bluuebunny/crossref_metadata_2025 huggingface dataset:
Drag coefficients at low Reynolds numbers for flow past immersed bodies
Authors: Jones A. M. , Knudsen J. G.
Published: June 2004

Drag coefficients were determined at low Reynolds numbers for cylinders (0.1 ⩽ Re ⩽ 1.0) and flat plates (0.05 ⩽ Re ⩽ 2.0) moving through a viscous medium. The drag coefficient was calculated from the force required to move the immersed body through the fluid, and preliminary work on spheres was used to calibrate the apparatus. For all bodies studied the drag coefficient was inversely proportional to the Reynolds number. The data were analyzed by a least‐squares method to obtain the relationship between drag coefficient and Reynolds number.

The diameter of the tank containing the viscous fluid had a very definite effect upon the drag coefficient of the various cylinders and flat plates studied. In the range of DT/D (tank diameter/cylinder diameter) studied the relationships recommended by White involving the wall effect and the end correction agree with experimental data for values of L/D (cylinder length/cylinder diameter) greater than 16. At L/D ratios less than this drag coefficients are lower than those predicted by White's equations, and the experimental curves are recommended for these ratios.

For flat plates in perpendicular flow no effect of the W/L (plate width/plate length) was detected in the range studied. The tank diameter however had a considerable effect, and a curve is proposed to predict drag coefficients for flat plates in perpendicular flow in the range of experimental conditions studied.
The mechanics of vertical moving liquid‐liquid fluidized systems: II. Countercurrent flow
Authors: Beyaert Bruce O. , Lapidus Leon , Elgin J. C.
Published: June 2004

In a previous publication it has been shown that for the case of liquid droplets moving through a second quiescent liquid the holdup vs. slip‐velocity ratio could be predicted on the basis of analogous rigid sphere fluidization data. The present paper extends these results to cover the countercurrent flow of both liquid phases. As long as the system is operated below the flooding point, the behavior of the spray column can be predicted from the corresponding solids fluidized data.
Heat transfer in a chemically reacting system (nitrogen tetroxide‐dioxide)
Authors: Irving J. P. , Smith J. M.
Published: June 2004

The effect of chemical reaction on heat transfer was investigated analytically for the dissociating system N2O4 \documentclass{article}\pagestyle{empty}\begin{document}$ \rightleftharpoons$\end{document} 2NO2 in turbulent pipe flow. The Reynolds, Colburn, and Deissler analogies were adapted to reacting systems to determine local values of h′/h, the ratio of the heat transfer coefficient for a reacting system to that for the same system under frozen nonreacting conditions. The coefficient h′ was determined by using effective thermal conductivities and heat capacities composed of a frozen and a reacting contribution. The equations for the effective properties, derived in this paper from heat transfer considerations, are in agreement with those developed from thermodynamics and statistical mechanics.

The effective properties vary significantly with temperature. Hence, the adaptation of Deissler's analogy, which was originally developed to consider the radial variation of physical properties across the pipe radius for an inert system, would be expected to give the most reliable results in this reacting system. In the range of variables studied it is found that the heat transfer coefficient for a reacting system may be as much as eighteen times the coefficient for a similar, frozen system. The results from the approximate Reynolds and Colburn analogies, which are evaluated by the use of mean physical properties, yield maximum values of h′/h of about 9.

The study covers a Reynolds number range of 10,000 to 200,000 and tube wall temperatures of 300° to 370°K.
Mass transfer from single solid spheres by free convection
Authors: Garner F. H. , Hoffman J. M.
Published: June 2004

Rates of mass transfer by free convection have been measured for spheres of three organic acids dissolving in three solvents, water, n‐butanol and benzene. The results fell into two groups, one in which flow is completely laminar and one in which turbulence had set in in the boundary layer. Turbulence appears to set in at N′Ra crit ∼ 6 × 108.
A comparison of propane and carbon dioxide solvent flooding processes
Authors: Holm L. W.
Published: June 2004

A laboratory investigation was conducted on oil displacement from porous media by the use of either a slug of propane followed by gas or a slug of carbon dioxide followed by water. A comparison was made of the efficiencies of these two solvent flooding processes for petroleum reservoirs. The results of flooding experiments on cores and on scaled pattern models showed the effect, on oil recovery, of type of porous medium, pore geometry, length to width ratio of the flood pattern, fluid viscosities, and miscibility. Oil recoveries of from 60 to 80% of the original oil in place were obtained by these solvent flooding processes as compared with conventional waterflood recoveries of between 35 to 50% on the same cores and linear models. Furthermore these recoveries were obtained with solvent slug sizes of 10 to 30% of a hydrocarbon pore volume, with less solvent being required as the length of the flood path increased. Data showing the relations between mobility ratio and volumetric sweep efficiency for the propane‐gas and carbon dioxide water flooding processes for two widely different types of porous medium are included in this paper.

