium ratios were estimated for propylene hydrates. The significant features of the phase diagrams for the system are discussed in some detail.
Effects of solids on turbulence in a fluid
Authors: Kada Hisao , Hanratty Thomas J.
Published: June 2004

The effect of solid particles on fluid turbulence was studied for fully developed flows of slurries in a vertical 3‐in. pipe for solids concentrations ranging from 0.13 to 2.5 volume %. Point source turbulent diffusion data in the slurry flows were compared with data for flows without solids present. The solids do not appear to have a large effect on the diffusion rate unless there is an appreciable average slip velocity between the solids and the fluid and unless the solids concentration is high enough.
Heat and momentum transport characteristics of non‐Newtonian aqueous thorium oxide suspensions
Authors: Thomas D. G.
Published: June 2004

Heat transfer and pressure‐drop measurements were made with non‐Newtonian aqueous thorium oxide suspensions. A comparison of the results of the two different kinds of measurement allowed the general features of non‐Newtonian thorium oxide suspension heat transfer to be readily identified, thus leading to a clear understanding of anomalies observed in previous suspension heat transfer studies.

Data were obtained at suspension concentrations up to 0.10 volume fraction solids, (1,000 g. of thorium/kg. of water) in systems having tube diameters of 0.318 and 1.030 in. In addition laminar‐flow data were taken with a capillary‐tube viscometer with a tube diameter of 1/8 in. and an L/D of 1,000. It was shown that laminar flow physical properties determined with the 1/8 in. diameter tube were satisfactory for correlating data taken with tubes up to 1.030 in. in diameter.

Until the present study information was not available which would permit a choice between two different viscosities for use in correlating non‐Newtonian turbulent heat transfer and flow data. The limiting viscosity at very high shear rates is shown to give a unique correlation of turbulent data for tube diameters from 0.124 to 1.030 in., whereas the use of the effective viscosity (that is the viscosity evaluated at the point value of the wall shear stress corresponding to each given flow condition) gives a pronounced diameter effect in turbulent‐flow correlations.

The data show that the onset of turbulence for both the pressure‐drop and heat transfer measurements occurs at the same Reynolds number and is approximated by the value predicted by the Hedstrom criterion (II). The heat transfer transition region extends to Reynolds numbers a factor of four times greater than the critical, as is also the case with Newtonian materials. Heat transfer to thorium oxide slurries in fully developed turbulent flow is the same as that predicted by the usual correlations for Newtonian fluids to within the precision of the experimental data, provided that the Reynolds and Prandtl numbers are calculated with the limiting viscosity at high rates of shear, η, for this viscosity. An approximate form of Martinelli's momentum heat transfer analogy correlates the experimental results within +17 and −36%.
Phase equilibria of the propane‐hydrogen sulfide system from the cricondontherm to the solid‐liquid‐vapor region
Authors: Brewer Jerome , Rodewald Newell , Kurata Fred
Published: June 2004

The phase‐equilibria data of the propane‐hydrogen sulfide system has been previously investigated from 32°F. to the critical locus. Since this represents about one‐half of the phase data, the primary purposes of the present study were to complete the data to the solid‐liquid‐vapor region which starts about —125°F. and to verify the results of other investigators at the higher temperatures.

Five mixtures of propane‐hydrogen sulfide were studied, ranging from 8.6 to 78.3% propane, with the dew‐ and bubble‐point method. A temperature‐composition diagram for six isobars from 400 to 20 lb./sq. in. abs. presents most of the essential data. Vaporization equilibrium constants are tabulated together with the x‐y data for these isobars. The data of Kay and Rambosek (3) and Steckel (4) were verified to within 2% except near the vicinity of the azeotrope.

A new method was used to fix the temperature of the azeotrope for two of the five mixtures and a sixth mixture. The determination of the azeotropic temperatures was made by a graphical method in which the differences between the dew‐ and the bubble‐point pressures for each mixture were plotted against the temperature. The minimum value of the curve corresponds to the temperature of the azeotrope. The application of this method to the data of Kay and Rambosek (3) gave results which were in agreement with this study, while the original results by these authors as determined by an indirect method were in poor agreement.

