BRIEFS Summary of papers published in this month’s research quarterly, IHEC Fundamentals
PARAMETRIC PUMPING. DYNAMIC PRINCIPLE FOR SEPARATING FLUID MIXTURES
IMPROVED TWO-DIMENSIONAL EQUATION OF STATE TO PREDICT ADSORPTION OF PURE AND MIXED HYDROCARBQNS
Parametric pumping is an adsorptive separation technique based on periodic, synchronous, coupled transport actions. The net consequence of the coupling of alternating adsorbent-fluid position displacements with the cycling of a thermodynamic intensive parametric variable (temperature) is a buildup of separation from cycle to cycle. Thereby the powerful separational effects of countercurrent action are released in the uncommon circumstance of a continuously regenerating separation column having only a single fluid phase. Thus cycle-to-cycle time-staging as well as position-staging occurs with a column. Parametric pumping also is a compound, macroscopic, active transport system in which a species is moved a t the expense of some form of energy (thermal, chemical potential) from a region of low concentration to high. The large separation capability of the direct mode of parapumping is demonstrated experimentally for a toluene-n-heptane mixture on silica gel. A very important theoretical phase-angle relationship between oscillatory parts of the system also has been verified experimentally for this mode. New results also are presented for the recuperative mode in which heat is exchanged internally; NaC1-Hz0 was separated in a continuous open system on ionexchange resins. Preliminary theoretical efficiencies have been cumputed.
A two-dimensional equation of state has been derived from the
R. H. Wilhelm, A . W . Race, R. W. Rolke, and N . H. Sweed, Prtnceton University, Prznceton, N .J . 08540 IND. END.CHEM.FUNDAMENTALS, 7,337-349 (1968)
EFFECT OF MIXING ON PERIODIC COUNTERCURRENT PROCESSES
The effect of mixing on the stage efficiency of a periodically operated countercurrent process for the case of difficult separations is investigated by modeling each stage, during the time of liquid transport, by a series of m well stirred tanks. The asymptotic value for the stage efficiency of such a column is found analytically. I n a column with a finite number of stages the difference between the asymptotic and the real value is inversely proportional to the number of stages. Columns with a finite number of stages are calculated numerically. The transport number, 7, which is defined as the ratio of the quantity of liquid transported per cycle to the liquid holdup of a stage, is an important parameter, since in practice it can be controlled easily. While for piston:flow ( m = m ) the maximum stage efficiency is obtained for 7 = 1, for the more realistic case where m is finite the transport number maximizing the stage efficiency may be larger than 1.
F. J.M . Horn and R . A . M a y , Race University, Houston, T e x . 77007
IND.ENG.CHEM.FUNDAMENTALS, 7, 349-354 (1968)
GENERALIZATION OF VARIOUS POLYMERIZATION PROBLEMS. THE CONCEPT OF SLOW INFLUX
Hirschfelder-Eyring modification of the van der Waals equation and applied to the prediction of high pressure adsorption of pure and mixed hydrocarbons on charcoal. Equations are derived to express the thermodynamic equilibrium between a mixed adsorbate and gas, assuming the validity of the mobile fluid model for the surface phase. Solution of these equations permits the total adsorption and surface composition to be calculated for a mixed isotherm from pure component adsorption data. New experimental data are presented for high-pressure adsorption of methane, propane, butane, and their mixtures on charcoal.
H . K. Payne, G. A . Sturdmant, and T. W. Leland, Rice University, Houston, Tex. 77001 IND. ENC.CHEM.FUNDAMENTALS, 7, 363-374 (1968)
ESTIMATION OF THE IDEAL GAS ENTROPY OF ORGANIC COMPOUNDS
Earlier methods for estimating the heat capacity and heat OJ formation of organic compounds from structure are extended to the estimation of the entropy of organic compounds. Unlike the case of heat capacity and heat of formation, it is necessary to allow for contributions due to symmetry effects and optical isomerism in the case of entropy. Contributions have been worked out for a variety of groups, from which the two constants of a linear equation can be immediately written for estimating the absolute entropy as a continuous function of temperature. This method predicts the entropy with an average deviation of 1.2%.
D. N . Rihani, Bombay University, Department of Chemical Technology, Bombay 79, Indza, and L. K. Doraiswamy, National Chemical Laboratory, Poona 8, India
IND. ENG.CHEM.FUNDAMENTALS, 7,375-380 (1968).