It was concluded that in reservoirs where pressure, oil viscosity and composition, and flooding pattern are favorable, either of these solvent flooding processes would give oil recoveries considerably higher than conventional waterflood or gas drive. It was further concluded that this improved recovery would be realized earlier in the life of a flood with carbon dioxide‐carbonated water than with propane followed by gas.
Deposition of aerosol particles in fibrous filters
Authors: Thomas D. G. , Lapple C. E.
Published: June 2004

The collection efficiency of glass fiber pads was investigated with a super cooled liquid aerosol. A filter‐velocity range of 0.02 to 20 ft./sec. was covered with filter pads having a bulk density ranging from 1 to 10 lb./cu. ft. and a fiber diameter ranging from 1 to 30 μ.

For the aerosol employed the results showed a minimum collection efficiency at a velocity of 2 to 5 ft./sec., dependent on fiber size. At the lower velocities, where diffusion is controlling, collection efficiency increased with decreased velocity; at higher velocities, where inertia is controlling, efficiency increased with increased velocity.

For purposes of generalization the data were correlated in terms of dimensionless parameters which allow for the combined effects of flow‐line interception, inertial interception, and diffusinal deposition. Evaluation of the data in terms of existing theories of deposition indicated nominal agreement with the theory of Langmuir, as modified by Natanson, for diffusional deposition. For inertial deposition the measured collection efficiencies were considerably lower than would be predicted from the theoretical values reported by Langmuir and Blodgett for potential flow around the fibers, presumably because of the viscous‐flow (low Reynolds number) conditions that prevailed in this study.
Turbulent convective heat and mass transfer from accelerating particles
Authors: Pasternak I. S. , Gauvin W. H.
Published: June 2004

The rate of evaporation of acetone from single particles accelerating freely in a downward concurrent turbulent air stream was studied over a range of air velocities from 40 to 70 ft./sec. and at a constant air temperature of 410°F. The particles consisted of celite in the shape of spheres, cubes, disks and cylinders, varying in size from 0.15 to 0.40 in. Accurate particle velocity data were obtained with a new radioactive tracer technique, and high‐speed photography at two positions along the column permitted measurement of the rate of rotation and showed that the particles rotated in a random manner.

Adequate prediction of the observed heat and mass transfer data could be obtained from the integration of a rate eequation previously reported for stationary particles. The concept of a new characteristic dimension, developed for the latter case, was found to be applicable to randomly rotating shapes and to account satisfactorily for the behaviour of nonspherical particles.
Entrainment from a submerged combustion evaporator
Authors: Rey George
Published: June 2004

Entrainment from a submerged combustion evaporator system was studied with sodium ion as a tracer. By measuring the ratio of the sodium concentration in the pot to that in the condensate the entrainment removal performance of the evaporator system was studied under various conditions. It was observed that the log of the concentration ratio decreases with an increase in the temperature of the gaseous products of combustion as they emanate from the combustion chamber into the solution. This is attributed to the fact that a greater amount of fine (< 5 μ) droplets of entrainment are formed in the evaporator as the temperature of the gases increases.
Application of the corresponding states principle to mixtures of low molecular weight gases at low temperatures and high pressures
Authors: Leland Thomas W. , Kobayashi Riki , Mueller William H.
Published: June 2004

This paper presents an extension of the corresponding states principle to mixtures of low molecular weight, nonpolar gases at low temperatures. It corrects the corresponding states principle for quantum mechanical effects but neglects any deviation from Maxwell‐Boltzmann statistics. A comparison is made between compressibility factors obtained from reduced second‐virial coefficients and those obtained from pseudo‐critical values. The use of reduced virial coefficients is limited by the fact that there are not enough experimental data to permit extensive correlations of third‐virial coefficients. The pseudo‐critical expressions derived for higher temperatures are accurate at cryogenic temperatures provided the reference substance chosen has a molecular weight close to that of the mixture as well as a similar molecular shape.
Mechanics of semifluidization of single size particles in solid‐liquid systems
Authors: Fan Liang‐Tseng , Wen Chin‐Yung
Published: June 2004

Mechanical and dynamical characteristics of semifluidized beds of single‐size particles in solid‐liquid system were investigated. A semifluidized bed is a type of fluidized bed in which the bed expansion is partially restricted. The emphasis was placed on the study of packed bed formation and pressure drop increase when the semifluidized beds were formed by the compression of fluidized beds. The data showed good agreement with the theoretical and semiempirical equations based on a simple model of fluidized beds.

The results of this investigation would also contribute to the understanding of fluidized beds.
The transport properties of carbon dioxide
Authors: Kennedy John T. , Thodos George
Published: June 2004

Experimental viscosity, thermal conductivity, and self‐diffusivity data available in the literature for carbon dioxide have been critically reviewed and used to develop reduced state correlations of the transport properties for this substance. These correlations should apply to nonpolar compounds having critical compressibility factors approximately equal to that of carbon dioxide,zc= 0.275.

In order to establish the dependence of these transport properties in the high pressure and liquid state regions, use has been made of relationships between the residual properties, μ‐μ*, k‐k*, and (P𝒟)*‐(P𝒟) and density. These residual quantities represent the differences between the values of the properties at any pressure and temperature and those at atmospheric pressure and the same temperature. These relationships also allow the determination of the values of the transport properties at the critical point. The resulting critical values along with the residual relationships enabled the construction of reduced state correlations for viscosity, thermal conductivity, and the product of self‐diffusivity and pressure for carbon dioxide.