A measure of the reliability of the composition, temperature, and pressure data of the solid‐liquid‐vapor region was indicated when checks within 5% were found with Dalton's law of partial pressures.
Turbulent diffusion in the core of fully developed pipe flow
Authors: Baldwin Lionel V. , Walsh Thomas J.
Published: June 2004

This paper summarizes an experimental study of turbulent diffusion downstream of a line source of heat. Mean temperature profiles in the core of nearly fully developed pipe flow were measured at four mean velocities, from Uc = 72.6 to 160 ft./sec. Hot‐wire anemometer surveys showed that the turbulence in the axial core was nearly homogeneous and isotropic. The objective was to find empirical relations between the anemometer (Eulerian) specification of the turbulence and the Lagrangian statistical properties which determine diffusion.

The diffusion results agreed with predictions of G. I. Taylor's theory of diffusion by continuous movements; the eddy diffusivity increased from zero at the heat source to a constant, asymptotic value far downstream. The Lagrangian correlation coefficients inferred from the diffusion data had shapes similar to the Eulerian correlations over most of the range of time and space. Empirical relations were found to relate the coordinates of the Lagrangian and Eulerian correlation coefficients over the range of this experiment. In addition preliminary measurements are reported for a general Eulerian correlation which is a function of both space and time; the results indicate that a special case of this new Eulerian function may be a fair approximation of the Lagrangian correlation.
A method of measuring thermal diffusivities of rocks at elevated temperatures
Authors: Somerton W. H. , Boozer G. D.
Published: June 2004

A method is presented for the measurement of thermal diffusivity of synthetic and natural rock materials at elevated temperatures. The method involves heating of cylindrical test specimens at a constant rate of rise of the edge temperature and measuring the temperature differential between a point just inside the sample edge and the center of the sample. It is shown that for a fixed geometry and a constant heating rate thermal diffusivity is inversely proportional to the temperature differential.

A record of the variation of diffusivity with temperature may be obtained through the temperature range of 150 to 1000°C. (except where thermal reactions occur) within a period of less than 2 hr.

Measurements are reproducible within ± 10% for a given material. Accuracy of the values obtained is believed to be good; however there are no data available for direct comparison with the materials tested. Use of an approximate equation for calculation of diffusivity from experimental data leads to errors of the order of only 0.5%. Fairly good agreement was obtained between steady state measurements and measurements by the present method.
Analytical study of heat transfer rates for parallel flow of liquid metals through tube bundles: II
Authors: Friedland Aaron J. , Bonilla Charles F.
Published: June 2004

A theoretical analysis of heat transfer to liquid metals in parallel flow through a tube bundle, following the method of Lyon, results in an equation which agrees within 10% with the calculated values. The conditions are fully developed turbulent flow, constant heat flux at the wall, and an infinite number of tubes arranged on an equilateral triangular pitch. The hexagonal flow area assignable to any tube is approximated by a circle of equal area, and the velocity distribution of Bailey for an annulus is assumed to apply from the inner wall to the circle of maximum flow. The range of conditions is: pitch‐to‐diameter ratio, 1.375 to 10; Reynolds number, 104to 106; Prandtl number, 0 to 0.1; and Peclet number, 0 to 105. Laminar and slug flow Nusselt numbers are also determined.
Use of boundary‐layer theory to predict the effect of heat transfer on the laminar‐flow field in a vertical tube with a constant‐temperature wall
Authors: Rosen Edward M. , Hanratty Thomas J.
Published: June 2004