PREDICTION OF AZEOTROPE FORMATION BASED O N INFRARED SPECTRAL DATA IN BINARY SOLUTIONS CONTAINING METHANOL
A correlation between the activity coefficient of methanol in binary mixtures and the shift of OH-stretching infrared spectra of methanol in these liquids is presented. Based on this correlation, a boiling point-infrared shift diagram has been prepared which can predict the formation or absence of azeotropes in binary solutions containing methanol at atmospheric pressure. Koichiro Nakanishi, Kyoto University, Kyoto, J a p a n , ana‘ Shogo Ichinose and Hideko Shirai, Shinshu University, Nagano, J a p a n IND.ENG.CHEM.FUNDAMENTALS, 7,381-387 (1968)
REACTORDESIGN’AND CONTINUOUS SAMPLING CRITERIA FOR AN ULTRASONIC REACTION
A realistic analysis of a polycondensation reactor performance must include the effects of the inevitable mixing operations, many of which can be represented by a general mathematical model. The nature of the general solution leads to a simplified formulation which permits incorporation of complex physical factors for specific systems. The solution can be used as a n element in modeling more complex problems and provides a concrete solution for several well-defined reactor types of practical interest.
Ultrasonically induced cavitation can bring about increased rates in liquid phase chemical reactions. If the variation in chemical yield is to remain a t a minimum in an ultrasoaic reaction, certain limits of the acoustic pressure must not be exceeded. If these limits are exceeded in some instances, the acoustic pressure will drop below the cavitation threshold and the reaction will cease. Design criteria for a continuous stirred tank reactor and batch reactor, along with the maximum sample size, are developed which meet the prescribed restrictions.
Henn Kilkson, E. I . du Pont de Nemours &? Co., Inc., Wilmington, Del.
Scott Fogler, University of Michigan, Ann Arbor, M i c h .
IND.END.CHEM.FUNDAMENTALS, 7,354-363 (1968)
IND.ENG.CHEM.FUNDAMENTALS, 7, 387-396 (1968) VOL. 6 0
NO. 8
AUGUST 1968
95
BRIEFS ACTION OF ULTRASOUND ON AQUEOUS SOLUTIONS OF METHYL IODIDE
The effect of ultrasound o n aqueous solutions of methyl iodide has been investigated a t a frequency of 820 kilohertz and a transducer acoustic output of 3.0 watts per sq cm. Quantitative chromatographic analysis using a hydrogen flame ionization detector revealed the following products: iodine, hydrogen iodide, methanol, hydrogen peroxide, methane, ethane, ethylene, propane, propylene with traces of acetylene, and methylene iodide. T h e sonochemical decomposition was zero-order with an average rate constant of 3.20 X l o e 6 mole per (liter) (sec) at 18' C. T h e results are discussed on the basis of cavitation phenomena, and a free radical mechanism is proposed.
T . M . T u s g n s k i and W. F. Graqdon, Department of Chemical Engineering and ApPlied Chemistry, University of Toronto, Toronto 5, Ont., Canada IND.
ENG.CHEM. FUNDAMENTALS, 7, 396-400 (1968)
DIFFUSION IN THREE-COMPONENT GAS MIXTURES IN THE TRANSITION REGION BETWEEN KNUDSEN AND MOLECULAR DIFFUSION
A solution to the differential equations for steady-state diffusion in a three-component gas mixture is obtained for the transition region between Knudsen and molecular diffusion through capillaries in an open system. Two sets of equations are obtained, one being in an exponential form similar to the molecular diffusion equations of Toor for three components in a closed system and the other being in a sine-cosine form. The proper set to be used must be determined by trial and error. The exponential form may have a maximum or minimum in the concentration-as.distance plot, and the sine-cosine form may possibly have several maxima or minima. The equations are shown to have two singular points. T h e equations also show that a diffusion barrier can exist in this system.
R. S. Cunningham and C. J . Geankoplis, T h e Ohio State ZlniLlersity, Columbus, Ohio 4 3 2 7 0 IND.
OXIDATION OF HYDROGEN CHLORIDE IN A MICROWAVE DISCHARGE
The oxidation reaction 4HCI f 0 2 -+ 2 H z 0 f 2C12 was carried out with yields of up to 557, by use of a 2450-megacycle microwave discharge. Experimental results confirm the theoretical prediction that the ratio of the electric field strength to gas density is the important parameter. A postulated kinetic scheme is shown to be supported by the experimental measurements.