These correlations extend from the saturated vapor and liquid states to reduced temperatures ofTR= 10 and reduced pressures ofPR= 50. Comparisons made between values resulting from these correlations and corresponding experimental values, including the region of high pressure for both the gaseous and liquid states and the vicinity of the critical point, produced an average deviation of 2.0% for viscosity, 1.4% for thermal conductivity, and 5.9% for self‐diffusivity.
Dynamics of fractional distillation
Authors: Ceaglske N. H.
Published: June 2004

One of the numerous equations needed to define the dynamics of a distillation column has been derived. This equation relates the feed composition to the product composition. Thederivation is accomplished by the reduction of the signal flow diagram. The poles and zeros of the equation are almost entirely determined by the ratio of the tray holdup to the liquid flow rates and the number of trays.
Three‐dimensional filtration on a circular leaf
Authors: Brenner Howard
Published: June 2004

The unconfined growth of a filter cake on a circular filter cloth was theoretically and experimentally studied as the simplest example of a three‐dimensional filtration. The results are compared with the one‐dimensional cake growth which ensues when the cake is laterally restrained by a cylindrical sleeve.
Heat transfer from the surface of a steam bubble in turbulent subcooled liquid stream
Authors: Bankoff S. G. , Mason J. P.
Published: June 2004

Turbulent heat transfer coefficients have been measured at the surface of single bubbles formed by injecting steam into a subcooled water stream at atmospheric pressure. Depending upon the steam flow rate (0.4 to 1.5 g./min), the water temperature (80° to 180°F.), and the water velocity (0.9 to 7.2 ft./sec.) the bubbles ranged from small, smooth, ellipsoidal bubbles, similar to those observed in highly subcooled nucleate boiling, to large, irregular bubbles which oscillated in size. The bubble frequencies were in the range 200 to 2,500 cycles/sec. and the surface heat transfer coefficients 13,000 to 320,000 B.t.u./(hr.) (sq. ft.) (°F.). Because of these exceptionally high heat transfer coefficients a significant fraction of the total heat flow in Gunther's subcooled boiling experiments is estimated to be attributable to latent heat transport.
Rates of reaction in a recycling system—dehydration of ethanol and diethyl ether over alumina
Authors: Butt John B. , Bliss Harding , Walker C. A.
Published: June 2004

A new method for measuring isothermal rates of heterogeneously catalyzed gas reactions is described. The method involves a differential reactor incorporated in a recycling system and affords ease of control, accuracy, and many rate measurements in one run.

The results for the reaction system investigated show that four reactions are important: the dehydration of ethanol to ethylene, the reaction of ethanol to form diethyl ether, the dehydration of diethyl ether to ethylene, and the reaction of diethyl ether to form ethanol.

It is also shown that the rate controlling steps are the monomolecular surface reactions for the two dehydrations and for the formation of ethanol from diethyl ether, and the bimolecular surface reaction for the formation of diethyl ether from ethanol.

The values and the temperature dependence of all pertinent rate and adsorption constants are determined and reported, and they are shown to correlate very well the data up to 80% conversion.
Physical and chemical forces in solvent selectivity for hydrocarbons
Authors: Anderson Ralph , Cambio Ronald , Prausnitz J. M.
Published: June 2004

An analysis is given of the role of physical and chemical forces in determining the selectivity of a solvent for different hydrocarbons. The physical contribution to selectivity depends on the polar energy density of the solvent and on the difference in size of the hydrocarbons to be separated; this effect is well‐demonstrated by solvent selectivity data for paraffins where no chemical forces are important. The chemical contribution depends on the ability of the solvent to form acid‐base complexes with the hydrocarbon. Chemical forces leading to complex formation can be detected by measurements on the heat of mixing, the volume change of mixing, and on the ultraviolet absorption of solvent‐hydrocarbon mixtures; some illustrations of such measurements are presented. Finally an equation is proposed for correlating selectivity data in extractive distillation, and its applicability is demonstrated with activity coefficient data for saturated and unsaturated hydrocarbons in various polar solvents.
Volumetric properties of gas mixtures containing one or more polar components
Authors: Blanks R. F. , Prausnitz J. M.
Published: June 2004

A study has been made of the second virial coefficients of binary gas mixtures containing one or two polar components. Methods for calculating these coefficients are presented. The interaction coefficient Bij for a polar‐polar interaction cannot be calculated with the Stockmayer potential with pure component parameters only; such calculations tend to underestimate the strong forces of attraction between dissimilar polar molecules. It is shown that the characteristic distance for the reduced dipole moment for two dissimilar polar molecules is less than the arithmetic average of the distance parameter of the similar molecules by an amount which can be related to the enthalpy of complex formation. When this corrected collision diameter is used in the Stockmayer potential, good results can be obtained for interaction coefficient Bij. In the case of a polar‐nonpolar mixture the coefficient Bij depends on dispersion and on induction forces. Techniques are proposed for estimating these forces from pure component parameters, and it is shown that for accurate calculation of Bij it is necessary to correct for the displacement of the dipole from the center of the polar molecule. The paper concludes with some illustrations of how these ideas may be applied to typical chemical engineering problems.
Diffusion of ideal gases in capillaries and porous solids
Authors: Scott D. S. , Dullien F. A. L.
Published: June 2004

