J. K. F E R R E L L
E.
P. S T A H E L
ANNUAL REVIEW
HEAT TRANSFER Activity in heat transfer research and development continues at about the same pace as in preuious years.
No distinctive trends are evident
other than the sustained interest in convective transfer and boiling. t the Sixth ASME-AIChE joint Heat Transfer
A Conference, 92 papers were presented, the majority of them to appear in various journals. As a matter of considerable interest to those working in heat transfer, The International Journal of Heat and M a s s Transfer is continuing the publication of heat transfer bibliographies with the presentation of several devoted to work done in the United States and the Soviet Union during the past year. This review covers the year preceding March 1964 with references being those of greatest utility to the chemical process industry. Thermal Properties and Measurements
Most of the research activity in thermal properties was devoted to the development of methods for measuring the thermal conductivity and thermal diffusivity of solids, and several excellent new methods were presented. The reports on this work are classified in Table I below. Also included are several papers on high temperature heating media (A23) and the use of organic liquids as heat transfer fluids ( A 78). Touloukian (A22) described the Thermophysical Properties Research Center at Purdue University. The Center is devoted to three interrelated activities : scientific documentation ; critical tables of properties ; experimental research to fill gaps and resolve discord.
conduction heat transfer. Of the published papers, the majority was concerned with mathematical solutions to the heat conduction problem, both exact solutions and numerical or approximate solutions. Several mathematical solutions to conduction problems were presented in connection with the development of methods for measuring thermal conductivity or thermal diffusivity and these are discussed under the section on thermal properties and measurements. A general mathematical method for solving threedimensional, transient heat conduction problems with time dependent heat sources and boundary conditions in finite regions was presented by Olcer (CQ). In this paper, he developed a very general method of solution using finite integral transforms. While the method presented is general, reducing the solutions to numerical answers would still be very difficult except in simple problems. Erdogan (C4) presented a method of considerable generality for obtaining approximate solutions to transient heat conduction problems by using integral transforms and the method of weighted residuals. The reduction to numerical answers should be fairly straightforward. A number of solutions to specific problems were obtained, e.g., a slab melting on one face and insulated on the other ( C I ) , temperature distribution in a thin-walled combustion chamber (C6), transient cooling of a heated
TABLE I. METHODS FOR MEASURING T H E R M A L C O N D U C T I V I T Y AND T H E R M A L Dl FFUSlVlTY
Material Solid materialn Porous media and beds of solids Gases and liquids Heat transfer media
1
References ( A 7 , A3-A8, A 7 7, A 72, A 15) (A2, A 1 4 ) (A73, AZO, A211 (A18, 1423)
Heat Transfer in Equipment
Once again this year there was considerable activity in research and development involving heat transfer in process equipment. The majority of the works listed
in the bibliography was devoted to heat exchanger equipment, although many papers have been included which cover heat transfer in other equipment. Most of the papers listed are classified in Table 11. Conduction Heat Transfer
During the past year relatively few papers were published which could be classified under the heading of
Equipment Heat exchangers Fin tubes Shell and tube Condensers Reboilers Regenerators Cross flow types Special types Calcination Coolers Screw conveyer Evaporators
VOL. 5 6
References (B3, B7, Bl6, B37) (BS, B14) (B70, 2324) (B77, B72, 6’15) (B13, B77)
(B19 (B4-B6, B33-B36) (BO
(B8,8 7 8 ) (B21) (BZ8,837)
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DECEMBER 1 9 6 4
53
enclosure (C77), and conduction of heat in a semiinfinite body ( 0 4 ) . The problem of heat conduction through edge sections with convective boundary conditions was solved by simulation with electrically conducting paper (C7). Several investigations were made on the resistance at the interface of two solids in contact (C70, C72, C73). The first two are concerned with nuclear reactor fuel elements, and the third presents a method for the theoretical calculation of the contact resistance. Convective Heat Transfer
Laminar Flow. Interest continues in the mathematical solution for temperature distribution involving generalized geometric shapes with specific boundary conditions. Semi-infinite plates under steady state (D773) and transient conditions (086) have been examined. Laminar flow in parallel plate channels under spatially variable heat fluxes was considered for a wide variety of transients (097,092),and of a heat-generating fluid (D96, 0 7 0 6 ) . The latter investigation was checked experimentally by use of an electrolyte undergoing ohmic heating. Heat generation in a non-Kewtonian fluid was considered for the case of a power law fluid whose heat generation rate is linearly dependent on local temperature ( 0 2 3 ) . Asymptotic solutions to the Graetz-Nusselt problem, more accurate than the Leveque asymptotic solutions, were obtained by Munakata (D69). The classical substitution procedure for solving Poisson's equation has been extended by the application of coordinate transformations (074).The dependence of stability on critical Reynolds number was examined for heated plane couette flow ( 0 3 8 ) and the laminar-turbulent transition in pipes, annuli and parallel plates (035). Laminar flow in pipes was studied experimentally and under large under varying axial heat fluxes (01) temperature differences (D79, 0 5 7 , 07 75). I n both cases standard approaches were able to predict experimental behavior. h-onisothermal velocity profiles in a horizontal tube indicate the effect of free convection (037). The effect of temperature on viscosity in the laminar region was the subject of two papers. Comparison of computed temperature changes in the fluid due to capillary flow and measured viscosity changes within isothermal boundaries indicates the effect can be significant (032). Graphical calculation of pressure drop for long pipe lines where temperature and viscosity changes are significant is illustrated (054). Specialized configurations were the subject of much study in laminar heat transfer and are indicated in Table 111. Special attention is drawn to the excellent agreement of experimental results with the complete analysis of the thermal problem of heat transfer in annular passages by Lundberg ( 0 6 3 ) . Heat and mass transfer rates are predicted for three dimensional flows with arbitrary boundary shapes in the limit of high Prandtl and Schmidt numbers (D99). The thermal entrance region was the subject of two theoretical analyses. Solutions were obtained for the 54
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
Graetz problem in an annulus ( 0 3 6 ) and for an clcctrically conducting fluid within a magnetic field (D67). The two cases of uniform heat flux and uniform wall temperature were considered. Turbulent Flow. Deissler (078) treated turbulciit heat transfer and temperature fluctuations in a field oi' uniform velocity and temperature gradients. Solutions to the momentum and energy equations were obtained by converting the equations to spectral form and neglccting triple and higher order correlations. Mean temperature fluctuations are calculated for the homogeneous turbulent field. Two theoretical approaches ( 0 J 2 , 088) yield the effects of Prandtl, Nusselt, and Rayleigh numbers on convection over a flat plate. Two ncw numerical methods of solution (suitable for large digital computers) are proposed (0700, D 702) and illustrated to solve the non-linear differential equations associated with convective transport. Studies of temperature and eddy diffusivity distributions near a wall ( 0 7 0 9 ) , a fluid moving in a Taylor TABLE 1 1 1 .
LAMINAR FLOW I N SPECIALIZED CONFIGURATIONS Conjguration
I
Plates, walls, strips Spheres and concentric rotating spheres Annular flow, coil flow Stirred vessels
I
TABLE
IV.
Conjguration
Disks Annuli Spirals Jets
I ~
1I
V.
SPECIALIZED
~-
References
(09)
(02,049, 050, 064, 0 7 3 , 0x4) (072) (020, 043, 070, 0104)
NATURAL CONVECTION CONFl GU RATIONS
I
Conjguration
_ _
1
(026, 037, 047, 052, 0 9 4 ) (04,045, 079, 0 8 5 )
Flat Plates Channels Fins Spheres and cylinders Heated Enclosures
TABLE V I .