Variations of density and viscosity with temperature cause distortions in the flow field and affect the rate of heat transfer to fluids in laminar flow in vertical tubes. The magnitude of these distortions is predicted through an approximate solution of the equations of motion and energy.
Chemical reaction processes in two‐phase systems: Theory and experimental results for slow chemical reactions in batch, column, and continuous stirred tank reactor operations
Authors: Trambouze Pierre , Trambouze M. T. , Piret Edgar L.
Published: June 2004

A theory of design of chemical reactors is developed for two‐phase fluid systems where the rates of chemical reaction are low relative to the rates of mass transfer. Equations are presented for batch, column, and continuous stirred tank operations. Experimental data on the continuous hydrolysis of acetic anhydride in a benzene‐water system operating countercurrently in a pulsed‐flow sieve plate column and in a packed column are analyzed in terms of the theory.
Mass transfer with liquid lithium in circular conduits
Authors: Gill William N. , Vanek Richard P. , Grove C. S.
Published: June 2004

Forced convection mass transfer between circular tubes and liquid lithium was experimentally investigated over a range of Schmidt numbers from 40 to 57 and Reynolds numbers from 5,550 to 22,500. Information concerning the mechanism for mass transfer was obtained by measuring local solution and deposition rates as a function of distance along the tubes. Observed entrance effects for the solution process suggest that it involves the parallel mechanisms of diffusion through a solid film and through occluded liquid in grain boundaries. It is indicated that the relative contributions of these processes changes with increasing temperature.

A j‐factor correlation of existing liquid metal mass transfer data for fully developed conditions in circular conduits is presented and indicates that an exponent of 0.112 forNRebest represents the data. This result agrees well with other studies (9).
Penetration theory for gas absorption accompanied by a second order chemical reaction
Authors: Brian P. L. T. , Hurley J. F. , Hasseltine E. H.
Published: June 2004

The penetration‐theory solution for the effect of a second‐order irreversible liquid‐phase chemical reaction on the rate of gas absorption has been computed numerically on an IBM‐704 computer. A linearized, time‐centered, implicit finite‐difference method was used to solve the nonlinear partial‐differential equations. The method was very effective, permitting the solution of the equations for a wide range of the parameters of interest. The penetration‐theory results are compared with the film‐theory solution, and it is shown that the solutions to the two theories agree within 16% if they are compared for conditions which produce the same asymptotic solution for an infinitely rapid chemical reaction. A simplified equation and some correction charts are presented which permit a rapid, accurate estimation of the penetration‐theory solution over a wide range of variables.
The mechanics of moving vertical fluidized systems: V. Concurrent cogravity flow
Authors: Quinn J. A. , Lapidus Leon , Elgin J. C.
Published: June 2004

An experimental investigation of the concurrent cogravity flow of particulate solids and water in a 1‐in. diameter vertical column is reported. Measurements were made of the particle concentration, or holdup, existing in the column as a function of the fluid and particle flow rates for two particle sizes, 0.0184‐ and 0.00396‐in. diameter glass spheres. The experimental results form the basis for a prediction of the generalized characteristics of concurrent cogravity fluidization.

The data for each particle size are correlated in terms of the slip velocity and the holdup. The slip velocity is demonstrated to be the same unique function of the holdup for concurrent cogravity flow and for batch fluidization. Therefore the holdup and the conditions of limiting operation for concurrent cogravity flow can be accurately predicted from the batch fluidization curve.
Volumetric properties of gas mixtures at low temperatures and high pressures by the Burnett method: The hydrogen‐methane system
Authors: Mueller William H. , Leland Thomas W. , Kobayashi Riki
Published: June 2004

A Burnett type of apparatus for the study of the volumetric behavior of gases at low temperatures and high pressures was constructed. The apparatus was used to study the volumetric behavior of methane and four mixtures of hydrogen and methane from +50° to −200°F. and pressures as high as 7,000 lb./sq. in.