The steady state diffusion of gases through capillaries or through the pores of a solid when the total pressure in the system is constant is considered. It is shown that the ratio of the molar diffusion rate of the lighter gas to that of the heavier gas must be equal to the square root of the ratio of the molecular weight of the heavier to the lighter.

From simple momentum transfer considerations a diffusion equation is derived to describe the diffusion rate as the nature of the process changes from ordinary mutual diffusion to Knudsen diffusion. This equation is shown to give good agreement with experimental measurements of diffusion rates in porous solids. A structural parameter of the porous solid, the diffusion ratio, is calculated from the experimental results and compared with the experimental value of the same ratio found from electrical resistance ratios and from flow measurements.
Sprays formed by flashing liquid jets
Authors: Brown Ralph , York J. Louis
Published: June 2004

Liquids forced from a high‐pressure zone into a low‐pressure zone often cross the equilibrium pressure for the liquid temperature and disintegrate into a spray by partial evolution of vapor. The ordinary aerosol dispenser is a common example of this operation, and flash boiling is another.

This paper reports on a study of the sprays formed by such a process and of the mechanism of spray formation. Sprays from water and Freon‐11 jets were analyzed for drop sizes, drop velocities, and spray patterns. The breakup mechanism was analyzed and data presented to show some of the controlling factors.

A critical superheat was found, above which the jet of liquid is shattered by rapid bubble growth within it. The bubble‐growth rate was correlated with the Weber number, and a critical value of the Weber number was found to be 12.5 for low‐viscosity liquids. The mean drop size was also correlated with Weber number and degree of superheat.

The spray from rough orifices and sharp‐edged orifices was compared with sprays produced from cold liquids by other techniques and was found to be comparable in all respects except temperature.
Heat transfer to pseudoplastic fluids in laminar flow
Authors: Christiansen E. B. , Craig S. E.
Published: June 2004

A simple temperature dependent equation τ = K [Ṡ exp(ΔH‡/RT)]n is proposed to represent the rheological properties of pseudoplastic fluids. This equation is combined with the differential equations describing steady state laminar flow and heat conduction to a moving fluid when natural convection and thermal energy generation are negligible. The resulting equations are solved numerically for heating of both Newtonian and non‐Newtonian fluids in laminar flow in tubes of circular cross section with constant wall temperature. These numerical solutions are presented as generalized plots of Nusselt number vs. Graetz number with n and (ΔH‡/R) (1/Ti — 1/Tw) as parameters.

Extensive experimental data were obtained for two pseudoplastic fluids, and, in the range where natural convection was unimportant, the mean deviation between the computed Nusselt numbers and measured Nusselt numbers was ± 7%.
The viscosity of polar gases at normal pressures
Authors: Stiel Leonard I. , Thodos George
Published: June 2004

The viscosity behavior at normal pressures (0.2 to 5 atm.) of fifty‐three polar gases was examined, and equations representing the dependence of viscosity on temperature for these gases were developed. A dimensional analysis approach was applied to the variables effecting the viscosity of polar gases at moderate pressures. These variables were assumed to be the molecular weight, temperature, and the critical constants of the substance.

Reliable viscosity data available in the literature for the polar gases investigated were utilized to determine the exact dependence of their viscosities on these variables. In contrast to the results of a previous study, which show that for nonpolar gases the viscosity parameter μ*ξ (where ξ =Tc⅙/M½Pc⅔) is independent ofzc; the results of the present study indicate that for polar gases this parameter is dependent onzc. The viscosity parameters of gases which exhibit hydrogen bonding were found to depend uniquely onzc5/4and reduced temperature, while the remaining polar gases were found to exhibit a different unique dependence onzc⅔and reduced temperature. For these two classes of polar substances separate viscosity relationships were developed.

For eleven gases which exhibit hydrogen bonding viscosities were calculated and compared with corresponding experimental values. An average deviation of 1.47% resulted from 129 experimental points. For the other polar gases the calculated values were also compared with experimental values and produced an average deviation of 2.59% for 197 experimental points.
Coalescence frequencies in agitated liquid‐liquid systems
Authors: Madden A. J. , Damerell Glenn L.
Published: June 2004

An experimental technique is described for estimating the coalescence frequency of droplets in an agitated liquid‐liquid system. Results are presented for dilute aqueous dispersions in toluene. Quantitative estimates of the coalescence frequency are based upon a simple model proposed to describe the coalescence process. The coalescence frequency is shown to increase markedly with increase in impeller speed and to a lesser extent with increase in the dispersed‐phase volume.
The flow of rarefied gases
Authors: Scott D. S. , Dullien F. A. L.
Published: June 2004

It has been shown experimentally by Knudsen and others that gases flowing at decreasing total pressures through small capillaries pass from a region of Poiseuille flow to a so‐called slip flow region which contains a flow minimum. Frequently the practice has been followed of approximating this behavior with a linear relationship which, although it gives a fairly good approximation to the actual curve, is incomplete in theory.

