bluuebunny/crossref_metadata_2025 huggingface dataset:
Cocurrent stratified flow of immiscible liquids
Authors: Darby Ron , Akers W. W.
Published: June 2004

Velocity profile data were taken in both phases of a cocurrent stratified flow system of two immiscible liquids in the turbulent regime. The data were correlated by a method which combined Pai's results for Poiseuille and Couette flows between parallel plates, resulting in values of the drag coefficients for the wall and interface for both phases. These and other dependent parameters were correlated with flow conditions over a range of flow rates for both phases. Correlations of all parameters except the interfacial drag coefficient were found to be symmetrical; that is, a given correlation applied equally well to data from either phase. The interfacial drag coefficient, on the other hand, depended primarily upon the flow intensity of the upper phase, in a manner which was further dependent upon which phase was the faster.
The absorption of carbon dioxide in aqueous monoethanolamine in a laminar jet
Authors: Thomas W. J.
Published: June 2004

The mechanism of the absorption of carbon dioxide by an aqueous solution of monethanol‐amine has been studied. Experimental results for the absorption of carbon dioxide into a laminar jet of amine solution have been used to examine the transfer process. Previously this process has been considered as pseudo unimolecular, but this has been disproved. When considered as a second‐order, fast, irreversible reaction by the film, penetration, and corrected penetration theories, the results are most satisfactory. It is possible by the corrected penetration theory to correlate the results such as to predict kL/kLo to within 3% of the experimentally determined value.
The dynamic behavior of a fixed‐bed catalytic reactor
Authors: Leder Frederic , Butt John B.
Published: June 2004

The dynamic behavior of a fixed‐bed catalytic reactor was studied under isothermal conditions by means of frequency response analysis. The investigation was conducted over a range of nonreacting and reacting conditions by using the hydrogen‐oxygen combination over supported platinum as the reaction system. The kinetics of the surface catalysis of this reaction were investigated separately and then were incorporated into the analysis of frequency response data under reaction conditions.

A method was developed whereby nonlinear chemical reaction effects appearing in the frequency response measurements could be separated from hydrodynamic factors for a plug flow reactor. Use is made of the describing function technique, often used to approximate nonlinear servomechanism response, to accomplish this. It is shown by this method that Peclet numbers measured for the reacting system agree with those measured in the absence of reaction.

Based on the semitheoretical value of 2 for the Peclet group at high Reynolds numbers, a value of 0.73 sq. cm./min. was determined for the effective diffusion coefficient of hydrogen at 100°C. within the porous catalyst particles. Analysis of frequency response data in which this diffusion is not accounted for leads to Peclet numbers which are unreasonable in view of previously reported results.
Entrained particle collection in packed beds
Authors: Jackson Stephen , Calvert Seymour
Published: June 2004

Small particle collection in packed beds is described by an inertial impaction theory which fits experimental observations. Rings, saddles, spheres, and spherical packing of 1/2‐, 1‐, and 1 1/2‐in. size were used at air velocities up to 30 ft./sec. for the collection of an oil mist of known size. Particle collection efficiencies up to 50% for 1.0‐micron particles were obtained.
Design variable selection to simplify process calculations
Authors: Lee Wooyoung , Christensen James H. , Rudd Dale F.
Published: June 2004

During the analysis of a large process system, the values of certain design variables must be preassigned to allow the solution of the design equations. A careless selection of these distinguished variables can lead to trouble, magnifying computational problems above what need be. A method is proposed for determining a set of design variables which could minimize the computational labor associated with process analysis. This work is part of a larger project on the computer aided design of process systems.
Upper and lower bounds for solutions to the transport equation
Authors: Finlayson Bruce A. , Scriven L. E.
Published: June 2004

The collocation method and a maximum principle are used to generate pointwise, improvable upper and lower bounds for solutions of the transport equation. This new method of analysis is applicable to the unsteady state transport equation with a specified velocity field as well as to other problems which have a maximum principle. An application to unsteady state transfer to a fluid in ideal stagnation flow illustrates the method.
Physical and chemical absorption in two‐phase annular and dispersed horizontal flow
Authors: Wales Charles E.
Published: June 2004

Overall mass transfer coefficients for physical desorption and chemical absorption of carbon dioxide in annular and dispersed two‐phase flow in a 1‐in. horizontal pipe have been measured. These coefficients have been correlated with gas and liquid flow rates and with the normality of the sodium hydroxide solutions used.