'
TURBULENT FLOW I N CON FIG U RAT I ONS
Parallel Plates Cylinders
TABLE
,
References (062, 0 7 4 , 0779) (055, 076) (063, 089) (048)
IN
SPECIFIC
References (093, 0 7 72) (07.2, 0 2 7 ) (056, D707) (078, 0107) (077, 0701)
HEAT TRANSFER FROM ROTATING SURFACES __ References Surface I ___
Spheres and cylinders Disks Cones Scraped surfaces
( 0 3 , 059) ~
I
(058, 0 7 7 7 ) (0710)
(05)
AUTHORS J . K . Ferrell is Professor of Chemical Engineering and E. P. Stahel is Assistant Professor of Chemical Engineering Prof. Ferrell autlioicd at the North Carolina State L'niversity. the I@EC Heat Transfer Reviews f r o m 795'4to 7959.
system of vortices ( 0 3 9 ) , and heat transfer in the critical region (D776) should lead to a broader understanding of turbulent transport. The extensive tabulation (028) of the Spalding function for Prandtl numbers of 0.7 to 1000 should prove useful in calculating heat transfer rates in fully developed turbulent boundary layers. Analysis of turbulent flow in a pipe with variable circumferential heat flux ( 0 8 3 , 0 9 5 ) indicates that this is not only a more pronounced effect than in the laminar region but of considerable importance. Interest continues in careful measurement of fluctuations (D60, D705) and profiles (070) in turbulent pipe flow. Lee and Bradkey (060) make use of a novel fiber optic light probe which enables measurement of rapid concentration fluctuations. Temperature and velocity fluctuations are found to be of similar nature (0705) and heat transfer data can be correlated with existing techniques ( 0 7 , 070, 080, 0105). Many studies, predominantly experimental, have been published on turbulent heat transfer in specialized configurations. These are indicated by types in Table IV. Transpiration cooling has been studied for cylinders ( 0 4 5 ) and flat plates (087). Natural Convection. Efforts are continuing to solve the mathematical problems associated with natural convection. Direct solutions have been obtained for the steady state velocity and temperature distributions above a horizontal line source and a point heat source ( 0 2 5 ) . Spatially nonuniform acceleration on a flat plate has been treated by an integral method (061). Integral techniques were also applied to transient responses from a vertical plate (D8, 030, 0 8 2 ) . The solution of transient temperature and velocity responses about a vertical plate can also be treated by perturbation analysis. An example utilizing the classical boundary layer solution as the zeroth-order approximation has been published (07 77). Table V summarizes some more important experimental studies involving specific configurations. Effects of External Forces. The enhancing effect of acoustic vibrations on convective heat transfer from plates ( 0 4 6 ) , cylinders (DZZ), and for laminar channel flow (081) has been determined experimentally. In addition, Purdy (087) presented an analytical solution for laminar channel flow under the influence of a resonant acoustic field. The presence of standing vortices is predicted and experimentally confirmed. Increased interest in heat transfer associated with magnetohydrodynamics is indicated by the number of publications. Theoretical developments in boundary layer analysis (075, 016, 044) represent the extreme complexity of problems in this area. A review of advances of such a nature is beyond the scope of this paper and the references will be included in the bibliography without further comment. Experimental studies are far less numerous and data correlated rather empirically. The heat transfer by free convection through plane layers of mercury and water has been studied and a decrease in heat transfer with applied magnetic field found (027). Natural convective heat transfer in an
'
electrostatic field has been analyzed and checked with the available experimental data ( 0 6 5 ) . Rotating Surfaces. Work on convection heat transfer to rotating surfaces is typified by the paper of Kreith on rotating spheres (059). Agreement between experimental data and the results of a theoretical analysis based on a solution of the boundary layer equation assuming constant thickness was reasonably good. However, a detailed study of the boundary layer flow by several visualization techniques showed a variable boundary layer thickness with a region of complex flow separation in the vicinity of the equation. Other experimental investigations are indicated in Table VI. High Velocity Heat Transfer. Computation procedures are given for the necessary variation in channel area to obtain the desired Mach number for a given heat exchange (066). The complex problem of the sensitivity of heat transfer in the stagnation-point boundary layer to the second-order effect of free stream vorticity is the subject of two theoretical investigations ( 0 7 7 , D 703). Results, while indicating the importance of the interaction, still are not conclusive as there are other second order effects that must be considered. The coupled effects of heat and mass transfer were studied at high velocities (090). A 65y0 reduction in stagnation-point heat transfer was measured for a system in which carbon dioxide was subliming. Radiation Heat Transfer
There were a number of papers in radiation heat transfer which described new or improved methods for analyzing radiation problems. A new method, based on tensor representation, which gives good accuracy and seems to have some advantage of simplicity was described ( E l ) . The calculation of radiation heat transfer in semigray enclosures with specularly and diffusely reflecting surfaces was described (E2). Sparrow (E17) presented a new and simpler formulation for radiative angle factors in which the usual area integrals are replaced by more tractable line integrals. I n a second paper (E18)angle factors for radiant interchange between parallel-oriented tubes were presented. Several special applications were described. Simultaneous radiative and convective heat transfer to a gassolid mixture in slug flow was the subject of a paper (E5). In a paper concerned with radiant heat transfer between people and their surroundings, geometric mean beam lengths were given (E6). In the field of absorbing and emitting gray gases, a Monte Carlo solution was described (E9). The problem of the interaction of conduction, convection, and radiation in the fully developed laminar flow of an absorbing and emitting fluid was considered (E25). Boiling Heat Transfer
Again this year, as has been the case for the past several years, there was a large research activity in the field of boiling heat transfer. Much of this research is still in the familiar area of pool boiling and some progress is being made toward a better understanding of this highly complex mode of heat transfer. VOL. 5 6
NO. 1 2
DECEMBER 1 9 6 4
55
A great deal of research is also in progress on the still more complex field of forced convection boiling of a liquid flowing inside a closed channel. Much of this work is concerned with the mechanism of the heat transfer and is centered on the determination of the flow regimes for the two-phase flow, measurement and correlation of vapor volume fraction, slip velocities, and critical heat flux. Progress in understanding the mechanism is slow, but appears to be steady. I n spite of the tremendous amount of work already done in boiling heat transfer, much remains to be solved before we achieve a n adequate knowledge of this least understood mode of heat transfer. An attempt has been made to classify the papers listed in the bibliography in Table VII.
evaluating the ratio of the eddy diffusivity of heat transfer to that for momentum transfer. He reports that thiy brings theoretical predictions and experimental results into good agreement for flow through pipes, annuli, and rod bundles. In another paper (H7) heat transfer to liquid sodium containing oxygen above the solubility limit was investigated. Packed Beds, Fluidized Beds, and Porous Media
Heat transfer in packed beds, fluidized beds and porous media was the subject of a considerable amount of research. Most of the papers listed in the bibliography arc classified in Table VIII. I t is interesting to note that there were several research papers on the very interesting subject of gas-solid suspension flow. Heat Transfer with Chemical Reaction
Condensation
In almost direct contrast to boiling heat transfer, the number of papers on condensation was very small. There were two reports on condensation in the presence of noncondensable gases. The first of these (G7) was a report of a computer solution for the determination of the condensation rate of vapors from noncondensing gases in laminar flow inside vertical cylinders. This solution could be adapted to wetted-wall columns and other similar problems. The second (G6) was a n experimental study of condensing steam-air mixture in turbulent flow. The condensation coefficient of water was measured (G5). This study reports the fraction of molecules which “stick” upon striking the liquid surface to be between 0.35 and 1.0. A study of dropwise condensation was reported (G4). liquid Metal Heat Transfer
There were very few reports during the past year on original investigations into heat transfer to liquid metals. In one of these Dwyer (H4) developed an equation for TABLE V I I .