A new equation for the flow of gases in capillaries is presented, in which all flow constants can be calculated from the simple kinetic theory of gases. It is shown that this equation reproduces the experimental results of Knudsen and others over the entire range of laminar, slip, and Knudsen flow within the accuracy that might be expected from the simple kinetic model adopted.

Some discussion of the use of this equation in the design of vacuum piping and its applicability to flow through porous solids is also given.
Lennard‐Jones force constants from viscosity data: Their relationship to critical properties
Authors: Flynn Lawrence W. , Thodos George
Published: June 2004

Lennard‐Jones force constants calculared from viscosity values at normal pressures for nearly forty nonpolar organic and inorganic substances have been used to develop relationships for the estimation of these constants from the critical temperature and volume of the substance. The product of the critical temperature and volume TcVc was found to correlate linearly with the force constant modulus \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{\varepsilon }{\kappa }\sigma ^3 $\end{document}.

When the collision diameter ρ was plotted against the cube root of the critical volume on log‐log coordinates, a straight line of slope 5/4 resulted. The corresponding relationship was found to predict ρ values with an average deviation of 3.1% when compared with values calculated from viscosity measurements. The temperature force constant ϵ/κ was found to vary as the 5/6 power of the critical temperature, and the resulting relationship produced an average deviation of 10%.
Adsorption of normal paraffins and sulfur compounds on activated carbon
Authors: Grant R. J. , Manes Milton , Smith S. B.
Published: June 2004

Adsorption isotherms on activated carbon were determined gravimetrically for normal C1 and C3‐C6 paraffins and subsequently for methyl, ethyl, and n‐propyl mercaptans, hydrogen sulfide, carbonyl sulfide, and carbon disulfide, at pressures up to 1 atm. and from −23° to 100°C. Orthobaric liquid densities at low temperatures of some of the sulfur gases were determined pycnometrically. The adsorption data on correlation by the method of Lewis, Gilliland, Chrtow, and Cadogan (1) gave two separate curves, one for the paraffins and one for the sulfur compounds. The results show the correlation to be useful for estimating the adsorptive capacity of chemically similar compounds from a minimum of experimental data.
Flow of gases through porous solids under the influence of temperature gradients
Authors: Gilliand E. R. , Baddour R. F. , Engel H. H.
Published: June 2004

The isothermal and isobaric flow of pure gases and vapors through microporous Vycor glass was investigated under such conditions that the gas‐phase flow occurred by Knudsen diffusion. The isothermal flows and the isobaric flow of nonadsorbed gases are correlated by existing relationships.

On the assumption that surface flow is a diffusive process and that equilibrium exists between the vapor and solid throughout the porous media, a correlation for the nonisothermal surface flow is developed. The factors determining the rate of surface flow are the physical properties of the solid, the temperature level and gradient, the enthalpy of adsorption, the surface concentration and spreading pressure of the adsorbed phase, and the activation energy and coefficient of resistance for surface diffusion. The latter two factors can be evaluated from isothermal surface flow measurements; hence no new arbitrary constants are required in the correlation. Agreement between predicted and measured surface flows is good for ethylene and propylene at a mean temperature of 25°C. Both the gas‐phase and surface flows are from the cold to hot end of the porous solid.

It is suggested that the use of temperature gradients in porous solids and plastic films for separating mixtures of vapors be investigated.
Transient and steady state, free and natural convection, numerical solutions: Part I. The isothermal, vertical plate
Authors: Hellums J. D. , Churchill S. W.
Published: June 2004

Numerical values are presented for the transient velocity field, temperature field, and local heat transfer coefficient. These results were obtained by solving the partial differential equations describing the conservation of mass, momentum, and energy on an IBM‐704 computer with finite difference methods in time‐dependent form. The computed values for short times agree very well with the analytical solution for conduction only, and the limiting values for long time agree well with previous solutions for the steady state. The existence of a temporal minimum in the heat transfer coefficient is confirmed. The time required for the heat transfer coefficient to approach its steady state is shown to be less than previously predicted.
Burnout conditions for flow of boiling water in vertical rod clusters
Authors: Becker Kurt M.
Published: June 2004

This paper deals with a new concept for predicting burnout conditions for forced convection of boiling water in fuel elements of nuclear boiling reactors.

The concept states the importance of considering the ratio of heated channel perimeter to total channel perimeter.

The perimeter ratio concept was arrived at from an experimental study of burnout conditions in rod clusters consisting of three rods of 13 mm. outside diameter and 830 mm. heated length. Data were obtained for pressures between 2.5 and 10 kg./sq. cm., surface heat fluxes between 50 and 120 W./ sq. cm., mass flow rates between 0.03 and 0.33 kg./sec., and steam qualities between 0.01 and 0.52.