A new method of analysis was used to separate overall coefficients into individual gas and liquid film coefficients. Penetration theory equations were used to calculate the effective inter‐facial surface area and the penetrotion contact time. Changes in these variables have been explained in terms of the changes in flow pattern.
On the ordering of recycle calculations
Authors: Lee Wooyoung , Rudd Dale F.
Published: June 2004

Algorithms are developed for organizing large recycle calculations. In particular, we discuss the problem of determining the minimum number of recycle parameters that must be assumed to render recycle calculations acyclic. This work has significance in the evolution of computer programs for the automatic design of process systems.
Heat transfer and frost formation inside a liquid nitrogen‐cooled tube
Authors: Reid R. C. , Brian P. L. T. , Weber M. E.
Published: June 2004

An experimental study was undertaken of simultaneous heat transfer and frost deposition inside a liquid nitrogen‐cooled tube for a range of humidities and Reynolds numbers. The data indicate that diffusion of water vapor within the frost layer caused the frost density and thermal conductivity to increase with time. The increase was so great that the heat transfer rate became constant even while frost continued to accumulate. In a separate study the thermal conductivities of frosts formed on a cryogenic surface were measured and found to be lower than values near the freezing point of water.
Laminar flow heat transfer
Authors: Christiansen E. B. , Jensen Gordon E. , Tao Fan‐Sheng
Published: June 2004

Numerical solutions of the equations of motion and energy for the heating of non‐Newtonian fluids in rectilinear, axisymmetric laminar flow in tubes of circular cross section are extended to the case of cooling at constant tube‐wall temperature. The fluid density, heat capacity, and thermal conductivity are assumed constant, but the flow properties are represented by the temperature‐dependent equation τ =m(Ṡ exp ΔH‡/RT)n. The results are presented as plots of averageNNuvs.NGz, with flow and temperature‐effect indices as parameters. The mean deviation of experimental data for the cooling of aqueous CMC and carbopol dispersions from the numerical solutions is ±8%.
Vapor‐liquid equilibria of light hydrocarbons at low temperatures and high pressures: The methane‐n‐heptane system
Authors: Chang Harry L. , Hurt Lewis J. , Kobayashi Riki
Published: June 2004

Recent experimental observations of the phase behavior of methane–n‐paraffin hydrocarbon binary systems are used to make a phase rule analysis of such systems. The vapor‐liquid equilibria of light hydrocarbon systems are complicated by liquid‐liquid immiscibility and solids formation at low temperatures.

The system studied here has limited liquid phase miscibility with a quadruple point involving a gas phase, two liquid phases, and a solid phase.

Experimental techniques were developed to sample and analyze gas phases containing concentrations of n‐heptane in the range of 0.00001 mole fraction with good precision. Binary K values for methane and n‐heptane are reported at intervals of 20°F. from 0° to −100°F. for pressures up to the criticals for the mixtures. The results are reported numerically and illustrated graphically. Additional phase observations were made below the critical temperature of methane to confirm and extend the phase behavior of the methane–n‐heptane system as reported by Kohn.
Freezing process based on the inversion of melting points due to applied pressure
Authors: Cheng Chen‐Yen , Cheng Sing‐Wang
Published: June 2004

A new freezing process for the desalination of seawater is being developed which utilizes a unique way of upgrading heat energy where there is no gas phase involved. This method takes advantage of the abnormal melting point curve of water. Water melts at a lower temperature under a higher applied pressure (that is, (dp/dT) melting < 0), while an ordinary substance melts at a higher temperature under a higher applied pressure (that is, (dP/dT) melting > 0). Due to this differnce a substance which melts at a temperature lower than the freezing point of an aqueous solution may melt at a temperature higher than the melting point of water at a sufficiently high pressure.

Thus, a suitably selected working medium can be used to form a cyclic auxiliary system which can be incorporated with the main system to: remove the heat of crystallization of water in the partial freezing of an aqueous solution by melting the working medium at a low pressure, and to supply the heat for melting the ice by solidifying the working medium at a sufficiently high pressure.
Vapor‐liquid equilibrium for the system hydrogen—benzene—cyclohexane—n‐hexane
Authors: Brainard Alan J. , Williams Brymer
Published: June 2004

This paper presents vapor‐liquid equilibrium data for the system hydrogen—benzene—cyclohexane—n‐hexane over the pressure range of 500 to 2,000 lb./sq.in.abs. and the temperature range of 200° to 300°F. Experimental equipment was constructed that was capable of operating at pressures of 3,000 lb./sq.in.abs. and at temperatures of 400°F. A static equilibrium cell, which had a sample port for both the liquid and vapor phases, was employed. Separation of the hydrogen from the hydrocarbons by means of a liquid nitrogen cold trap was utilized before performing the hydrocarbon analyses on a mass spectrometer. Three hydrocarbon mixtures were charged to the equilibrium cell, and for each charge, isotherms of 200°, 250°, and 300°F. were run for equilibrium pressures of 500, 1,000, 1,500 and 2,000 lb./sq.in.abs. These thirty‐six quaternary equilibrium runs resulted in a total of one hundred and forty‐four equilibrium data points. In addition, four binary equilibrium runs were determined both for the hydrogen‐benzene and hydrogen‐cyclohexane systems. A modified version of the Chao‐Seader correlation was used to predict the data. This correlation was able to predict all the quaternary equilibrium ratios with an average deviation of 4.86%.
The gas and liquid solubility relations in hydrocarbon‐water systems
Authors: Rebert Charles J. , Hayworth Kenneth E.
Published: June 2004

The typical solubility boundaries of binary simple hydrocarbon‐water systems are outlined for temperatures and pressures ranging into the neighborhood of the critical point for pure water. These systems are characterized by two unique states, a critical vaporization end point and a critical solution end point. The former defines the limit of mutual solubility of two liquid phases, and the latter defines a point of complete solubility at a minimum pressure. Experimental P‐T‐x data for cyclohexane‐water and n‐hexane–water mixtures are presented.
Transient response and feed‐forward control of a distillation tower subject to a sequence of upsets
Authors: Distefano G. P. , May F. P. , Huckaba C. E.
Published: June 2004

A mathematical model of dynamic distillation was verified experimentally for transients resulting from a sequence of upsets in operating conditions, that is, for upsets occurring in the unsteady state before the effects of previous upsets died out.