The experimental data were used to obtain the second virial coefficients for pure methane and for the mixtures. The results of approximately 600 experimental points were used to obtain a table of compressibility factors for methane and the mixtures at even increments of pressure and temperture.
A finite‐difference method of high‐order accuracy for the solution of three‐dimensional transient heat conduction problems
Authors: Brian P. L. T.
Published: June 2004

A finite‐difference method is presented for solving three‐dimensional transient heat conduction problems. The method is a modification of the method of Douglas and Rachford which achieves the higher‐order accuracy of a Crank‐Nicholson formulation while preserving the advantages of the Douglas‐Rachford method: unconditional stability and simplicity of solving the equations at each time level. Although the method has not yet been applied, the analysis in this paper suggests that it will prove to be the most efficient method yet proposed for the numerical integration of three‐dimensional transient heat conduction problems.
Laminar boundary layer flow and heat transfer past a flat plate for a liquid of variable viscosity
Authors: Hanna O. T. , Myers J. E.
Published: June 2004

A solution for the problem of incompressible laminar boundary‐layer flow and heat transfer with variable viscosity is presented. Because of the variation of viscosity with temperature the velocity and temperature fields interact mutually. This necessitates the simultaneous solution of the momentum and energy equations. The analysis is carried out for the case where heating begins at the leading edge of the plate. The results show the effect of the important variable property parameters on the friction factor and the heat transfer coefficient. These parameters are seen to be the temperature difference between wall and free stream, the viscosity temperature variation law, and the Prandtl number at the wall. The results are applicable to liquids.
Hydrates in systems containing methane, ethylene, propylene, and water
Authors: Snell L. Eric , Otto Frederick D. , Robinson Donald B.
Published: June 2004

The initial hydrate forming conditions for the systems ethylene‐water and methane‐ethylene‐water were investigated to about 9,000 lb./sq.in.abs. It was found that at a given pressure the initial hydrate forming temperature for mixtures containing greater than about 65 mole % ethylene was higher than the initial formation temperature for either methane or ethylene. Solid‐vapor equilibrium ratios were calculated for the ethylene hydrate. A comparison between experimental and predicted hydrate forming conditions for the system methane‐ethylene‐propylene‐water was made for several different mixtures of these gases. This comparison showed that the predicted hydrate forming temperature was slightly higher than the experimental at a given pressure.
Heterogeneous phase and volumetric behavior of the methane n‐heptane system at low temperatures
Authors: Kohn James P.
Published: June 2004

The phase behavior of the methane‐n‐heptane system was determined at temperatures from −200° to 340°F. at pressures up to 1,500 lb./sq. in. abs. The system was found to have a miscibility gap in the liquid‐vapor region. The compositions of phases along the three phase (L1—L2—V) locus indicate that the L1 phase is approximately 0.64 mole fraction methane and that the L2 and V phases are substantially pure methane phases. The quadruple point (L1—L2—S1—V) was found at a temperature of −154.4°F. and a pressure of 339 lb./sq. in. abs. A singular point (type k) at which the L2 phase is in critical identity with the vapor phase was found at −114.6°F. and at a pressure of 694 lb./sq. in. abs.

The fugacity of methane at constant temperature as a function of the composition of dissolved methane was found to be linear in the low‐temperature range. The plot of Henry's law constant expressed as fugacity mole fraction methane ratio vs. reciprocal absolute temperature was linear in the temperature range from −130° to approximately 100°F. These data indicate that the solution thermodynamics of methane‐n‐heptane is particularly simple in the low‐temperature range.
Relation of interfacial shear stress to the wave height for concurrent air‐water flow
Authors: Lilleleht Lembit U. , Hanratty Thomas J.
Published: June 2004

Waves at an interface between a concurrent air‐water flow cause an increase in the interfacial stress. This increase in stress is correlated with the root‐mean‐square displacement of the liquid from its average height. The data are compared with Nikuradse's measurements with sand roughness.
Multicomponent mass transfer I. Theory
Authors: Toor H. L. , Sebulsky R. T.
Published: June 2004

As the primary phase in the development of multicomponent mass transfer theory, equations are derived which predict the rate of mass transfer of each species from an interface to a ternary gas mixture in turbulent flow for equimolal‐countercurrent transfer and for transfer with one of the three gases stagnant.