REFERENCES ON BOILING HEAT TRANSFER
‘
I
Subject Pool Boiling Theory Bubble Behavior Boiling Mixtures
~
~
Liquid Metals Critical Heat Flux Film Boiiing Convection Boiling Theory Heat Transfer Coefficients Boiling Mixture Swirl Flow Mechanism of Two-Phase Flow Critical Heat Flux Film Boiling
TABLE V I I I .
References (F34, F43, F51,F60) (FlO, F71, F77, F18, F19, FZQ) (F8, F42) (F5, F23, F24, F30)
,
(F37) (F5,F6, F7, F35, F57, F58)
~
11
(F1O’ F50) (F26, F4Q) ( F I , F76, F21, F25, F32) (F16) (F13) ( F I Z , FZO, F28, F33, F36, F45, F46, F 5 2 ) (FQ, F13, F53, F54, F55. F56) (F40)
1
i 1
i
DISPERSED AND POROUS MEDIA ~
Subject Packed Beds Fluidized Beds Gas-solid Suspensions in Flow Porous Materials
56
~
I
References (ri, 15,18,113,114, 118, 122, 124) (12,13, r4, ria, 116, 121) ( m , r 7 , m, 120) ( 1 1 7 , 119)
INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY
Simultaneous heat transfer and reaction of a fluid in turbulent pipe flow is analyzed numerically using Deissler’s eddy diffusivity function ( J 7 ) . The problem is linearized by restricting it to cases of small temperature differences. The effects of Reynolds, Schmidt, and Prandtl numbers upon the reaction are presented. An analog computer solution is given for a homogeneous gas phase reaction occurring between two infinitc parallel plates (J4). Reversible reactions were considered with large temperature differences existing between the plates. The recombination of dissociated diatomic gases on a catalytic surface is of major interest (JZ, J3, J5, J 6 ) . This coupled problem of heat transfer through a laminar boundary layer has been treated for different shapes ; plate, wedge, and cone flows ( J 6 ) ,surface distributions of‘ catalycity ( J 6 ) ,as well as free stream states. Coupled Transport Processes
Mass and heat transfer to a fluid in fully developed turbulent pipe flow is described by a new correlation (K78). This correlation, based on a theoretical continuous eddy-viscosity distribution from wall to center, is in excellent agreement with existing data. Surface roughness and its effect on heat and momentum transfer were measured for random granular protuberances (Krl) and uniform transverse grooves (K72). Carefully restricted experimental conditions were used to verify the mass and heat transfer analogy for gases flowing through packed and distended beds of spheres (K74). Conditions were such that conductive and radiative heat transfer were eliminated and low mass fluxes existed. A second study of transport from spheres to gas streams were published correlating experimental data over a range of sphere sizes from droplet to one foot in diameter and Reynolds numbers from 2 to l o 6 (K6). The resultant empirical correlation had a n over-all standard error of estimate of 15%. Thermal diffusion was the subject of experimental interest (K7, K2) and an exact solution of the thermodynamic coupling of such heat and mass transfer for boundary layers was achieved ( K 7 ) . Interest continues in the coupled processes of heat and mass transfer at a gasporous solid interface. Cases of evaporation ( K 8 , K9) and injection or suction of gases (K7 7 ) were presented.
REFER ENC ES Books Boelter, L. M . K. Cherry, V. H . , others, “Heat Transfer Notes,” McGrawHill, New York (1 963). Holman, J. P., “Heat Transfer,” McGraw-Hill New York (1963). Irvine, T. F., Jr., Hartnett, J. P., “Advances in Heat Transfer, Vol. I,” Academic Press, New York (1964). Kutateladze S. S. edited b Cess R. D. “Fundamentals of Heat Transfer,” trans. from Russian, A’cademic %ress,h e w Ybrk (1964). Schenck H. Jr., “Fortran Methods in Heat Flow,” Ronald Press, New York (19633. Thermal Properties a n d Measurements
J. V., “Calculation of thermal diffusivity from temperature measurements, J . Heat Transfer 85, Ser. C, No. 2, 181 (1963). (A2) Brailsford A. D Major K . G. “The thermal conductivity of aggregates of several phases, inc1;bing pdrous mAterials,” Brit. J. Appl. Phys. 15, No. 3, 313 (1964). (A3) Cape, J. A., Lehman, G. W., “Temperature and finite pulse time effects in the flash method for measuring thermal diffusivity,” J . Appl. Phys. 34, No. 7, Pt. 3, 1909 (1963). (A41 Cape, J. A,, Lehman, G. W., Nakata, M . M. “Transient thermal diffusivity technique for refractory solids,” Ibid., No. 12, p. 3150. (A5) Cerceo, M., Childers, H. M., “Thermal diffusivity by electron bombardment heating,” Ibid., No. 5, Pt. 2, p. 1445. (A6) Cowan, REbert D., “Pulse method of measuring thermal diffusivity a t high temperatures, Ibid., Pt. 2 , p. 926. (A7) Cutler, M Ck,eney, G. T., “Heat-wave methods for the measurement of thermal diffus&ty, Ibtd., No. 7, Pt. 3, p. 1902. (AB) Cutler, hl., Cheney, G. T., “Measurement of thermal conductivity of electrical conductors at high temperatures,” Ibid., No. 6, Pt. 2, p. 1714. (A9) Dougherty, J P “The conductivity of a partially ionized gas in alternating electric fields,” J.’FLzidMecfi.16,126 (1963). (A10) Gibson, C. H., Schwarz, W. H., “Detection of conductivity fluctuations in a turbulent flow field,” Ibid., p. 357. ( A l l ) Jeschke, P., Karsch K H Schwiete H. E. “The thermal conductivityof fire-resistant material," b e ; . In;. Tech. 3 5 , k o . 8 , 185 (1963). (A12) Jones, C. E “A method for predicting the mean thermal conductivity of insulatin materi& a t other than experimental conditions,” J . Heat Transfer 85, Ser. No. 2, 185 (1963). (A13) Keyes F G Vines R. G “The thermal conductivity ofsteam,” Intern. J . Heat Mass ?rakfi;7, No.’l, 33 (ib64). (A14) Masamune S Smith J. M “Thermal conductivity of beds of spherical particles,” Ind. 1Sng’:Chem.$undamerhs 2 , No. 2 , 136 (1963). (A151 Morris, R. G., Martin, J. J., “Thermal conductivity measurements ofsilicon from G80°to 1000°K,” J.Appl. Phys. 34, No. 8 , Pt. 3,2388 (1963). (AlG) Nani ian, J., “Thermal Properties of Thermocouples,” Instr. Control Systems 36, No. 18, 87 (1963). (A17) Patterson D. J. Van Wylen G. J. “Em irical Heat capacity equations for idealgases,” j.Heat’Transfer 8 5 , deries d, No. 281 (1963). (A18) Pinchera, G. C., “Heat transfer by means of organic liquids,” Enegin Nucl. 10, 319-335 (1963). (A1 9) Sadykov, B. S., “The emissive ower of metals and its relationship to thermal conductivity,” Intern. Chem. Eng. 4, Go. 1, 132 (1964). (AZO) Schlunder, E. U., “Messung der warmeleitfahigkeit von gas/dampfgemischen mit einem kurzzeitverfahren,” Chem. Ing. Tech. 36, No. 2 , 115 (1964). (A21) Stiel, L. I., Thodos, G., “The thermal conductivity of nonpolar substances in the densegaseous and liquid regions,” A.I.Ch.E.J. 10, No. 1, 26 (1964). (A22) Touloukian, Y. S., “The thermophysical properties research center. An effective answer to information needs on thermophysical properties of matter,” Intern. J . Heat Mass Transfer 6 , No. 4, 301 (1963). (A23) Uhl, V. W., Voznick, H. P., “High temperature heating media. Molten salt as a heat transfer medium,” Chem. Eng. Progr. 59, 33 (1963).