The equations for feed‐forward control of the top product composition by reflux ratio control action were derived and a computer program was written in FORTRAN for solution on a digital computer. This control model was employed in the feed‐forward control of an experimental distillation column when subjected to an upset in feed composition.

Experimental data were obtained from a twelve‐plate, 10‐in. diameter distillation column with a methanol‐tertiary butyl alcohol system. The numerical technique employed is a completely general divided difference method which can be utilized in the solution of any system of first‐order differential equations.
Heat and mass transfer between an evaporative interface in a porous medium and an external gas stream
Authors: Morgan Robert P. , Yerazunis Stephen
Published: June 2004

Steady state heat and mass transfer between a submerged evaporative interface in a porous medium and an external gas stream were analyzed theoretically. Local and average evaporation rates for laminar and turbulent flow over a flat plate as well as for fully developed laminar or turbulent flow near the thermal entry region of a duct were obtained as a function of the position of the evaporative interface. Calculated local evaporation rates are significantly lower than values computed by Luikov, who did not take into account the variation of evaporative surface temperature with recession, indicated both by the present analysis and by observations related to the drying of thick porous materials. Application to the analysis of the drying process is discussed.
Kinetics of the nonisothermal pyrolysis of propane
Authors: Kershenbaum Lester S. , Martin Joseph J.
Published: June 2004

A method was devised to yield chemical reaction kinetic parameters from nonisothermal, nonisobaric flow experiments. The system studied was the pyrolysis of propane at high temperatures (800° to 1,000°C.). At these temperatures the rates of the various reactions are so high that a batch or even an isothermal flow experiment is impossible. To keep the conversions low so that the initial stages of decomposition could be studied, the feed gas was diluted with varying amounts of nitrogen. Residence times in the reactor were in the millisecond range. The reactor exit gas was analyzed by mass spectrometry. The method developed in this work is not limited to simple kinetic studies, but can be useful in complicated series and parallel reactions which often require nonisothermal conditions.
A generalized differentiation method for interpreting rheological data of time‐independent fluids
Authors: Lescarboura J. A. , Eichstadt F. J. , Swift G. W.
Published: June 2004

A generalized differentiation method for analyzing rheological data of time‐independent fluids is presented. The method is demonstrated to be valid and useful in analyzing rheological data and comparing such data obtained on the same time‐independent fluid in rheometers of the capillary, annular, coaxial cylinder rotational, and falling cylinder types.
Gas absorption in packed columns: Liquid phase resistance in the loading region
Authors: Vivian J. E. , Brian P. L. T. , Krukonis V. J.
Published: June 2004

Data on liquid phase‐controlled gas absorption in the loading regime are presented. Carbon dioxide was desorbed from water by using a 6‐in. Diameter tower and 1/2‐ and 3/4‐in. Ceramic rings. Below the loading point, HL increases approximately as the 0.25 power of the liquid rate and is independent of gas rate. In the loading regime, however, it was found that at high gas rates HL increases less rapidly and may even decrease with increase in liquid rate. At intermediate gas rates, the effect of liquid rate on HL is intermediate. These effects are explained on the basis of the interaction of the gas and liquid flow rates and the effect of this interaction on KL and a. The results suggest that in some cases tower capacity may be increased without increasing HL.
Gas compressibility factors at high temperature and high pressure by the Burnett method: Methyl chloride
Authors: Suh K. W. , Storvick T. S.
Published: June 2004

An instrument based on the Burnett method for determining gas compressibility at high temperature and high pressure was constructed. An estimate of the accumulated measurement errors indicate the data should be accurate to eight parts in 10,000. The instrument was calibrated up to 1,000 lb./sq.in. with helium at 200° and 300°C. The average absolute difference between the experimental and the smoothed helium compressibility factor data was 4 and 6 parts/100,000 for the 200° and 300°C. isotherms, respectively. Compressibility factor data for methyl chloride from 200° to 350°C. at 25°C. intervals and at pressures to 5,000 lb./sq.in. are reported. Second virial coefficients for helium and methyl chloride were also obtained.
Kinetics of xylene isomerization over silica‐alumina catalyst
Authors: Hanson K. L. , Engel A. J.
Published: June 2004

Eleven mixtures of the three isomers of xylene and ethylbenzene were isomerized over a silica‐alumina catalyst in a differential tubular reactor at temperatures from 700° to 900°F. and pressures from 0 to 100 lb./sq. in. gauge. Analysis showed that meta‐xylene isomerizes reversibly to ortho‐ and para‐xylene, but the direct interconversion of ortho‐xylene to meta‐xylene does not occur. Further, it appears that the isomerization reactions are first order and, by the Hougen‐Watson technique, follow a single‐site reaction model.
Behavior of suspended matter in rapidly accelerating viscoelastic fluids: The Uebler effect
Authors: Metzner A. B.
Published: June 2004

The observation that large bubbles entrained in accelerating viscoelastic fluids may suddenly stop and remain stationary for long periods of time, although imbedded in a region of high fluid velocities, is noted and described. An analysis of this phenomenon, termed the Uebler effect, shows that it may be expected to occur with all particulate matter provided that the continuum field fluid is accelerating sufficiently rapidly to generate high stresses as a result of fluid stretching, and provided these stresses change sufficiently rapidly in the direction of the velocity vector in the flow field.
A method for the noninteracting control of a class of linear multivariable systems
Authors: Foster Robert D. , Stevens William F.
Published: June 2004

A method is presented by which a particular class of interacting linear multivariable systems may be decoupled into independent, first‐order subsystems containing a single output as a function of a single manipulatable input and a single measurable input. This is accomplished by application of compensators in the form of feedforward amplifiers and proportional plus derivative feedback controllers. Simultaneous application of a stabilizing feedback controller and a feedforward amplifier to each decoupled subsystem results in perfect control of system outputs yi (t), that is, yi (t) = 0 for all t ≧ 0. In addition, the compensating device contains degrees of freedom that make it possible to set output forms within any limits desired in the case that subsystem feedforward controllers operate imperfectly, and obtain better fit between the linear system model, which forms the basis for controller design, and the corresponding nonlinear system model.
A fourth parameter for the vapor pressure and entropy of vaporization of polar fluids
Authors: Halm Roland L. , Stiel Leonard I.
Published: June 2004

Pitzer's acentric factor approach has been extended to the vapor pressure and entropy of vaporization of polar fluids. Normal fluid vapor pressure functions have been determined for 0.44 ≤TR< 0.56. A polarity factor has been defined and polar correction terms established for the vapor pressure for 0.44 ≤TR< 0.70 and for the entropy of vaporization for 0.56 <TR< 0.72. The polar correction terms enable the accurate calculation of the vapor pressure and entropy of vaporization of a polar fluid from its normal boiling point and normal latent heat of vaporization. The results of this study also form the basis for the extension of this approach to other thermodynamic properties of polar fluids.
Frequency response of gas mixing in a fluidized‐bed reactor
Authors: Barnstone Leonard A. , Harriott Peter
Published: June 2004

Frequency response methods were used to compare dynamic models for gas mixing and first‐order reaction in a fluidized‐bed reactor and for the experimental determination of interphase transfer characteristics. Theoretical predictions of frequency response characteristics were derived for two models based on the two‐phase theory of fluidization. Experimental frequency response for a 1‐ft. high bed were correlated better by a model based on perfect mixing in the dense phase than by a model based on plug flow in the dense phase. Excellent correlation was also obtained by a simple empirical model.
Hot‐film anemometry measurements of turbulence in pipe flow: Organic solvents
Authors: Patterson Gary K. , Zakin Jacques L.
Published: June 2004

Longitudinal turbulence intensities, autocorrelations, and energy spectra have been measured in the flow of toluene, benzene, and cyclohexane in smooth, round 1‐ and 2‐in. I.D. tubes. These measurements were made with a constant‐temperature hot‐film anemometer and covered radial positions from the center to r/a = 0.85 in the 2‐in. tube and to r/a = 0.75 in the 1‐in. tube.

The turbulence intensity data were found to be similar to those obtained for air in a 10‐in. pipe by Laufer. A slight diameter effect was observed, the intensities in the 1‐in. tube being slightly lower than those in the 2‐in. tube at equal Reynolds numbers.

The energy spectra were similar to the spectrum reported by Lee and Brodkey for water. The spectra reached higher frequencies at the lowest measurable energy levels for higher velocities. There was little effect of tube diameter or radial position on the spectra from the center to r/a = 0.85. A short inertial subrange with a log‐log slope of −5/3 seemed evident in high velocity spectra, and the log‐log slope of −7 was approached at high frequencies by the lowest velocity spectrum.

The peak energy dissipation frequencies for all the energy spectra measured were approximately proportional to bulk mean velocity to the 1.4 power with little effect of tube diameter or radial position from the center to r/a = 0.85.

Integral scales of the turbulence were proportional to bulk mean velocity to a power less than one for a given tube. These measurements indicated that the ratio of integral scale to pipe diameter is not a function of Reynolds number only.

Microscale values were relatively independent of velocity and pipe diameter.
Dynamics of a tubular reactor with recycle: Part II. Nature of the transient state
Authors: Reilly M. J. , Schmitz R. A.
Published: June 2004

A theoretical study of the transient state of a plug‐flow tubular reactor with recycle is presenred for a model in which axial dispersion of heat and mass is negligible. A qualitative description of the temporal behavior near the steady state is obtained from an analysis of the linearized transient equations, and some large‐scale transient characteristics are studied by means of numerical solution of the nonlinear transient equations. A cursory study of the application of the Liapunov's direct method to predict regions of asymptotic stability is also presented. Numerical examples illustrate sustained oscillatory behavior as well as the transient nature of systems with multiple steady states.
Transition and film boiling from horizontal strips
Authors: Kesselring R. C. , Rosche P. H. , Bankoff S. G.
Published: June 2004

Measurements of heat flux and surface temperature fluctuations are reported for transition and film boiling of Freon 113 from flattened horizontal stainless steel tubes. The strip width is found to have a definite effect upon the heat flux in the film boiling regime. Photographic measurements indicate the absence of any appreciable long‐range periodicities, from which it is inferred that random turbulent effects are quite important. Also, a spectrum of bubble diameter, frequencies, and spacings is observed. On the other hand, some short‐time spatial periodicities were observed, and the theoretical values of the parameters fell well within the experimental range. Based upon the photographic and heat transfer measurements, a recommended expression for the minimum heat flux was developed.
Forced convection mass transfer: Part IV. Increased mass transfer in an aqueous medium caused by detached cylindrical turbulence promoters in a rectangular channel
Authors: Watson J. S. , Thomas David G.
Published: June 2004

Enhanced rates of mass transfer in aqueous systems were studied with an electrochemical technique. Detached turbulence promoters (cylinders supported away from the surface) were shown to cause increases in mass transfer in aqueous systems in a manner similar to that observed in gaseous system. As in air studies, peaks in the local rate of mass transfer were observed directly beneath the cylinders and a wake effect was observed downstream from the cylinders.
A method of finding simultaneously the values of the heat transfer coefficient, the dispersion coefficient, and the thermal conductivity of the packing in a packed bed of spheres: Part I. Mathematical analysis
Authors: Turner G. A.
Published: June 2004

The response of a packed bed to a sine wave of temperature in a stream of fluid through it will depend upon the amount of dispersion in the resistance to transfer between fluid and solid, and the thermal properties of the soild. A method is presented that allows the effects of these three phenomena on the amplitude and phase angle to be unravelled and hence all their magnitudes to be computed simultaneously. It thus presents a way of determining these three quantities in situations where they were previously obtainable either with great uncertainty or not at all. The method requires measurements of the relative amplitudes and phase angles at three frequencies, and (preferably) at ω → 0 as well, all to be carried out with high accuracy.
Limiting relation for the eddy diffusivity close to a wall
Authors: Son Jaime S. , Hanratty Thomas J.
Published: June 2004

Experiments on mass transfer for fully developed flow in a pipe show that the eddy diffusivity for mass close to the wall is described by the functionality

The best interpretation of presently available data in a pipe and in an annulus is given by the following, more explicit relation

The evidence for this latter relation is not as conclusive as one would like. Accurate measurements of concentration profiles close to a wall are needed.
A new apparatus for liquid phase thermal diffusion
Authors: Halle Edward Von , Jury S. H.
Published: June 2004

A horizontal thermal diffusion column is described in which the inefficiencies caused by the forgotten effect and parasitic remixing are avoided. Experimental results obtained on the separation of water‐ethyl alcohol mixtures are presented along with a phenomenological theory for the performance of the column.
The phase and volumetric relations in the helium—n‐butane system: Part I. Phase and volumetric behavior of mixtures of low helium concentration
Authors: Jones Allan E. , Kay Webster B.
Published: June 2004

The P‐V‐T‐x phase relations of helium—n‐butane system were measured in the region of low helium content (up to 10.4 mole % helium). The system exhibits the gas‐gas equilibrium originally predicted by Kamerlingh‐Onnes and Keesom. The term gas‐gas equilibrium is applied because the critical temperatures of the mixtures are higher than the critical temperature of either component. This behavior is quite unlike that observed in most binary systems, in which the critical temperature of the mixtures lie between those of the pure compounds. As a consequence of the shape of the critical locus curve, the system exhibits isothermal retrograde condensation of the second kind.
On a conjecture of Aris: Proof and remarks
Authors: Luss Dan , Amundson Neal R.
Published: June 2004

In this paper a conjecture of Aris is proved to be correct, that of all catalyst particles of fixed volume for isothermal first‐order chemical reactions the spherical particle has the lowest effectiveness factor. The method of proof uses a process of symmetrization. Some conjectures are also made about other chemical reactions. The method of proof is also valid for two‐dimensional domain (infinite cylinder).
Diffusion and chemical reaction in isobutylene hydration within cation exchange resin
Authors: Gupta Vijai P. , Douglas W. J. M.
Published: June 2004

The chemical reaction and diffusion rate parameters were determined for the hydration of liquid isobutylene to t‐butanol with a cation exchange resin catalyst. High reaction rates were found to result from a high diffusivity of isobutylene within the resin catalyst. Both the high value for diffusivity and its negative temperature coefficient are consistent with the transport mechanism within the resin, being that of surface diffusion of isobutylene in an adsorbed state.
Some new results on momentum and heat transfer in compressible turbulent free jets
Authors: Tomich John F. , Weger Eric
Published: June 2004