The mass transfer equations obtained, regardless of whether a film, Prandtl‐Taylor, or modified Chilton‐Colburn model is used, differ in form from the usual binary equations and predict qualitative as well as large quantitative differences between binary and ternary transfer.

A criterion is obtained which any consistent multicomponent mass transfer theory must satisfy, and although the ternary film and Prandtl‐Taylor models satisfy this criterion, the modified ternary Chilton‐Colburn model does not.
Microscopic study of bubble growth during nucleate boiling
Authors: Strenge P. H. , Orell Aluf , Westwater J. W.
Published: June 2004

A photographic technique was used to determine bubble growth rates for ether and pentane boiling on vertical metal surfaces of zinc and an aluminum alloy at atmospheric pressure at saturation conditions. Motion pictures were taken at about 3,000 frames/sec. through a microscope which produced a 13X magnification on the film. The heat flux was varied from about 3,000 to 13,000 B.t.u/(hr.)(sq.ft.). In seven runs out of nine the late‐growth equations of Forster and Zuber, Plesset and Zwick, and others were in error by less than 40% for bubble diameters from about 0.1 mm. up to the full field of view of about 0.75 mm. For sizes below 0.1 mm. the growth was too rapid to be measured. Interesting observations which are described quantitatively include bubble vibrations, irregularities in nucleation, and statistical variations in growth rates.
A general correlation of vapor‐liquid equilibria in hydrocarbon mixtures
Authors: Chao K. C. , Seader J. D.
Published: June 2004

A general correlation of vapor‐liquid equilibria in hydrocarbon mixtures is developed. The vaporization equilibrium ratio (K‐value) is calculated through a combination of three factors

The quantity ν0 is a pure liquid component property and is correlated within the framework of Pitzer's modified form of the principle of corresponding states. The quantity γ is calculated from Hildebrand's equation, with regular liquid solutions assumed. The necessary parameters in this equation are specially determined for the very light components. The vapor state quantity ϕ is calculated from Redlich and Kwong's equation of state. The correlation is in the form of a compact set of equations which are especially suitable for application with an electronic digital computer.

The correlation applies to hydrocarbons of various molecular types, including paraffins, olefins, aromatics, and naphthenes. Hydrogen in hydrocarbon mixtures is likewise correlated. The correlation has been tested with a systematic compilation of literature data on mixtures of these components. The over‐all average deviation from 2,696 data points is 8.7%.
The drag coefficients of single spheres moving in steady and accelerated motion in a turbulent fluid
Authors: Torobin L. B. , Gauvin W. H.
Published: June 2004

Drag coefficients of aerodynamically smooth spheres having a density variation of from 0.252 to 1.91 g./cc. and a diameter variation from 1.56 to 3.21 mm. were obtained for acceleration rates varying from 103.5 ft./sec.2 to ‐30 ft./sec.2 and for relative intensities of up to 45%. The particle‐to‐Eulerian macroscale ratios varied from 0.50 to 0.16, and the diameter‐to‐Eulerian microscale ratios varied from 10 to 2.

The drag coefficients were found to be a function of the particle Reynolds number and of the relative intensity but not of the acceleration and relative macro‐and‐microscale variations.

A transition theory for the system investigated is presented, which predicts that the product of the critical Reynolds number and the square of the relative intensity should be a constant; it is supported by the experimental results obtained.
Holdup and pressure drop with gas‐liquid flow in a vertical pipe
Authors: Hughmark G. A. , Pressburg B. S.
Published: June 2004

Vertical upward concurrent air‐liquid flow was investigated under isothermal conditions in a test section of 1‐in. schedule 40 pipe. Pressure drop was measured with a mercury manometer connected to two pressure taps 20 ft. apart in the section. Liquid was trapped between two quick shutoff valves activated by two solenoid valves. The liquid was druined from the section to provide the holdup data. Six liquids were used to determine the effect of density, viscosity, and surface tension.