W . W . Cooper, H . S. Mickley, and R. F . Baddour, dMassachusetts Institute of Technology. Cambrdge, M a s s . 0 2 7 3 9 I K D .EXG.CHEM.FUNDAMENTALS, 7, 400-409 (1968)
EKG.CHEM. F U N D A M E N T A L S , 7,429-432 (1968)
DIFFUSION IN POLYMER SOLUTIONS
, i n expression has been developed to account for the variation of the diffusion coefficient, D , in polymer solutions. This expression, with heat of mixing and viscosity data, can be used to predict D in polymer solutions in terms of D for the pure solvent. D was measured for seven polymeric systems; polymer concentration was up to 40c0 by weight.
S. C'. L i and J . L. Gainer, Unwersio of Virgania, Charioftesuille, Vu. IND.
ESG. CHEM. F U K D A M E N T A L S , 7, 433-440 (1768)
OPTIMAL LINEAR CONTROL OF DISTRIBUTED SYSTEMS
T h e optimal controller for a linear-distributed system relative to a quadratic error criterion is shown to be a linear feedbackfeedforward control system in which the gains may be entirely precomputed. hf.M . Denn, L'nzversity of Delaware, iVeewark, Del. 1977 7
IND. ENG.CHEM.FUSDAMENTALS, 7,410-413 (1968) OPTIMAL CONTROL OF A CLASS OF DISTRIBUTED-PARAMETER SYSTEMS WITH DISTRIBUTED CONTROLS
A strong minimum principle is derived for the distributed-parameter system b x / a t c(i)dx/dr = f[x(r,t), u ( r , t ) ] with performance
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index P ( u ) = L ' u ' t J
1
F [ x ( r , t ) ,u ( r , t ) ] dr.
Tubular reactors and
heat exchangers are descrlbed by these system equations. Optimal controls are found by solving a related lumped-parameter problem; some analytical solutions are presented.
L . B . Koppel and Y.-P. Shih, Purdue Cmuersity, Lafayette, Ind. 4 7 9 0 1 IKD.
ENG.CHEM. FUNDAhIEUTALS, 7, 414-422 (1968)
SENSITIVITY ANALYSIS IN OPTIMAL SYSTEMS BASED ON THE MAXIMUM PRINCIPLE
The sensitivity equations, necessary for determining the effects of the first-order variations in parameters on the optimal objective function and decisions of a continuous process, are derived based on Pontryagin's maximum principle. Methods for optimal design of parameter-sensitive systems are presented. T h e algorithm of the maximum principle is extended to problems with sensitivity constraints. T h e sensitivities to changes in the kinetic data of the optimal temperature and the maximum conversion owing to a single exothermic reaction taking place in a tubular reactor are calculated.
T. M . Chang and C. Y . W e n , "est W. Va. IND.
96
Virginia UniuersiQ, Morgantown,
END.CHEM. FUNDAMENTALS, 7 , 422-429 (1968) INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY
HEAT TRANSFER IN THERMALLY DECOMPOSING OZONE. EXPERIMENTAL INVESTIGATION
The purpose of this study was to investigate experimentally the effect of the homogeneous, gas phase thermal decomposition of ozone upon heat transfer to ozone-oxygen mixtures in turbulent flow past a solid surface. Effluent from a silent discharge ozone generator passed through the 5/8-inch diameter, IO-in. long electrically heated glass test section. Seven in. from the test section inlet, local heat transfer coefficients were measured. Reynolds numbers in the test section were from 6000 to 13,000, and the wall temperatures investigated were from 623' to 755 O K . T h e experimental procedure consisted of measuring local heat transfer coefficients for both pure oxygen and ozone-oxygen mixtures (2.0 to 3.4% ozone by volume) at the same Reynolds number and temperature driving force. The chemical reaction reduced the heat transfer coefficient by as much as 277,. A mathematical analysis based on the film theory model is in agreement with experimental results.