The results of an analytical and experimental study of compressible, axially symmetric, turbulent free jets exhausting into quiescent air are presented. A finite‐difference technique was used to obtain a general solution which has eliminated the need for the simplifying assumptions required in previous investigations. The jet Mach number and jet temperature ratio have been found to be the only two initial jet properties which are necessary to characterize the dimensionless velocity and temperature variations in this type of jet. Modifications of dynamic eddy transfer coefficients given in the literature are used in the solution An experimental program was carried out to obtain data on free jet velocity and temperature variation at high initial jet temperatures and high subsonic Mach numbers where there has been a lack of experimental data. The numerical solutions of the time‐averaged conservation equations have been shown to agree well with the experimental data of the present study and of previous investigations.
Part V. Quasilinearization and state‐constrained systems
Authors: Rothenberger B. F.
Published: June 2004

The quasilinearization algorithm is examined as a means of determining the optimal control of a nonlinear tubular reactor system with state constraints. It is shown that the use of penalty functions in an unconstrained algorithm can effectively solve the constrained problem. The method is quadratically convergent to the optimal control and seems more successful than methods which require gradients in the computation.
An experimental investigation of the flow of aqueous non‐Newtonian high polymer solutions past a sphere
Authors: Turian Raffi M.
Published: June 2004

The terminal velocities of spheres falling in aqueous solutions of hydroxyethyl cellulose and polyethylene oxide were determined with ruby and steel spheres. For each sphere the terminal velocity was obtained in seven cylinder sizes covering a range of sphere‐to‐cylinder diameter ratio from 0.0067 to 0.18. The data were used in an extrapolation to correct for the cylindrical wall effect. Several alternative extrapolation procedures for estimating the zero shear viscosity were attempted and the results were compared. An empirical correlation for the drag coefficient was developed in terms of the Ellis parameters of the fluids, and the Faxén wall correction for Newtonian flow. the correlation gives the drag coefficient within 4% for all cases in which the quantity ηvt/Dτ1/2 is less than 0.3.
Flow of viscoelastic fluids through porous media
Authors: Slattery John C.
Published: June 2004

Local volume averaging of the equations of continuity and of motion over a porous medium is discussed. For steady state flow such that inertial effects can be neglected, a resistance transformation is introduced which in part transforms the local average velocity vector into the local force per unit volume which the fluid exerts on the pore walls. It is suggested that for a randomly deposited, although perhaps layered, porous structure this resistance transformation is invertible, symmetric, and positive‐definite. Finally, for an isotropic porous structure (the proper values of the resistance transformation are all equal and are termed the resistance coefficient) and an incompressible fluid, the functional dependence of the resistance coefficient is discussed with the Buckingham‐Pi theorem used for an Ellis model fluid, a power model fluid, a Newtonian fluid, and a Noll simple fluid. Based on the discussion of the Noll simple fluid, a suggestion is made for the correlation and extrapolation of experimental data for a single viscoelastic fluid in a set of geometrically similar porous structures.
The calculation of heat transfer coefficient for combustion driven transverse oscillations in a gas‐air burner
Authors: Dent J. C.
Published: June 2004

In this paper a method is presented for the computation of the heat transfer coefficient in a gas‐air burner in the presence of combustion‐driven transverse mode oscillations. By considering the oscillations in pressure within the chamber to be small compared with the mean chamber pressure, and to be known, methods of acoustics may be used to determine the average energy density of the acoustic waves at the wall. Consideration of this acoustic energy to create greater mixing in the boundary layer enables the heat transfer problem to be considered by the Dankwerts‐Mickley model for turbulent heat exchange. With suitable definition of a friction velocity in terms of the friction velocity v* for fully developed turbulent pipe flow and the root mean square particle velocity of the acoustic wave (ar.m.s.ω), it is found that agreement exists between the computed ratio of heat transfer coefficients, with and without combustion‐driven oscillations and the experiments of Zartman, which appear to be the only experimental data for transverse oscillations in a gas‐air burner.
Prediction of pressure drop for two‐phase, two‐component concurrent flow in packed beds
Authors: Turpin Jim L. , Huntington R. L.
Published: June 2004

Two‐phase, gas‐liquid concurrent flow in packed beds was investigated with the use of an air‐water system and 2‐, 4‐, and 6‐in. diameter columns packed with tabular alumina particles of 0.025 and 0.027 ft. diameters. Total pressure drop, column operating pressure, and liquid saturation were measured as functions of gas flow rate, fluid temperatures, and flow direction at several constant liquid flow rates for each column.

Correlation of the frictional pressure loss was achieved in terms of a defined two‐phase friction factor and a second correlating parameter which is a function of the liquid and gas Reynolds numbers. A viscosity correction factor was required to extend the friction factor correlation to include liquid viscosities widely divergent from that of water.