The experimental holdup, and two‐phase pressure drop data were not in agreement with Lockhart‐Martinelli type of correlation for horizontal flow. A statistical correlation for holdup was developed to include fluid physical properties, total mass velocity, and the air‐liquid ratio entering the pipe. Similarly a pressure drop correlation was developed which expressed the two‐phase pressure drop as a function of the slip velocity, liquid physical properties, and total mass velocity. This correlation showed an average percentage error of less than 15% between the observed and the calculated total pressure drop.
An experimental study of three component gas diffusion
Authors: Duncan J. B. , Toor H. L.
Published: June 2004

Equimolal countercurrent diffusions runs were made in a two bulb diffusion cell with the system hydrogen, nitrogen, and carbon dioxide. The initial bulb compositions were chosen so that various types of ternary interactions occurred. These interactions were well‐described by the Maxwell‐Stefan equations. The average deviation of the experimental mole fractions for all runs from those predicted by the Maxwell‐Stefan equations was 0.45 mole %.
Kinetics of reduction of iron oxide with carbon monoxide and hydrogen
Authors: Kawasaki Edwin , Sanscrainte Jack , Walsh Thomas J.
Published: June 2004

This investigation was undertaken to determine the rate controlling step in the reduction of iron oxides with hydrogen and carbon monoxide. For the reduction of porous hematite pellets, and bars it was found that the reduction rate is controlled by the counterdiffusion of reactant gas and product gas between the reaction zone and the main gas stream.

The reduction specimens were spheres ranging in size from 1.5‐ to 4.4‐cm. diameter and 5.1‐ by 7.6‐cm. bars either 0.69 or 1.24 cm. thick. They were prepared from electrolytic iron powder, partially oxidized in a rotary kiln. The final oxidation of the specimens to hematite was accomplished by firing them at 1,149°C. in an oxidizing atmosphere. The bulk density was 3.5 g./cc. The specific surface area was 0.08 sq.m./g. and the void faction was 0.31. The oxide specimens were reduced in streams of pure hydrogen or carbon monoxide at temperatures between 700° and 1,200°C. The reduction was followed by measuring the sample weight during the reaction. Reduction rates were studied at system pressures of 1 and 2 at.

The samples reduced step by step, to magnetite, to wüstite, and finally to iron. A shell of reduction, clearly visible in sections of partially reduced specimens, moved concentrically into the core of the samples. Ahead of the receding interface the specimens were known to be pervious to the reactant gases. This led to the conclusion that the gas composition at the interface was in equilibrium with the oxide phases present.

Except for the removal of the last portions of oxygen at the lower reduction temperatures, the course of the reduction followed Fick's first law of diffusion. Values of the diffusion co‐efficients, determined from the experimental data, were in close agreement with values predicted from empirical equations. Varying the total pressure of the system had no effect on the rate of reduction, which is consistent with the equations developed from Fick's law for the diffusion‐controlled reaction under investigation.

It is speculated that the retarding of the reduction reaction at the lower reduction temperatures is due to the entrapment of oxide inside shells of iron, which are impervious to the reducing gas. Reduction of the trapped oxide then proceeds by solid state diffusion in a manner proposed by Edström (6).
The viscosity of pure substances in the dense gaseous and liquid phases
Authors: Jossi John A. , Stiel Leonard I. , Thodos George
Published: June 2004

Viscosities available in the literature for the gaseous and liquid states of eleven substances have been correlated with reduced density by the use of dimensional analysis and the Abas‐zade expression for the residual viscosity to produce a single generalized relationship which is presented both graphically and analytically. The substances are argon, nitrogen, oxygen, carbon dioxide, sulfur dioxide, methane, ethane, propane,i‐butane,n‐butane, andn‐pentane. The properties required for the calculation of viscosity with this relationship are the molecular weight, the critical constants, and the density of the substance at the temperature and pressure considered.