L . L . Edffiards and R. R. Furgason, Chemical Engineering Defiartment, Unicersity of Idaho, Moscow, Idaho 83843 IND.END.CHEbI. FUKDAMENTALS, 7,440-445 (1968) BUBBLING BED MODEL. MODEL FOR THE FLOW OF GAS THROUGH A FLUIDIZED BED
A simple rhree-region model for the flow of gas through fluidized beds views uniformly sized bubbles, surrounded by clouds and followed by wakes, rising through an emulsion of downward-moving solids. Interchange of gas occurs continuously among bubble, cloud-wake, and emulsion regions. This model contains one parameter, the effective bubble size, and all internal flows and interchanges in the bed are derived from it. Qualitative and quantitative checks with reported bed behavior are presented. Daizo Kunii, Chemical Engineering Department, llniuersity of Tokyo, Tokyo, Japan, and Octave Leuenspiel, Chemical Engineering Defiartment, Illinois Institute of Technology, Chicago, Ill. 60676
IKD.ENG.CHEM. FUNDAMENTALS, 7,446-452 (1968)
ELUTRIATION FROM A MULTlSlZE PARTICLE FLUIDIZED BED
Elutriation in a multisize particle fluidized bed was studied by fluidizing spherical glass beads of size range less than 595 and greater than 88 microns, in a 3-inch diameter column using air as the fluidizing medium. The variables studied were particle size distribution and superficial gas velocity. Particle distributions were made to follow a straight line on log-probability coordinates. The rate of elutriation could be described mathematically by an equation of the form: X / X , = b e - k l @ ( 1 - b)e-kl@ in which X and X, are the concentrations by weight of particles below a given size in the bed at times 0 and 0, respectively; b is a constant with value 0 5 b 5 1 ; kt < k z , both constants having dimensions of reciprocal time units. kl increased with increasing superficial gas velocity and decreased with increasing particle size. The size distribution of the elutriated particles formed a log-normal distribution in which the geometric mean diameter increases with elutriation time, while the standard deviation decreases with time.
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Deran Hanesian and Albert Rankell, Newark College of Engineering, Newark, N . J. 07102
THICKENING OF CALCIUM CARBONATE SLURRIES. COMPARISON OF DATA WITH RESULTS FOR RIGID SPHERES
A means of correlating the sedimentation behavior of three different calcium carbonate slurries based upon the reduced flux curve for rigid spheres is presented and used to explain various sedimentation and thickening phenomena which have been reported. The effective solids (aggregate) volume fraction is shown to have an important bearing upon both the mode of settling and the concentration zones which form in a continuous thickener. Three regimes are postulated: dilute, in which the behavior is “ideal”; intermediate, in which channel formation gives rise to abnormally high static batch settling rates; and concentrated, in which the aggregates are in mechanical compression. Observed deviations from the flux theory are explained, and the doubly humped flux curve is discussed.
K . J. Scott, Chemical Engineering Group, S.A. Council f o r Scient@ and Industrial Research, Pretoria, South Africa IND.ENC.CHEM.FUNDAMENTALS, 7, 484-490 (1968)
IND.ENG.CHEM.FUNDAMENTALS, 7,452-458 (1968)
CONTRIBUTION OF THE CONTINUOUS AND DISPERSED PHASES TO THE SUSPENSION OF SPHERES BY A BOUNDED GAS-SOLIDS STREAM
The air velocity, Us, a t which spheres are suspended in a vertical riser of diameter D by an air stream containing dispersed particles has been correlated by U,/(gD)1’2 = K(dt/D)z(di/D)Y where K , x , and y are functions of the air mass flow ratio solids to, and dl and dz are the mean particle and sphere diameters, respectively. Measurements using high speed and stroboscopic photography of the distribution of particle velocities and concentrations are reported: The particles were approximately uniformly dispersed, and local particle velocities correlated by a power law. Comparison with a theoretical model shows that the coefficient of the axial drag force for the dispersed solids can be predicted from Newtonian collision theory and has a value of approximately 2. The corresponding drag coefficient for the continuous phase has a value of 0.66 for the Newtonian region of sphere drag. The velocity term in these drag coefficients is the particle or fluid veIocity approaching the center of the suspended sphere from upstream. The comparison also allows indirect measurement of the mean dispersed solids velocity to be obtained from the sphere suspension studies and suggests a less tedious method of obtaining this information.
I. D . Doig and G. H. Rojer, Universiv of New South Wales, Kensington, AustraJia
EXPERIMENTAL TECHNIQUE. STEADY-STATE METHOD FOR THE MEASUREMENT OF TERNARY LIQUID DIFFUSION
An apparatus for measuring ternary liquid diffusion is described. Steady-state diffusion is established in a vertical column open a t both ends to horizontal channels carrying solutions of different compositions. Composition profiles and fluxes are determined by spectrophotometry in situ. From two measurements with different end compositions, the four ternary diffusivities at the common composition are determined. Neither calibration with a system of known diffusivity nor an assumed relation between diffusivity and concentration is required. Diffusivities (mass-fixed, mass per unit volume driving forces) determined at 20.0 “C. for 0.326 g per cc. of benzene (B) and 0.265 g per cc. of 2-propanol (P) in carbon tetrachloride are: DBB = -0.059 f 0.012, D B = ~ -0.028 i 0.009, D ~ = B -0.006 f 0.02, and D p p = -0.048 f 0.009, in cm2/hr. An order of magnitude improvement in precision is to be expected by a modification in the technique for flux determination.