(Al) B ,!e:
8,
{
H e a t Tranafer i n Equipment (Bl) Allemann R. T., Johnson, B. M., “Radiant-heat, spray-calcination process for so1idifica;ion of radioactive waste,” Ind. Eng. Chem. Process Design Develop. 2, No. 3, 232 (1963). (BZ) Andersen, H. E., “Heat transfer and stirring efficiencyin astirrer vessel fitted with boundary-layer and blade stirrers,” Chem. Ing. Tech. 35, No. 12, 824 (1963). (B3) Briggs, D. E., Katz, D. L Young, E. H. “How to design finned tube heat exchangers,” Chem. Eng. Prog. 39, No. 11,49 (lb63). (B4) Bump, T. R “Average temperatures in simple heat exchangers,“ J . Heal Transfer 85, S e d C, No. 2, 182 (1963). (B5) Buonopane, R . A,, Troupe R . A. Morgan J. C. “Heat transfer design method for plate heat exchangers,” Ciem. E&. Prog. i , 5 7 i1963). (B6) Collicott, H. E., Fontaine W. E. Witzell 0. W. “Radiation and free convection heat transfer from wire dnd tude heat e;chang&s,” ASHRAE J . 5, Pt. 2, 79 (1963). (B7) Danilov, I. B., Keilin, V. E “Heat transfer and hydraulic resistance in flow along tubes withspiral fins,” Br;;. Chem. Eng. 8, Pt. 2,424 (1963). (BB) Davidmann, M., “Design of direct-cooling plant,” Chem. Proc. Eng. 44, No. 8 , 657 (1963). (B9) Emerson, W. H “Shell-side pressure dro and heat transfer with turbulent flow in segmental$ baffled shell-and-tube geat exchangers,“ Intcrn. J . Heat Mass Transfer 6 , No. 8 , 649 (1963). (B10) English, K G Jones W T others “Flooding in a vertical updraft partial condenser,” Chkm.’kng.P;og. 59, Go. 7, 5 i (1963). (B11) Fair, J. R., “Vaporizer and reboiler design,” Chem. Eng. 70, Pt. 3, 101 (1963). (B12) Ibid., p. 119. (B13) Goeke, E., “A regenerative high-temperature heater for air blast and gases,” Chem. Ing. Tech. 35, No. 9, 654 (1963). (B14) Grens E. A. I1 McKean R. A,, “Temperature maxima in counter-current heat exchkgers wit‘h internal’heat generation,” Cfiem. Eng. Sci. 18, No. 5, 291 (1963). (B15) Guy, R . F. W., “Development of the shell boiler,” Chem. Proc. Eng. 44, No. 11, 638 (1963). (B16) Haller, H. C., Stockman, N. O., “A note on fin-tube view factors,” J . Heat Transfer 85, 380-381 (1963). (B17) Hausen H “Berechnung der warmeubertragung in regeneratoren bei temperaturabhazgigen stoffwerten and warmeubergangszahlen,” Intern. J . Heat Mass Transfer 7, No. 1, 113 (1764).
(B18) Henley, J. A “A European approach to air cooling,” Chem. Proc. Eng. 44, No. 8, 481 (183) Reynolds, W. C., “Turbulent heat transfer in a circular tube with variable circumferential heat flux,” Intern. J . Heat Mass Tranrjer 6, 445-54 (1963). (1184) Reynolds, W. C., Lundberg, R. E., McCuen P. A. “Heat transfer in annual passages. General formulation of the problem’for aibitrarily prescribed wall temperatures or heat fluxes,” Ibid., pp. 483-93. (1185) Richardson, P. D., “ O n Hilpert’s measurement of heat transer from cylinders transverse to an aintream,” J. Heat Trunsfer 85, Ser. C, So. 3, 283 (1963). (D8G) Riley, N., “Unsteady heat transfer for flow over a flat plate,” J . Fluid Mech. 17, Part 1, 97 (1963). (D87) Romanenko, P. N., Kharchenko, V. N., “The effect of transverse mass flow on heat transfer and friction drag in a turbulent flow of compressible gas along an arbitrarily shaped surface,” Intern. J . Heat M a s s Transfer 6 , No. 8 , 727 (1963). (D88) Rotta, J. C., “Temperaturverteilungen in der turbulenten grenzschicht an der ebenen platte,” Ibid., 7, KO,2, 215 (1964). (D89) Seban, R. A,, McLaughlin, E. F., “Heat transfer in tube coils with laminar and turbulent flow,” Ibid.,6 , No, 5 , 387 (1963). (D90) Sho;t, W. W., Dana, T. A., “Eflect of sublimation on stagnation-point heat transfer. A.1.Ch.E.J. 9.No. 4., 509 ,11963). , (D91) Siegel, R., “Forced convection in a channel with wall heat capacity and with wall heating variable with axial position and time,” Intern. J . Heat M a s s Transfer 6 , KO.7, p. 607 (1963). (D92) Siegel, R., Perlmutter M., “Laminar heat transfer in a channel with unsteady flow and wall heat& varying with position and time,” J . Heat Transfer 85, Series C, No. 4, 358 (1963). (D93) Simon, H . .4., Eckert, E. R. G., “Laminar free convection in carbon dioxide near its critical point,” Intern. J . Heat M a s s Transfer 6 , l i a , 8, 681 (1963). (D94) SpaLrow, E. M., Lin, S. H., “Turbulent heat transfer in a parallel-plate channel, Ibid.,6 , No. 3, 248-249 (1963). (D95) Sparrow, E. M., Lin, S. H., “Turbulent heat transfer in a tube with circumferentially-varying temperature or heat flux,” Ibid., 6, No. 102, 866-7 (1963). (D96) Spzxrow, E. M., Novotny, J. L., Lin, S.H., “Laminar flow of a heat-generating fluid in a parallel-plate channel,” A.1.Ch.E.J. 9, 797-804 (1963). (D97) Squire, W., “Temperature profiles for turbulent flow of air in pipe I. T h e fully developed heat transfer region,” Chem. Ene. Sci. 19, No. 1, 87 (1964). (D98) Starner, K . E., McManus, H. N., Jr., ”An experimental investigation of free-convection heat transfer from rectangular-fin arrays,” J . Heat Transfer 85, Ser. C, No. 3, 273 (1963).