The rod clearance for the experiment were 2 and 6 mm. The diameter of the channel was 41.3 mm. Additional runs were also performed after unheated displacement rods were introduced in the channel. The rod clearance in this case was 6 mm.

In the ranges investigated the measured burnout steam qualities at the outlet of the channel decrease with increasing heat flux and decreasing pressure. Furthermore it has been found that the influence of rod clearance is, in the range investigated, of small significance for engineering purposes.

It has also been observed that the present burnout steam quality data for the rod clusters are much lower than those earlier obtained for round ducts. This may be explained physically by means of the perimeter ratio concept.

It has also been found that the surface shear stress distribution around the channel perimeter and especially the position of maximum shear stress is of great importance for predicting burnout conditions for flow in channels.

Finally the new method has helped in understanding and interpreting experimental results which earlier may have seemed inconsistent.
Estimation of enthalpies: Multicomponent hydrocarbon mixtures at their saturated vapor and liquid states
Authors: Stevens W. F. , Thodos George
Published: June 2004

Based on the data reported by Rossini et al. (9) analytical expressions have been developed for the calculation of enthalpies at zero pressure as functions of temperature for normal paraffins ranging from methane through octane. The coefficients of these equations have been found to correlate linearly with molecular weight, thus allowing the enthalpy relationships for hydrocarbons heavier than octane to be determined by extrapolation. The enthalpy of mixtures at zero pressure can then be obtained by combining the enthalpies of the individual components on an additive basis, weighted by the mole fractions

Corrections due to nonideal gaseous behavior have been developed in equation form from the work of Lydersen, Greenkorn, and Hougen (7) in terms of the reduced temperature TR and the critical compressibility factor zc of the substance. These corrections have been developed for both the saturated vapor and saturated liquid states and can be applied to the determination of the enthalpy of mixtures at these conditions. The results of this method have been compared with the experimental enthalpy data available for three ternary mixtures and were found to be in excellent agreement.
Flow and diffusion characteristics of alumina catalyst pellets
Authors: Robertson J. L. , Smith J. M.
Published: June 2004

Steady state constant pressure diffusion measurements were made on a series of alumina pellets using the nitrogen‐helium system at 1 atm. and 80°F. The pellets were prepared from the same alumina powder but compressed to different densities. Pore size distribution data indicate that all the pellets had approximately the same micropore sizes and volume, but different macropore volumes. Flow measurements with nitrogen were also carried out for the same pellets over a pressure range, up to 1 atm. The data show that the pellet density, or macropore volume, has a pronounced effect

On the basis of a simplified model of the pellet, path lengths were evaluated from the flow data. On the assumption that the diffusion path length is the same, a method is presented for predicting diffusion rates. The results so computed are independent of the path tortuosity. The method correctly evaluates the effect of pellet density on diffusion, but measured rates are 40 to 80% of the calculated values.
Selectivity in experimental reactors
Authors: Tichacek L. J.
Published: June 2004

Unpacked pipes or tubes, commonly called flow reactors, are often desirable for carrying out homogeneous reactions. Unless these reactors are properly designed and operated, axial mixing will alter both the rate of conversion and the distribution of products from successive reactions. Several hypothetical reaction schemes are analyzed here to show how axial mixing affects the production of an intermediate. The analysis represents mixing by an axial diffusion coefficient and is valid when mixing is not extreme. Results from several particular cases are compared, showing that reactor‐product distribution is generally distorted in proportion to a reactor Peclet number. G. I. Taylor's theory of axial mixing is used to relate this Peclet number to the physical characteristics of the reactor

Although the effects of axial mixing are concluded to be negligible in most commercial or large‐scale equipment, they are serious in the case of experimental or pilot‐scale apparatus. Charts are drawn to illustrate design problems for these reactors.
Problem of solidification with Newton's cooling at the surface
Authors: Hrycak Peter
Published: June 2004

An approximate solution to the problem of freezing of an isotropic, semi‐infinite slab is proposed for the situation where Newton's cooling at the surface of the slab applies. Comparison with the existing exact solution shows the approximate solution to be practical.

The heat‐balance integral method is used with the assumptionof linear temperature distribution in the frozen zone and of a parabolic temperature profile in the liquid zone. The final expression for the depth of solidification, however, seems to be only little affected by the particular temperature profiles chosen.
Numerical and experimental study of damped oscillating manometers: I. Newtonian fluids
Authors: Biery John C.
Published: June 2004

The time‐dependent behavior of Newtonian oscillating manometers was studied experimentally and mathematically. The manometers were simulated by numerically integrating the axial component of the equation of motion in cylindrical coordinates. Modifications in the driving‐force term were made to include end effects of surface tension and flow reversal. The integrations showed that the velocity profiles in the manometer were not parabolic and contained many maxima and minima, particularly when the fluid had a low viscosity. Good agreement was obtained between experimental and simulation frequencies and damping factors.
Adiabatic, evaporating, two‐phase flow of steam and water in horizontal pipe
Authors: Pike Ralph W. , Ward Henderson C.
Published: June 2004