The liquid saturation data for both upward and downward flow were correlated in terms of the ratio of mass flow rates of the respective phases.
A conjugate inequality for general means with applications to extremum problems
Authors: Eben Carl D. , Ferron John R.
Published: June 2004

Inequalities are derived for a general class of convex‐functional means which may contain negative weights. Specific cases include the arithmetic‐mean–geometric‐mean inequality and other power‐mean inequalities. These inequalities make possible the solution of a wider class of extremum problems than are susceptible to the classical means with positive weights. In particular, it is shown that the geometric programming algorithm may in some cases be extended to functions with negative coefficients. A weaker result is derived for application without restrictions on the signs of the coefficients or variables. This leads to a computational scheme which is useful in the solution of certain classes of nonlinear programming and inequality‐constrained multistage optimization problems.
An analytic solution for the dynamics of a packed adiabatic chemical reactor
Authors: Crider J. E. , Foss A. S.
Published: June 2004

Locally linearized equations for dynamic disturbances from a steady state have been solved analytically for an adiabatic chemical reactor with chemically inert packing and a homogeneous chemical reaction. The solutions, in the form of transfer functions, include the effects of heat capacity of the packing and heat transfer between the packing and the fluid, as well as the coupling effects of chemical reaction and the associated heat generation.

Several limiting cases of the transfer functions are discussed and the transfer functions are simplified by an approximation of the temperature dependence of the reaction rate. Frequency responses and step responses of the reactor are calculated from the transfer functions.
The correlation of vapor‐liquid equilibria of light hydrocarbons in paraffinic and in aromatic solvents at low temperatures and elevated pressures
Authors: Van Horn Lloyd D. , Kobayashi Riki
Published: June 2004

A correlational procedure was developed to predict the vapor liquid equilibrium behavior of light hydrocarbons in heavier hydrocarbon solvents at low temperatures and elevated pressures. The method is applicable to paraffinic as well as aromatic solvents.

The method employed the Benedict‐Webb‐Rubin equation of state to predict the vapor phase fugacities. Methane liquid fugacities in the various hydrocarbon solvents were based upon Henry's law which included terms to account for compositional and pressure effects. The liquid fugacities for ethane and propane were calculated using infinite dilution data to modify empirically the Scatchard‐Hildebrand equation. Excellent agreement between the correlated and low‐temperature data available on this class of systems was obtained.
Laminar dispersion in capillaries: Part V. Experiments on combined natural and forced convection in vertical tubes
Authors: Reejhsinghani N. S. , Barduhn Allen J. , Gill William N.
Published: June 2004

An approximate theory for transient dispersion with combined free and forced convection in vertical tubes is developed and tested experimentally. It is found that the dispersion coefficient in such systems depends on a parameter α, which is defined by Equation (38). The analytical expression developed for the dispersion coefficient, Equation (33), is found to be a reasonably good approximation in the range −50 < α < 300.

Experimental results are reported for a rather wide range of parameters for tubes with both 1 1/2 and 5 mm. diameters.

It is found that the extent of dispersion is enhanced significantly when lighter fluid is on the bottom and displaces a heavier one. On the other hand, the dispersion coefficient is inhibited when the situation is reversed. It is found that these effects are not symmetrical with respect to the absolute magnitude of the parameter α as is illustrated in Figure 12.
Turbulent flow in concentric annuli
Authors: Clump Curtis W. , Kwasnoski Daniel
Published: June 2004

An eddy diffusivity model was developed and used to predict velocity distributions for turbulent flow of air in annuli. Comparison of distributions calculated by the model with experimental data shows that good agreement between calculated and measured values can be attained for core‐to‐shell ratios from 0.001 to 0.990. The significant advantage of using a diffusivity model to predict velocity distributions lies in the inherent ability to consider systems with nonlinear stress distributions.
A study of the effect of sample size on the analysis of power mixtures
Authors: de Chazal L. E. Marc , Hung Yen‐Chi
Published: June 2004

One of the greatest difficulties in the analysis of mixing operations for powders is that of specifying the degree of mixedness in a quantitative manner. This problem is studied for on idealized model. A precise index of the degree of mixing is found for this model, which holds promise of being useful for real mixtures. It is shown that samples of a single size provide all the necessary information. The effect of sample size is defined quantitatively, and a minimum sample size is recommended.
Mass transfer between immiscible liquid metals
Authors: Pasternak Alan D. , Olander Donald R.
Published: June 2004

The extraction of lanthanum and barium from single falling drops of the uranium‐chromium eutectic into magnesium was studied at 1,000°C. Because of the short contact times involved, the data best fit the stagnant diffusion model for lanthanum. For barium, the fraction extracted was governed by external resistance of the magnesium phase. Drop velocities were adequately represented by the Hu‐Kintner correlation.
Stability of reaction on a spherical particle
Authors: Winegardner D. K. , Schmitz R. A.
Published: June 2004

This paper presents a theoretical study of the stability of chemical reaction on the external surface of a single spherical particle in stagnant surroundings. The analysis, which invokes methods of linear stability theory, yields necessary and sufficient conditions for stability of a steady state solution to small disturbances for the cases of very small and very large solid thermal conductivity. It is shown that heat losses from the solid surface may lead to transient behavior which is characteristically different from that for adiabatic surfaces, and that the unsteady state is strongly affected by the thermal capacity of the solid material. A numerical example is employed to illustrate the possible significance of unstable situations.
Comparison of kinetic and diffusional models for solid‐gas reactions
Authors: Ishida M. , Wen C. Y.
Published: June 2004

A comparison of the kinetic and diffusional models for solid‐gas reactions occurring in a spherical particle is presented. The similarities and differences of the unreacted‐core shrinking model and the homogeneous model are examined in light of the rate‐controlling factors. In view of the similarity of the two models, it is shown that erroneous conclusions in regard to the mechanism and the activation energies may be drawn from an analysis of the experimental data. A more versatile model is presented in order to augment the two models so that wider varieties of solid‐gas reaction systems may be treated. The concept of effectiveness factors in solid‐gas reactions is introduced, and the influence of diffusion is ascertained.
Effect of orientation on the settling characteristics of cylindrical particles
Authors: Blumberg Paul N. , Mohr C. Michael
Published: June 2004

The characteristics of cylindrical particles settling in the Stokes regime in a bounded fluid are discussed. Applicable theory is reviewed and experimental data showing the effect of orientation on the terminal velocity are presented.
Solids mixing in fluidized beds
Authors: Woollard I. N. M. , Potter O. E.
Published: June 2004

The movement of solids associated with the rise of a single gas bubble in an incipiently fluidized bed has been determined. The bulk volume, measured at the porosity of incipient fluidization, of tracer solid which is transported across the original interface between undyed glass spheres in the upper region and dyed glass spheres (tracer solid) in the lower region, is approximately 30% of the bubble volume. The measurements relate to bubble volumes from 14 to 200 ml. in a glass column, 4 in. diam. Solids used were glass spheres of diameter 380 μ. The profile created when a bubble rises through a layer of fluidized tracer solids into the fluidized solids above the tracer layer has been approximately determined. The distance by which the solids were displaced upward, due to the passage of the bubble, was found to be greater than would have been the case if the behavior were that of a sphere in an inviscid liquid.
Concentration‐dependent time‐lag measurements
Authors: Phillips J. R. , Dodge B. F.
Published: June 2004

In gas‐metal permeation, diffusion is normally considered to be the rate‐controlling step. In addition, the diffusivity is usually taken to be independent of concentration. Under these conditions, the time lag (a characteristic of the system which depends on the time required to achieve steady state flow) is found to be (and theoretically should be) independent of the gas pressure applied to the inlet surface of the metal membrane. Furthermore, the time lag can then be directly related to the diffusivity of the system.

In this paper, data on the hydrogen type 321 stainless steel system are presented which show a pronounced effect of pressure on measured values of the time lag. Taken alone, these data can be explained either by a concentration‐dependent diffusivity or by resistance to flow at the metal surface. From steady state data it is shown that surface resistance is the better explanation. A model of the permeation process is presented which is consistent with the time lag data, and an estimate is made of the diffusivity of hydrogen in type 321 stainless steel.

The variables studied were hydrogen pressure at the entrance surface of the membrane (0.1 to 30.0 atm.), temperature (300° to 800°C.), and membrane wall thickness (0.0252 to 0.2475 cm.).
Effect of suspension density on crystal size distribution
Authors: Larson M. A. , Timm D. C. , Wolff P. R.
Published: June 2004

The concept of a continuous mixed suspension–mixed product removal crystallizer was used both as an analysis and experimental tool to study the effects of suspension density on crystal size distribution. If the crystals present in suspension are not a source of nuclei, larger crystals will be obtained in the presence of higher suspension densities. If the rate of new particle formation is proportional to the amount of crystals present, the crystal size obtained will not be changed by the suspension density level. There was evidence of nucleation rate dependency on the quantity of suspended crystals in the two systems studied experimentally.
Effect of nucleation kinetics on the dynamic behavior of a continuous crystallizer
Authors: Timm Delmar C. , Larson Maurice A.
Published: June 2004

The nucleation kinetics of three materials were related to the growth kinetics using steady state data obtained at various degrees of supersaturation. The power models obtained from the three crystallizaitons exhibited widely different kinetic orders. These materials were then crystallized under unsteady state conditions in a mixed suspension–mixed product removal crystallizer and the transient size distributions were determined. The unsteady state model previously developed by Randolph and Larson was solved on a digital computer for the three systems. Good agreement was obtained. It was found that unsteady state experiments have some advantages over steady state experiments in determining the kinetic order of nucleation.
A generalized B‐W‐R equation of state
Authors: Edmister W. C. , Vairogs J. , Klekers A. J.
Published: June 2004

The Benedict‐Webb‐Rubin Equation of State has been generalized by expressing the eight constants as functions of critical pressure, critical temperature, and acentric factor. An evaluation of the resulting generalization against the observed P‐V‐T data of thirteen hydrocarbons and carbon dioxide shows 0.3 to 2.0% average deviations of the calculated pressures from the observed, as compared with 0.2 to 1.4% when using the individual (that is, nongeneralized constants for each component). Standard errors of estimate for 1,464 experimental data points were 0.0089 for the proposed generalization vs. 0.0084 for the original B‐W‐R Equation.