6,
I
(D99) Stewart, W. E., “Forced convection in three dimensional flows. I. Asymptoticsolutionsfor fixed interfaces,” A.I.Ch.E.J. 9, No. 4, 528-535 (1963). (D100) Stone H.L Brian P. L. T “Numerical solution of convective transport problems,” )A.Z.Ch:k.J. 9,’No. 5, 6g1 (1963). (DlOl) St. Pierre C., Tien, C., “Experimental investigation of natural convection heat transfer in’confined space for nowNewtonian fluid,” Can. J . Chem. Eng. 41, 122-127 (1963). (D102) Strunk, M. R., Tao, F. F., “A numerical method for the solution of the energ equation for steady turbulent heat transfer,” A.Z.f.7h.E.J. 10, NO. 2, 269 (1964r. (D103) Sutera, S. P., Maeder, P. F., Kestin, J., “On the sensitivity of heat transfer in the stagnation-point boundary layer t o free-stream vorticity,” J . Fluid Mecir. 16, 497 (1963). (D104) Szablewski, W., “Turbulente vermischung runder Kaltluftstrahlen mit umgebender ruhender heissluft,” Intern. J . Heat Mass Transfer 6 , NO. 8, 739 (1963). (D105) Tanimoto S. Hanratty T. J. “Temperature fluctuations accompanying turbulent heat tran;fer in a piie,” Chkm. Eng. Sn’. 18, No. 5, 307 (1963). (D106) Tao, L. N., “On unsteady heat transfer of combined free and forced convection in circular tubes,” J . Appl. Much. 30, Ser. E, No. 2, 257 (1963). (D107) Twefik, 0. E., Yang, J., “The thermodynamic coupling between heat and mass transfer in free convection with helium injection,” Intern. J . Heat Mass Transfer 6 , No. 10, 915 (1963). (D108) Thomas R A Cobble M. H . “Radial fiow heat transfer,” J . Heat Transfer 85, Sdries‘C,’ho. 2, 18; (1963): (D109) Tien, C. L., “A note on distributions of temperature and eddy diffusivity for heat in turbulent fiow near a wall,” Z A M P 15, No. 1, 63 (1964). (DllO) Tien, C. L., Campbell, D. T., “Heat and mass transfer from rotating cones,” J . Fluid Mech. 17, Part 1, 105 (1963). (Dill), Tien, C. L., Tsuji, J., “Heat transfer by laminar forced flow against a non-mothermal rotating disk,” Intern. J . Heat Mass Transfer 7, No. 2, 247 (1964). (D112) Tritton, D. J “Turbulent free convection above a heated plate inclined a t a small angle t o thd’horizontal,” J . Fluid Mech. 16, 282 (1963). (D113) Vansant, J. H., Larson, M . B., “Heat transfer from a semi-infinite rectangularstrip,” J . Heat Transfer 85, Series C , No. 2, 191 (1963). (D114) Viskanta R., “Effect of transverse magnetic field o n heat transfer to a n electrically codducting and thermal radiating fluid flowing in a parallel-plate channel,” Z A M P 14,No. 4,353 (1963). (D115) Wethern, R. J., Brodkey, R. S., “Heat and momentum transfer in laminar flow: Helium initially a t plasma temperatures,” A.I.Ch.E.J. 9, 49-54 (1963). (D116) Wood, R. D., Smith, J. M., “Heat transfer in the critical re ion temperature and velocity profiles in turbulent flow,” Ibid., 10,No. 2, 180 6964,. (D117) Yang, K.-T., Jerger, E. W., First-order perturbations of laminar freeconvection boundary layers on a vertical plate,’> J . Heat Transfer 86, Ser. C, No. 1, 107 (1964). (D118) Yen, J. T., “Effect of wall electrical conductance on magneto-hydrodynamic heat transfer in a channel,“ Zbid., 85, Ser. C, No. 4, 371 (1963). (D119) Young, R. J., Yang K.-T. “Effect of small cross flow and surface-tem era ture variation on lamina: free cAnvection along a vertical plate,” J . ~ p p ~ . 30, Ser. E, No. 2, 252 (1963).
Lei
Radiation H e a t T r a n s f e r ( E l ) Adrianov V. N Polyak C L. “Differential methods foi studying radiant heat transfer,’” Intern: J . Htat)M& ?ransfer 6,No. 5, 355 (1963). (E2) Bobco, R . P., “Radiation heat transfer in semigra enclosures with s ecularly and diffusely reflectingsurfaces,” J . Heat Transfer 86, ger. C, No. 1, 123 8964). (E3) Chao, K . C., “Reradiation to furnace tubes. Effect of tube-to-wall clearance,” A.I.Ch.E.J. 9. No. 4. 555-558 (19641. (E4) Chon, J. C., “Simultaneous radiative and convective heat transfer in an absorbing, emitting, and scattering medium in slug flow between parallel plates,” Ibid., 10, No. 2, 253 (1964). (E51 Costello b. A., A note on the paper, “Analysis, results, and interpretation for radiatioh between some simply arranged gray surfaces,” J . Heat Transfer 8 5 , Ser. C, No. 2, 182 (1963). (E6) Dunkle, R V. “Geometric mean beam lengths for radiant heat-transfer calculations,” ibid.,’ 86, Ser. C, No. 1, 75, (1964). (E71 Haller H C. Stockman N. O., “A note on fin-tube view factors,” Ibid.? 85, Series No. 380 (19633. (E8) Heaslet, M . A., Fuller F. B “Cylindrical sections with uniform difluseradiation characteristics,” htern. j : H e a t Transfer 6 , No. 12, 1049 (19G3). (E9) Howell J. R. Perlmutter, M., “Monte Carlo solution of thermal transfer through mdiant Aedia between gray walls,” J . Heat Transfer 86, Ser. C , No. 1, 116 (1946). (E10) Khosla P. K Murgai M. P., “A study of t h e combined effect of thermal radiative tr6nsfer ‘6nd rotahon on the gravitational stability of a hot fluid,” J . Fluid Mech. 16, 97 (1963). ( E l l ) Kutateladze, S. S., Leont’ev, A. I., Robtsov, N. A., “An a p raisal of the role of radiation in the consideration of heat transfer in a turbulent goundary layer,” Intern. Chem. Eng. 4, No. 1, 32 (1964). (E12) Madejski, J., “Radiative heat transfer between moving surfaces,” Intern. J . Heat Mass Transfer 6 , No. 12, 1019 (1963). (E13) Mikk, I. R., “Approximation calculation of radiant heat transfer in a duct of rectangular cross section,” Zbid., 7 , No. 3, 293 (1964). E14) Olmstead W. E Raynor S “Solar heating of a rotating solid cylinder,” Quurt. &I. M h 21,’ho.2, 81’(1$63). (E15) Pennington, C . W., Smith, William A,, others “Experimental analysis of solar heat gain through insulating glass with indodr shaking,” ASHRAE J . 6 , No. 2, 27 (1964). (E16) Perlmutter M Howell J. R. “A strong1 directional emitting and absorbing surface,” J .kea7 Tram/er)ll5, Sir. C, No. 3, l 8 2 (1 963). (E17) Sparrow, E. M., “A new and simpler formulation for radiative angle factors,”Zbtd., 85,Ser. C,No. 2, 81, (1963). (E18) Sparrow, E. M., Jonsson, V. K., “Angle factors for radiant interchange between parallel-oriented tubes,” Ibid., 85, Ser. C , No. 4, 382 (1963). (E19) Sparrow, E. M., Jonsson, V. K., “Fluid flow and convective-radiative energy transfer in a arallel plate channel under free-molecule conditions,’’ A.2.Ch.E.J. 9, No. 4, 51f!(1963j. (E20) Sparrow E. M Jonsson, V. K., “Simultaneous heat tiansfer in a circular tube by free-’molec;ie convection and thermal radiation,” Intern. J. Heat Mass Transfer 6 , No. 9, 841 (1963). (E21). Sparrow, E. M., Johnsson, V. K., “Thermal radiation in rectangular-groove cavities,’‘ J . &pi. Mech. 30, 237-244 (1963). ~I
0,
4,
(E22) Sparrow, E. M., Jonason V K., “The transport of radiant energy through tapered tubesor tapered gaps,:’ J : Heat Transfer 86, Ser. C , No. 1,132 (1964). (E23) Stops D. W., “Heat transfer by simultaneous conduction and radiation through a’non-absorbing medium,” B n t . J . Appl. Phys. 15, No. 3, 311 (1964). (E24) Vetlutskii, V. N., Onufriev, A. T., “Radiation cooling of a gas flowing in a flat channel,” Intern. Chem. Eng. 3, No. 2, 230 (1963). (E25) Viskanta R., “Interaction of heat transfer b conduction, convection, and radiation in a’radiating fluid,” J . Heat Transfer85, Zer. C, No. 4, 318 (1963). (E26) Wiebelt, J. A,, “Comparison of geometric absorption factors with geometric mean beam lengths,”Ibid., 85, Ser. C, No. 3, 287 (1963). (E27) Yellott, J. I., “Selective reflectance-A new approach to solar heat control,” ASHRAE J . 6 , No. 1, 87 (1964).