Separate relationships were developed for hydrogen, ammonia, and water which do not follow the consistent behaviour of the other substances. Viscosity values for ethylene calculated with the generalized relationship compared favorably with the corresponding experimental values.
A note on latent heat transport in nucleate boiling
Authors: Bankoff S. G.
Published: June 2004

A simple one‐dimensional transport calculation is made which indicates that latent heat transport, by simultaneous evaporation and condensation at different portions of the bubble surfaces, can account for the major portion of the total heat flux in the neighborhood of the departure from subcooled nucleate boiling (burnout). This differs from the previously held view that the stirring action of the bubbles accounted for most of the heat flow in subcooled nucleate boiling. Other evidence is discussed which favors the latent heat transport theory.
The photochlorination of chloroform in continuous flow systems
Authors: Huff James E. , Walker Charles A.
Published: June 2004

Data on the vapor phase photochlorination of chloroform in flow reactors are interpreted on the basis of reaction mechanisms presented in the literature. In order to estimate the rates of light absorption it is also necessary to interpret the rate data obtained for the uranyl sulfateoxalic acid reaction.

The chlorination results are represented quite well by a mechanism in which the most important termination step is a termolecular reaction between trichloromethyl radicals and chlorine. Deviations from this model are observed as the flow of reactants becomes turbulent and as the light intensity increases. The observed decrease in reaction rate under such conditions is attributed to the increased significance of a second termination step, the unimolecular deactivation of chlorine radicals at the reactor wall.
Thermal cracking of ethane and ethylene in a stock tube
Authors: Miller I. F. , Churchill S. W.
Published: June 2004

The rates of decomposition of ethane and ethylene were measured at temperatures between 1,250° and 2,800°K. and pressures between 0.25 and 2.0 atm. by exposing the gases to high temperature during the interval between the arrival of a compression wave and a reflected rarefaction wave in a shock tube. As contrasted with cracking at lower temperatures the ethane apparently reacted to hydrogen, ethylene, and acetylene and the ethylere to hydrogen and acetylene with negligible side reactions or polymerization. The over‐all decomposition rates at high temperature fall off sharply from those extrapolated from low temperature, indicating a change in mechanism. Additions of air, oxygen, carbon monoxide, and chlorine in amounts up to 17% did not effect the rate constants significantly.
A unified vectorial approach to difference point methods in stagewise operations
Authors: Lemlich Robert , Leonard Ralph A.
Published: June 2004

A fundamental unified approach from vectorial considerations is presented from which the usual rectangular and triangular difference point methods are derived as special cases. The approach is then extended to yield other difference point methods including some of higher order. Results are applicable to blending, distillation, extractio, foam fractionation, and other operations.
Measurement of instantaneous rates of mass transfer to a small sink on a wall
Authors: Reiss L. Philip , Hanratty Thomas J.
Published: June 2004

A technique has been developed for measuring the average rate of transfer and the fluctuations in the rate of transfer at a small source or sink on a wall. The transfer area consists of a small polarized electrode mounted flush with the wall. An electrochemical redox reaction whose rate is limited by mass transfer is employed. The technique can be used to study the flow pattern in the vicinity of the wall. By measuring the mass transfer simultaneously to two wall electrodes at varying distances apart the extent of unsteady flows in the vicinity of the wall can be measured.
Fundamental aspects of rotating disk contactor performance
Authors: Strand C. P. , Olney R. B. , Ackerman G. H.
Published: June 2004

The principles used in analyzing the performance of rotating disk contactor liquid extraction columns are discussed. The behavior of a swarm of drops in the rotating field is found to be adequately represented in most respects by single‐drop dynamics, which leads to tested relations for countercurrent capacity, limiting drop holdup, axial diffusion of the continuous and dispersed phases, and point mass transfer coefficients that are independent of column size effects.