R . A . Graff and T . B. Drew, Columbia University, New York, N . Y . 70027
IND.ENC. CHEM.FUNDAMENTALS, 7, 490-497 (1968)
IND.ENG.CHEM.FUNDAMENTALS, 7, 459-471 (1968)
TURBULENT FLOW OF GAS-SOLIDS SUSPENSIONS
An investigation of gas-solids flow at high N R (lo6 ~ to 106) and low solids loading (W,/W, < 0.6) is given. Pressure drops were measured and friction factors calculated in the center section of a l inch diameter glass tube where acceleration effects were small. The friction factor decreased with increased solids loading. Solid particle velocities were measured photographically; axial velocities were found to be uniform in the turbulent core. The momentum equation is developed considering the two-phase gassolids suspension as a continuum. Using standard drag coefficients, this model agrees with the experimental data, including acceleration effects. A model which considers the two phases separately does not agree with the experimental results. An analytical solution is presented for the piston flow of a compressible fluid or a fluid-solid mixture in which the slip velocity of the solid is small.
H . E. McCarthy, E . I. du Pont de Nemours B Co., Inc., Wilmington, Del., 79898, and J. H. Olson, University of Delaware, Newark, Del. 1971I IND.ENG.CHEM.FUNDAMENTALS, 7,471-483 (1968)
EXPERIMENTAL TECHNIQUE. RAPID DETERMINATIONOF OXYGEN PERMEABILITY OF POLYMER MEMBRANES
The oxygen permeability, Pm,and diffusivity, D,, of polymer membranes were measured electrochemically by exposing an electrode covered by the membrane to an atmosphere with a definite partial pressure of oxygen. For membranes with higher oxygen permeability values, such as tetrafluoroethylene, polyethylene, and polypropylene, good agreement was obtained between P, (and B,) determined by this method and measured by the conventional pressure method. For the less permeable membrane-e.g., poly(vinylidene chloride)-the agreement was not always satisfactory; this was attributed to the fact that one surface of the membrane was in contact with an electrolyte solution. T h e procedure reported permits rapid measurement of P, and D , values of polymer membranes, eliminating some of the disadvantages associated with determination by the pressure method.
Shuichi Aiba, Minoru Ohashi, and Shih-Yotv Huang, Institute of Applied Microbiology, University of Tokyo, Tokyo, Japan IND. END.CHEM.FUNDAMENTALS, 7,497-502 (1968) VOL. 6 0
NO. 8 A U G U S T 1 9 6 8
97
COMMUNICATION. FEED PLATE MANIPULATION IN DISTILLATION COLUMN FEEDFORWARD CONTROL
COMMUNICATION. COMPOSITION DEPENDENCE OF BINARY DIFFUSION COEFFICIENT
Feedforward control schemes for distillation columns have traditionally used only reflux and/or vapor boil u p as manipulative variables. This communication suggests a n alternative technique that may have significant advantages in some systems. Its basic idea is to change feed tray location to compensate for feed composition disturbances. Steady-state and dynamic feedforward controller synthesis techniques are presented. Effectiveness of control is demonstrated by digital simulation of a 20-tray column.
A geometric mean rule for the lattice spacing is proposed as a n alternate basis for the variation of the binary diffusion coefficient with composition. The implications of this viewpoint are discussed, and a comparison with some available data is offered in support.