Boiling H e a t Transfer ( F l ) Anderson, G. H., Haselden G. G. Mantzourank, B. G., “Two-phase (gasliquid) flow phenomena. IV.’ Expehmental study of water evaporation in a vertical tube,” Chem. Eng. Sa. 17, 751-769 (1963). (F2) Asch, V., “Predicting and using liquid-boiling behavior,” Chem. Eng. 70, Pt. 2 , 125 (1963). (F3) Bentwich, M., Sideman, S., “Temperature distribution and heat transfer in annular two-phase (liquid-liquid) flow,” Can. J . Chem. Eng. 42, No. 1, 9 (1964). (F4) Brauer, H., “The calculation of heat transfer during bubble evaporation,” Chem. Is. Tech. 35, No. 11, 764 (1963). (F5) Carne, M., “Studies of the critical heat-flux for some binary mixtures and their components,” Can. J . Chem. Eng. 41, No. 6, 235-241 (1963). (F6) Chang T -P “Some possible critical conditions in nucleate boiling,” J . Heat Tranifer 85,’ber. C, No. 2, 89 (1963). (F7) Costello, C. P., A d a m , J. M., “The interrelation of geometry, orientation, and acceleration in the peak heat flux problem,” A.Z.Ch.E.J. 9, No. 5 , 663 (1963). (F8) Darby, R., “The d namics of vapour bubbles in nucleate boiling,” Chem. Eng. Sci. 19,No. 1, 39 (r964). (F9) Doroshchuk, V. E., Lantsman, F. P., “Effect of pressure and mass flow rate on burnout heat fluxes in a water and steam-water mixture flow i n tubes,” Intern. J . Heat Mass Transfer 7, No. 2, 187 (1964). (F10) Frederking H. K., “Laminar two-phase boundary layers in natural convection film boilin$,” Z A M P 14, No. 3,207 (1963). (F11) Fritz W., “The fundamentals of heat transfer on evaporating liquids,” Chem. Zng: Tach. 35, No. 11, 753 (1963). (F12) Fukie H., “A relation between steam quality and void fraction in two-phase ffow,” A.i.Ch.E.J. 10, No. 2, 227 (1964). (F13) Gambill W. R., Bundy, R. D., “High-flux heat transfer characteristics o f pure ethylend glycol in axial and swirl flow,” Ibid., 9,55-59 (1963). (F14) Githinji P. M., Sabersky, R . H., “Some effects of the orientation of the heatingsurface in nucleate boiling,” J . Heat Transfer 85,379 (1963). (F15) ,Grassman;, P., Hauser, I. J., “Heat transfer from wire to rubcooled and boiling water, Intern. J . Heat Mass Transfer 7, No. 2, 211 (1964). (F16) Green G. H., Furse, F. G., “Effect of oil o n heat transfer from a horizontal tube to boiiing refrigerant 12-oil mixtures,” ASHRAE J . 5 , Pt. 2, 63 (1963). (F17) Hamill, T. D., Bankoff, S. G., “Growth of a vapour film a t a rapidly heated planesurface,” Chem. Ens. Sa’.18, No. 6, 355 (1963). (F18) Hamill, T. D., Bankoff, S. G., “Maximum and minimum bounds for the growth of a vapour film a t the surface of a rapidly heated plate,” Ibid., 19, No. 1, 59 (1964). (F19) Hara, T., “The mechanism of nucleate boiling heat transfer,” Intern. ~ J Heat . Mass Transfer 6 , 959-69 (1963). (F20) Hewitt G. F King I Lovegrove, P. C., “Holdup and pressure drop measurements i; the &o-ph&e’)annular flow of air-water mixtures,” Brit. Chem. Eng. 8, No. 5, Pt. 2, 311 (1963). (F21) Hirata M . , Nishiwaki, N., “Skin friction and heat transfer for liquid flow over a POI-ous wall with gas injection,” Intern. J. Heat Mass Transfer 6 , No. 11, 941 (1963). (F22) Holt, V. E Grosh R . J., “Free convection heat transfer up to near-critical conditions,” N;heonics 41, No. 8, 122 (1963). (F23) Hovestreudt, J., “The influence of the surface tension difference on the boiling of mixtures,” Chem. Ens. Sci. 18, No. 9, 631 (1963). (F24) Huber, D. A., Hoehne, J. C., “Pool boiling of benzene, diphenyl, and benzene-diphenyl mixtures under pressure,” J.Heat Transfer 85, Ser. C, No. 3, 215 (1963). (F25) Hughmark, G. A. “Heat transfer in horizontal annular gas-liquid flow,” Chem. Eng. Progr. 59,NA. 7, 54 (1963). (F26) Jiji L. M., Clark, J. A,, “Bubble boundary layer and temperature profiles for forcdd convection boiling in channel flow,” J.Heat Transfer 86, Series C, No. 1, 50 (1964). . . (F27) Kast, W., “Investigations into heat transfer in bubble columns,” Chem. Ing. Tech. 35. No, 11.. 785 .(1963). . (F28) Levy S., “Prediction of two-phase ressure dro and density distribution from mix:ng length theory,” J . Heat Trans& 85, Series No. 2, 137-52 (1963). (F29) Lienhard J. H., Schrock, V. E., “The effect of pressure, geometry, and the e uation ofstAte upon the peak and minimum boiling heat flux,” Ibid., 85, Ser. C , 3, 261 (1963). (F30) McEligot, D. M., “Generalized peak heat flux for dilute binary mixtures,” A.I.Ch.E.J. 10, No. 1, 130 (1964). (F31) Markels, M., Jr., Durfee, R. L., “The effect of applied voltage on boiling heat transfer,” Ibid., p. 106. (F32) Miropolski, E. L., “Heat transfer a t the film-type boiling of water-vapour mixture inside the vapour-generating tubes,” Brit. Chem. Eng. 8, No. 8, Pt. 2, 580 (1963). (F33) Moissis R . “The transition from slug to homogeneous two-phase flows,” J . Heat Tra&ferh5, Ser. C, No. 4, 366 (1963). (F34) ,Moissis R., Berenson P J., “ O n the hydrodynamic transitions in nucleate boiling,” Zdd., 85, Ser. C,ko’. 3, 221 (1963). (F35) Mostinski I. L “Application of the rule of corresponding states for the calculation of’heat t;ansfer and critical heat flux to boiling liquids,” Brit. Chem. Eng. 8, No. 8 , Pt. 2, 580 (1963). (F36) Nedderman, R. M., Shearer, C. J., “The motion and frequency of large disturbance waves in annular two-phase flow of air-water mixtures,” Chem. Eng. Sci. 18, No. 10, 661 (1963). (F37) Noyes, R C. “An experimental study of sodium pool boiling heat transfer,” J . Heat Transj&r 8k, Ser. C, No. 2, 125 (1963). (F38) Nussbaum, 0. J., “Eva oration of refrigerant 12 inside horizontal tubes, ASHRAE J . 5 , Pt. 2,41 (19637.