The adiabatic, evaporating, two‐phase flow of steam and water in horizontal pipe including the critical flow was successfully described by a system of nonlinear differential equations which include different phase velocities, fluid acceleration, wall shear forces, interface shear forces, and mass and energy transfer between the phases. The solution of the differential equations by the method of Runge‐Kutta was facilitated with a high‐speed digital computer. Experimental data were obtained which included void fraction measurement by X‐ray attenuation and showed that the theoretical equations described the complex flow phenomena to ± 10% when radial temperature gradients were small. Design charts based on the numerical solution of the theoretical equations are presented for rapid evaluation of the flow variables for the system steam‐water including critical flow for inlet pressures from 30 to 150 lb./sq.in.abs., mass flow rates per unit area from 300 to 1,000 lb./sq. ft. sec., andL/Dratios from 25 to 1,000. The critical flow is defined as the maximum flow rate for a given pressure at the point of initial vaporization andL/Dratio.
Simultaneous radiative and convective heat transfer in an absorbing, emitting, and scattering medium in slug flow between parallel plates
Authors: Chen John C.
Published: June 2004

The problem of coupled radiation and convection to a medium in slug flow between infinite, parallel plates was formulated in terms of discrete fluxes. Steady state, uniform heat input, and gray boundaries were assumed. The effects of absorption, emission, scuttering, and flow were taken into account. For the general case where all these effects are present, it was necessary to approximate the fourth‐order temperature term by a truncated Taylor series. This approximation was not necessary for the special case where conductivity of the medium is negligible.

Approximate, analytical solutions in closed form for profiles of temperature, radiant fluxes, and heat fluxes were obtained for both the special case and the general case. Sample results are presented, showing the effects of convection, absolute temperature, absorption coefficient, scattering coefficient, and wall emissivities. The two cases of equal wall temperatures and unequal wall temperatures were both examined.

It was found that for a medium with properties approximately representative of those for air carrying a suspension of dust or mist, radiation can account for 60 to 95% of total heat transfer in the temperature range of 900° to 2,800°R. It was also found that for some situations the scattering phenomenon can have a much greater effect on heat transfer than the absorption and emission phenomena.
Phase‐volume relationship at the point of phase inversion in liquid dispersions
Authors: Yeh George C. , Haynie Fred H. , Moses Rex A.
Published: June 2004

The point of inversion of a water‐in‐oil type of dispersion to an oil‐in‐water type is investigated for several water‐oil systems by studying the volume ratios of the phases in relation to their physical properties. The point of inversion for each system of an immiscible organic liquid and water and organic liquid mixture and water is obtained by varying the phase‐volume ratios and determining the type of dispersion after complete mixing. The effects of temprature, interfacial tension, and density are found to have no correlation generally applicable to the systems studied. A volume‐viscosity relationship is found to exist within limits. This correlation is that the phase‐volume ratio at the point of inversion is equal to the square root of the ratio of teh viscosities of the respective phases at the interface. The theoretical aspects of this relationship are studied along with its limitations.
Asymptotic solution for combined free and forced convection in vertical and horizontal conduits with uniform suction and blowing
Authors: Carter Leo F. , Gill William N.
Published: June 2004

Significant changes in heat and momentum transfer rates can be caused by finite interfacial velocities and external field forces. This study considers the nonlinear problem of combined free and forced convection in vertical and horizontal two‐dimensional conduits with finite transverse velocity.

Similarity transformations for the temperature function have been found which reduce the energy, momentum, continuity, and state equations for these configurations to nonlinear systems of two coupled ordianary differential euqations. These equations are solved by approximate methods to give Nusselt numbers and friction factors as well as velocity and temperature profiles.

Stream to wall temperature differences increase with suction and decrease with injection. The effects of interfacial velocity on temperature profiles and heat transfer increase dramatically with Prandtl number. Because blowing and suction strongly affect temperature profiles they substantially modify natural convection effects in vertical flows. Suction creates steeper transverse temperature gradients and accentuates buoyancy effects in vertical flows. Conversely injection flattens temperature profiles and thus decreases the influence of buoyancy on the velocity field.
An analytical study of heat and mass transfer in multiparticle systems at low Reynolds numbers
Authors: Pfeffer Robert , Happel John
Published: June 2004

This investigation was undertaken to obtain an analytical solution to the problem of predicting particle‐to‐fluid heat and mass transfer rates in multiparticle systems at low Reynolds numbers. The energy equation based on the free surface model was solved by expanding the fluid temperature distribution in even powers of the spherical angle and by assuming that the fluid properties remain relatively constant with temperature. Solutions were obtained for Peclet numbers between 0.1 and 100 and fractional void volumes between 0.4 and 1.0. They show that the average Nusselt or Sherwood number in a bed of particles is a function of both the fractional void volume and the Peclet number, the effect of Peclet number decreasing as the bed becomes more concentrated in the low Peclet number range. A plot of the results in terms of the j factor vs. the Reynolds number shows good agreement with published experimental mass and heat transfer data and indicates that the j factor is not independent of the Schmidt or Prandtl numbers at low Reynolds number, low Peclet number flow.
Vapor‐liquid equilibria for aqueous sulfuric acid
Authors: Gmitro John Irving , Vermeulen Theodore
Published: June 2004

Because the precise composition of the vapor phase over aqueous sulfuric acid is not accessible experimentally a method is described for calculating the partial pressures of water, sulfuric acid, and sulfur trioxide starting from liquid‐phase partial molal thermodynamic quantities. Graphs and tables are provided which give the partial pressures from −50° to 400°C., between 10 and 100 wt. % acid.
Generation of waves in the concurrent flow of air and a liquid
Authors: Cohen Leonard S. , Hanratty Thomas J.
Published: June 2004

If air flows concurrently with a liquid, there are critical air velocities above which two‐dimensional and three‐dimensional waves appear at the interface. The physical process responsible for these transitions is as follows: The disturbance in the velocity field in the air caused by these waves gives rise to pressure and shear stress variations over the wavy surface. Pressure variations in phase with the wave slope and shear stress variations in phase with the wave height transmit energy from the air flow to the liquid film. If the rate at which energy is transmitted to the waves by these mechanisms is not larger than the rate of viscous dissipation in the liquid, the waves will decay.

The model of the gas flow proposed by Miles and Benjamin is used to calculate shear stress and pressure variations over the wavy surface. The agreement between predicted and measured critical air velocities, wave lengths, and wave velocities is good.
Pseudocritical constants
Authors: Reid R. C. , Leland T. W.
Published: June 2004

Pseudocritical rules provide a means to determine reduced properties for mixtures so that pure component corresponding states correlations may be used to estimate mixture properties. The most common pseudocritical rules are examined and shown to stem from a common base. Points of divergence as well as similarity are pointed out in tracing out the development of the rules. Reduction of all rules to simpler forms is made and criteria attached to allow one to determine when such simplifications are justifiable. All rules reduce to Kay's rule in certain limiting cases.
Measurement of some basic parameters in two‐phase annular flow
Authors: Quandt E. R.
Published: June 2004

The vertical upflow of air‐water mixtures in the dispersed‐annular flow regime has been studied in a ¼ × 3‐in. rectangular channel. Dye injection into the wall film was used to determine film and gas core properties along with the rate of droplet interchange between the core and the film. Visual observations demonstrated that the most important characteristic of this flow regime is the surface waves generated by the gas flow over the liquid film. Despite the surface waves, these data indicate that the liquid film approximately follows the generalizedu+—y+relationship for turbulent pipe flow. The droplet motion is discussed in terms of transverse diffusion and momentum transfer.
Estimation of vapor and liquid enthalpies
Authors: Yen Lewis C. , Alexander R. E.
Published: June 2004

The Lydersen‐Greenkorn‐Hougen (L‐G‐H) charts correlating the isothermal pressure effects on enthalpy for pure compounds based on a modified corresponding states principle have been improved with the aid of reliable literature data. To facilitate machine computations, the improved charts, divided into the superheated vapor region, the subcooled liquid region, the saturated vapor, and the saturated liquid lines, have been expressed in analytical forms. This correlation reproduces the literature enthalpy data including those in the critical region for pure compounds with an average deviation of about 5 B.t.u./lb. It can also be used for the estimation of enthalpies of nonpolar mixtures with satisfactory results.
An analysis of fully developed laminar flow in an eccentric annulus
Authors: Snyder William T. , Goldstein Gerald A.
Published: June 2004

An analysis is presented of fully developed laminar flow in an eccentric annulus. An exact solution for the velocity distribution is presented. From this solution may be obtained expressions for local shear stress on the inner and outer surfaces of the annulus, friction factors based on the inner and outer surfaces, and the overall friction factor. Curves of these data are presented covering a range of eccentricity values and radius ratio values.
Pressure drop studies in a plate heat exchanger
Authors: Smith Vernon C. , Troupe Ralph A.
Published: June 2004

Recent studies on heat transfer in plate heat exchangers have pointed out the need for quantitative expressions for pressure drop in this type of apparatus. This paper presents the results of experimental studies to obtain pressure drop relationships useful in plate heater design.

A plastic prototype of a commercial model (Chester‐Jensen) exchanger was fabricated and used to obtain entrance, exit, crossover, ribbed section, and overall pressure drops as a function of velocity with water as the fluid. These individual losses were combined into an expression for overall pressure drop for a series plastic plate pack having any number of plates and employing any fluid.

Overall pressure drop data on a commerical Chester‐Jensen Model HTF plate heater were available from several heat transfer studies reported previously. The data for series patterns were resolved by inserting overall pressure drop, physical properties of the fluid, and number of plate passes into the general form of the equation derived for plastic plates and by solving for a new set of constants. The resulting computer‐derived expression was found to predict series pressure drops in the apparatus to ± 10%.

From a similar approach it was possible to correlate the overall pressure drop data for the heater for looped flow patterns.