H. T . Cullinan, Jr., State University of iVew York at Buffalo, Bufalo, N . Y . 74214 IND.ENG. CHEM.FUNDAMENTALS, 7, 519-520 (1968)
W .L . Luyben, Lehigh University, Bethlehem, P a . 1 8 0 1 5
IND. END.CHEM.FUNDAMENTALS, 7,502-508 (1968) COMMUNICATION. DROP FORMATION
COMMUNICATION. EFFECT OF ADSORPTION ON THE FOULING OF CATALYST PELLETS
T h e Langmuir-Hinshelwood kinetic model was used to study the effect of adsorption on three types of catalyst fouling-series, parallel, and independent. T h e results were compared with fouling experiments and other theoretical models reported by previous investigators. T h e relative effectiveness a t any time (ratio of the current effectiveness factor to the initial effectiveness factor) is usually higher than but very close to the average vacancy factor (fraction of adsorption sites remaining unoccupied by the fouling material) of the pellet a t that time. T h e relative effectiveness, vR can, in many cases, be expected to follow the equation 78 = e - a g where e is a dimensionless time and a is a constant. T h e relative rate of deactivation is strongly influenced by the adsorption equilibrium constants, K , and the partial pressures, f i t , of components i a t the catalyst external surface. If z is the predecessor or the fouling material, increase in K , or p t increases the rate of deactivation. The reverse is true if i is some other component.
Chieh Chu, Unioersity of Calafornia, Los Angeles, Calif, 90024 IND.ENG.CHEM.FUNDAMENTALS, 7, 509-514 (1968)
EFFECT OF MASS TRANSFER ON
T h e size distribution of drops formed by injection of one liquid into another was quantitatively determined as a function of the direction of mass transfer between the phases. T h e experiments indicated a profound influence of mass transfer on the character of the drop size distribution.
C. A . Bayens and R. L. Laurence, The Johns Hopkins University, Baltimore, Md. 2 1 2 1 8 IND.
ENC.(=HEM. FUNDAMENTALS, 7,521-522 (1968)
COMMUNICATION. STOCHASTIC TEST FUNCTIONS FOR OPTIMIZATION TECHNIQUES
The effects of various methods of adding noise to object functions used in testing optimization search techniques are examined. The mean value of a noise-corrupted object function is a variable and, in the neighborhood of the extremum, is less desirable than that of the noise-free function. The variance also is a function of the independent variable, even though input variances are constant. These effects are second-order with respect to the independent variable and cannot be legitimately approximated by a linear noise addition to the object function.
R. H. Luecke, University of iMissouri, Columbia, M a . 6 5 2 0 1 IND.ENG.CHEM.FUNDAMEKTALS, 7,523-524 (1968)
COMMUNICATION. NUMERICAL SOLUTION OF COUPLED, ORDINARY DIFFERENTIAL EQUATIONS
COMMUNICATION. PLANE FLOW
A wide variety of problems involving ordinary differential equations can be linearized about a trial solution a n d then put into finite difference form. T h e resulting coupled, tridiagonal matrices can be solved readily on a digital computer, and the nonlinear problem can then be solved by iteration.
The solutions of the equations of motion and energy for a power-law liquid with temperature-dependent consistency in plane flow in the absence of a pressure gradient are obtained. For a n exponential temperature dependence of the consistency the problem is formally the same as that for Newtonian liquids, provided the Brinkman number is properly defined. T h e temperatures developed a t corresponding values of the Brinkman number differ, depending upon the power-law index, n.
J o h n Newman, Lawrence Radiation Laboratory and Department of Chemical Engineering, University of California, Berkeley, Calif. 94720
IND. ENG.CHEM.FUNDAMENTALS, 7,514-517 (1968).
VISCOUS HEATING OF A POWER-LAW LIQUID IN
Jerome Gauis and R. L. Laurence, Defiartment of Chemical Engineering, T h e Johns Hopkins UniversiQ, Baltimore, iMd. 27218 IND.ENG.CHEM. FUNDAMENTALS, 7, 525-527 (1968)
COMMUNICATION.
FILM BOILING FROM A SPHERE
An analysis of film boiling from a sphere to a saturated liquid in forced convection is presented. The heat transfer coefficient from a sphere is similar to that obtained by Bromley for forced convection film boiling from cylindrical tubes.
CORRESPONDENCE.
HYPERFILTRATION
Comments on a published article on hyperfiltration and a rebuttal.
L . C. W i t t e , Argonne National Laboratory, Argonne, Ill: 60439
J . L. Cooney and A . E. Rabe, E. I. du Pont de n'emours & Co., Inc., Wilmington, Del.; A . J . Shor, K . A . Kraus, and J . S. Johnson, Jr., Oak Ridge National Laboratory, Oak Ridge, Tenn. 37830, and W . T. Smith, J r . , University of Tennessee, Knoxville, Tenn. 3 7 9 1 6
IND.END.CHEM.FUNDAMENTALS, 7, 517-518 (1968)
IND.ENG.CHEM.FUNDAMENTALS, 7, 527-528 (1968)
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INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY