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DECEMBER
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(F39) Pike, R., Ward, H. C., “Adiabatic, evaporating, two-phase flow ofsteain and water in horizontal pipe,” A.I.Ch.E.J. 10, No. 2,206 (1964). (F40) Polomik, E. E., Levy, S., Sawochka, S. G., “Film boiling of steam-water mixtures in annular flow at 800, 1100, and 1400 psi,” J. Heat Tronsfer 8 6 , Ser. C, No. 1, 81 (1964). (F41) Ratiani, G . V., Agalinani, D. V., “Heat transfer to boiling refrigerants 12 and 22,” A S H R A E J . 5 , Pt. 2, 53 (1963). (F42) Rennie, J., “Some qualitative observations of bubble behavior resulting from photographic and schlierenstudies,” Chem. Eng. Sci. 18, No. 9, 641 (1963). (F43) Ruckenstein E. “A physical model for nucleate boiling heat transfer,” Intern. J.Heat .’11;ss ?ransfer7, No. 2, 191 (1964). (F44) Satterfield, C. N., Audibert, F . P., “Nucleate and film boiling in the catalytic decomposition of hydrogen peroxide,” Ind. Eng. Chem. Fundamentals 2 , No. 3, 200 (1963). (F45) Schrock, V. E,, Angelino, G., others, “Density measurements in a boiling channel,” Energia Nucl. 10, S o . 10, 525 (1963). (F46) Schrock, V. E,, van Erp J. B. Possa G. “Analysis of steady state density changes in boiling coolants,” ?bid., li, No. 2: 57’(1964). (F47) Shitsman M . E. “The problem of critical heat exchange in steam-generating channels,”Int.kn. Cheh. Eng. 3, No. 3, 355 (1963). (F48) ,Sims, G. E Aktuerk, U., Evans-Lutterodt, K . 0 . “Simulation of pool boiling heat tran:fer by gas injection at the interface,” Inter;. J . Heat Mass Transfer 6 , 531 (1963). (F49) Snyder, W. T., “An analysis of slug flow heat transfer in a n accentric annulus,”A.I.Ch.E.J. 9, 503-6 (1963). (F50) Sparrow, E. M., “The eflect of radiation on film-boiling heat transfer,” Intern. J . Heat Mass Transfer 7, No. 2, 229 (1964). (F51) Stephan, K., “A mechanism and picture 9f the processes involved in heat transfer during bubble evaporation,” Chem. Ing. Tech. 35, No, 1, 775 (1963). (F52) Taylor, N. H., Hewitt, G. F., Lacey, P. M. C., “The motion and frequency of large disturbance waves in annular two-phase flow of air-water mixtures,” Chem. Eng. Sci. 18, No. 8, 537 (1963). (F53) Tippets, F. E., “Critical heat fluxes and flow patterns in high-pressure boiling water flows,” J. Heat Transfer 86, Ser. C, No. 1, 12 (1964). (F54) Tippets, F. E., “Analysis of the critical heat-flux condition in high-pressure boiling water flows,” Ibid., p. 23. (F55) Tong, L. S., Cnrrin, H. B., Thorp, A. G. 11, “New correlations predict DNR conditions,” NucIeonicr 21, No. 5, 43-7 (1963). (F56) Topper L. “A diffusion theory analvsis of boiling burnout in the fog flow regime,” J . k e a ; Transfer 85, Ser. C, No. 3,‘284 (1963). (F57) Vliet G. C. Leppert G. “Critical heat flux for nearly saturated water flowing n&al td a cylind&,” ?bid., 8 6 , Ser. C, No. 1, 59 (1964). (F58) Vliet, G. C. Lep ert G “Critical heat flux for subcooled water flowing normal t o a cylinber,” fbid.: 68:) (F59) Waters E D Fitzsimmons D. E. “DNB varies with rod spacing in 19-rod bundles,” i u c i e o n h 21, No. 10, b6 (19i3). (F60) Zuber, N., “Nucleate boiling, T h e region of isolated bubbles and the similarity with natural convection,” Intern. J . Heat .Mass Tranrjer 6 , 53-79 (1963).
Condensation
(Gl) Baasel W. D., Smith J. C “.4 mathematical solution for the condensation of vapors ‘from non-condknsing’gases in laminar flow inside vertical cylinders.” A.I.Ch.E.J. 9, No. 6, 826 (1963). (G2) Gyarmathy, V. “Zur wachstumsgeschivindigkeit kleiner, flussigkeitstropfen i n einer ubersattigten atmosphere,” ZA,I.lP 14, KO.3, 280 (1963). (G3) Hill, P. G., Witting H. Demetri E. P. “Condensation of metal vapors during rapid expansion,” J.~ e 57ansfer d d , Ser.’C, No. 4, 303 (1963). (G4) Kast, W., “Heat transfer in dropwise condensation,” Chem. Ingr, Tech. 35, 163-168 (1963). Nabavian K. Bromley L. A,, “Condensation coefficient of water,” Chem. (Gi!g, Sn‘. 18, do. Ib, 651 (19i3). (G6) Stewart, P. B., Clayton, J. L., others, “Condensing heat transfer in steam-air mixtures in turbulent flow,” Ind. Eng. Chem. Process Design DeaIop. 3, No. 1, 48 (1964). Liquid M e t a l H e a t Transfer (Hl) Borishanksii, V. M., Firsova, E. \’., “Heat transfer in the longitudinal flow of metallic sodium around a bundle of tubes,” At. Energy (USSR) 14, KO. 6, 584-585 (1963). (H2) Brooks, R. D., Bonilla, C. F., “Liquid-metal heat transfer,” Nzcleonics 2 2 , No. 3, 43 (1964). (H3) Bueckner, H., Horvay, G., “Heat-transfer coefficient of inviscid fluid freezing onto a moving heat sink,” J . Heat Transfer 8 5 , Ser. C, No. 3, 246 (1963). (H4) Dwyer, 0. E., “Eddy transport in liquid-metal heat transfer,” A.I.Ch.E.J 9, 261-268 (1963). (H5) Fraas, A. P., “Boiling potassium reactor for space,” Nucleonics 2 2 , No. 1, I72 (1964). (H6) Strauss, S. W., “The tem erature dependence of the density of liquid metals,” h’ucl. Sci. Eng. 18, S o . 2,280 b964). (H7) Zablotxkaya, T. V., Ivashchenko, N. I., “Heat transfer to a liquid metal flowinginsidea tube,” At. Energy (USSR)14, No. 3, 320-322 (1963).
Packed Beds, Fluidized Beds, a n d Porous Media
(11) Baskakov, A. P., Vershinina, V. S., “An investigation of heat transfer between a packing and a fluidized bed in the interstices,” Intern. Ckem. Eng. 4, No. 1, 119 (1964). (12) Blacker, P. T., McLain, D. R. “Heat transfer coefficient and temperature gradientsin fluidized beds,” Brit. C h n . Eng. 8 , S o . 6, Pt. 2, 422 (1963). (13) Bprodulya V. A,, “Thermal calculations in a thin fluidized bed with transverse wotionofthe)heat transfer medium,” Intern. Chem. Eng. 4, No. 1 , 110 (1964). (14) Bradshaw, R . D., Myers: J. E., “Heat and mass transfer in fixed and fluidized beds oflarge particles,” A.2.Ch.E.J. 9, KO.5, 590 (1963). (15) Cbukhanov, Z. F., “Heat and mass transfer between gas and granular material,” Intern. J . Heat M o s s Transfer 6 , No. 8, 691 (1963). (16) Danziger, W. J. “Heat transfer to fluidized gas-solids mixtures in vertical transport,” Ind. Eng: Chem. Process Design Develop. 2 , No. 4, 269 (1963). (17) Depew, C. A,, Farbar L. “Heat transfer to pneumaticallv conveyed glass particles on fixed size,’’ J.’Heo; Transfer 85, Series C, No. 2, 164 (1963).
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(18) Elukhin, K., Starovitskii, S. I., “Heat exchange and hydraulic resistance in dumped packings of regenerators,” Intern. Chem. Ens. 4, No. 1, 114 (1964). (19) Farbar, L., Depew, C. A,, “Heat transfer eflects to gas-solids mixtures using solid spherical particles of uniform size,” Ind. Etig. Ciiem. Fundamentals 2 , No. 2, 130 (1963). (110) Gel’perin, N . I., Ainshtein, V. G., Aronovich, F. D . , “ T h e eflect ofscreening on heat transfer in a fluidized bed,” Intern. Chem. Eng. 3, KO. 2, 185 (1963). (111) Kaganer, M. G., Glebova, L. I., “The effect of the bulk weight of a porous material on heat transfer,” Ibid.,.3, No. 4, 487 (1963). (112) Malek, M. A,, Lu, B. C. Y., “Heat transfer in spouted beds,” Can. J . Chen!. Eng.42,No. 1,14(1964). (113) McConnachie, J. T. L., Thodos, G., “Transfer processes in the flow of gases through packed and distended beds of spheres,” A.I.Ch.E.J. 9, 60-64 (1963). (114) Nordon, P., Mchlahon, G. B., “The Theory of forced convective heat transfcr in beds offine fibers-I,” Intern. J . Heat M a s s ~ ‘ m n i f e r6 , No. 6, 455 (1963). Nordon, P., McMahon, G . B. “Theory of forced convective heat transfer iri ‘Ib5,’ds of fine fibres-11,’’ Ibid.,p. 467. (116) Rowe, P. N., “Comments on heat transfer between solid particles and a gas in a non-uniformly aggregated fluidized bed,” Ibid., No. 11, 989-91 (1963). (117) Shabanov, S. I., “An analytical investigation of the beating of a granular material mixed with a solid heat-transfer medium,” Intern. Chem. Eng. 3, No. 2, 225 (1963). (118) Solntsev, M. Ya., Bobe, L. S., Korotarva, G. K., “Determination of the coefficients of heat transfer from a gas to a bed of free-flowing materials,” Ibid., 21 5. (119) Sugawara, A,, “Heat transfer accompanying fluid flow in porous materials,” Australian J . Appl.Sci. 14, No. 2, 109 (1963). (120) Themelis, N. J., Gauvin, W. H., “Heat transfer to clouds of particles,” Brit. Chem. Eng. 8,No. 6 , Pt. 2, 422 (1963). (121) Vakhrushev, I. A,, Botnikov, Ya. A., Zenchenkov, N. G., “Heat transfeerfroni a fluidized bed of hot coke to the surface of horizontal tubes,” Intern. Chem. Eng. 3, No. 2, 207 (1963). (122) Yagi, S., Kunii, D., Endo, K., “Heat transfer in packed beds through which water is flowing,” Intern. J . Heat M o s s Tronrfer 7, No. 3, 333 (1964). (123) Zabrodsky, S. S., “Heat transfer between solid particles and a gas in a nonuniformly aggregated fluidized bed,” Ibid., 6 , 23-31 (1963). (124) Ziegler, E. N., Brazelton, W. T . , “Radial heat transfer in a packed-fluidizwl bed,” Ind. Eng. Chem. Process Design Deueio,b. 2, No. 4, 276 (1963).
H e a t Transfer with Chemical Reaction (Jl) Brian, P. L. T . , “Turbulent pipe flow heat transfer with a simultaneous ihsniical reaction of finite rate,” A.I.Ch.E.J. 9, KO.6, 831 (1963). (52) Cottingham, W.B., Grosh, R. J., “Surface recombination and heat transfer in a dissociated diatomic gas-Part I,” J . Heat Transfer 85, Ser. C, No. 2, 101 11963). . . (J!) Cottingham, W.B., Grosh, R. J., “Surface recombination and heat transfer Ln a dissociated diatomic gas-Part 11;” Ibid., p. 107. (54) Fan, S. S. T.. Rozsa, R. B., Mason, D. hl., “Heat transfer in reacting system,” Chem. Eng. Sci. 18, No. 12, 737 (1963). (J5) Fenster, S. J., Heymen R. J. “Heat transfer in dissociated air with variable heat of dissociation,” Inled. J . Hiat ‘Uass Transjtr 6 , No. 12, 1063 (1963). (J6) Inger G. R “Dissociated !aminar boundarr laver flows o\’er surfares with arbitrar; continuous distributions of catalycity,” Ibid., 6 , No. 9, 815 (1963). (57) Knurh, E. L., “A preliminary study of the use of reference states in Dredicting transport rates in flows with chemical reactions,” Ibid., 6 , No. 12, 1083 (1963). Coupled Transport Processes
( K l ) Baron J. R . “Thermal diffusion eflects in mas? transfer,” Intern. J . Heat Mass T r a & f e r6 , N o . 12, 1025 (1963). (K2) Berkau: E. E., Fisher, G. T., “Soret cell diffusion in two anion-two cation salt solutions,” Ibid.,7, No. 2, 253 (1964). (K3) Brusset, H., Peuscet, J., Levan, J. C., “Eflects of heat and mass transfer in rectification,” Brit. Chem. Eng. 8 , No. 11, 746 (1963). (K4) Dipprey, D. F., Sabersky, R. H., “Heat and momentum transfer in smooth and rough tubes a t various Prandtl numbers,” Intern. J . Heal M a s s Transfer 6 , No. 5, 329 (1963).
(Kj) Freedman, S. I., Kaye, J., “Simultaneous heat and mass transfer in the com-
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