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INDUSTRIAL AND ENGINEERING CHEMISTRY
(5J) Kippenhan, C. J., and Croft, H. O., Trans. Am. SOC.Mech. Engrs., 74, No. 7, 1151-6 (1952). (6J) Kistiakowsky, G. B., J . Chem. Phys., 19, No. 12, 1611-12 (1951). (75) Ledinegg, M., 2. V e r . deut. Ing., 94,No. 28, 921-7 (1952). (85) Lessen, M., J . Aeronaut. Sci., 19, No. 12, 852-64 (1952). (9J) Manton, J., Elbe, G. von, and Lewis, B., J . Chem. Phzls., 20, NO,1,153-7 (1952). (105) Oppenheim, A. K., J . A p p l . Mechanics, 19, No. 1, 63-71 (1952). (113) Price, E. W., J . A p p l . Phys., 23, No. 1, 142-6 (1952) (12J) Roy, M., Compt. rend., 234, No. 2, 168-70 (1952). (135) Ibid., 234, NO.3,268-71 (1952). (145) Scheller, K., and Bierlein, J. A , , J . Am. Rocket SOC.,22, 245 (1952). Aerodynamics (1K) Flax, A. H., J . Aeronaut. Sei., 19,No.6, 361-74 (1952). (2K) Germain, P., Publ. sci. el tech. m i n i s t h e uir(France), No. 250,
217-50 (1951). (3K) Hoerner, S. F., “Aerodynamic Drag,” Midland Park, New Jersey, 1951. (4K) Longhorn, A. L., Quart. J . Mechanics and A p p l . Math., 5 , Part 1,64-81 (1952).
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(5K) Manwell, A. R., Quart. A p p l . M a t h . , 9, No,4, 405-12 (1952). (6K) Mohr, E., 2. ungew. Math. u. Mech., 32, No. 2/3, 87-8 (1952). (7K) Neumark, S., J . Aeronaut. Sei., 19, No. 3, 214-15 (1952). (8K) Scholz, N., Ibid., 19, No. 1, 70-2 (1952).
(1L) Carrier, G. F., “Foundations of High Speed Aerodynamics,” New York, Dover Publications, 1951. (2L) Dickman, H., 2. V e r . deut. Ing., 94,No.31, 1015-19 (1952). (3rd) Drucker, D. C., and Lee, E. H., A p p l . Mechanics Revs., 5 , KO. 12,497-8 (1952). (4L) Grad, H., Commun. Pure and A p p l . Math., V, No. 4, 455-94 (1952). (5L) Guthmann, K., 2. Tier. deut. I n g . , 94,No. 28, 934-8 (1952). (6L) Kuznetsov, D. S., “Hydrodynamics,” Gidrometeoizdat (Leningrad) (1951). (7L) Redding, T. K., “Flow through Orifices and Parallel Throated Nozzles,” London, Chapman and Hall, 1952. (8L) Rouse, H., A p p l . Mechanics Revs., 5 , No. 2, 49-50 (1952). (91,) Taylor, J., “Detonation of Condensed Systems,” England, Oxford Clarendon Press, 1952. ( 1 0 ~ )Truesdell, C., J. Rational Mechanics and Analysis, 1, No. 1 , 125-71, NO. 2, 173-300 (1952). ~~
HEAT TRANSFER _-
E. R. G. E C K E R T University of Minnesota, Minneapolis, Minn.
*
Pronounced interest in heat transfer was demonstrated by a number of special meetings devoted to this field. I n convective heat transfer special attention was given to the influence of a local variation of surface temperature and of property values varying with temperature. Calculations of heat transfer coefficients in laminar flow of air were extended to very large supersonic velocities. Heat transfer to configurations which cause the flow to separate and to rough surfaces is widely studied. Several papers dealt with natural convection flow, boiling liqulds, and passages with noncircular cross sections. Progress on instrumentation techniques was reported. Applications that received special attention were different types of heat exchangers, regenerators for gas turbines, and deicers for aircraft wings and propellers.
C
ONSIDERABLE activity existed during the past year in the field of heat transfer research. The results of investigations were reported not only a t regular sessions devoted to this field at the different meetings of engineering societies but also a t special meetings. To the “General Discussion on Heat Transfer” which was held in London between the eleventh and thirteenth of September, 1951, 61 papers from England and from Continental Europe and 35 American papers were submitted. (The volume containing these papers and the subsequent discussions was published by the Institute of Mechanical Engineers and the American Society of Mechanical Engineers in 1952.) The American Institute of Chemical Engineers held a special “Heat Transfer Symposium” in December, 1951. (Preprints of the 16 papers submitted are available through the American Institute of Chemical Engineers.) The “1952 Heat Transfer and Fluid Mechanics Institute” was held a t the University of California in Los Angeles in June, 1952. (Preprints of 12 papers are available through the University of California). A lecture series on heat transfer was held during the summer of 1952 a t the University of Michigan. (These lectures will be available as an Engineering Research Institute Bulletin through the University of hfichigan in April, 1953.) Papers presented a t the “Lecture Series” are not included in this review since they are not yet generally available.
Heat Conduction Among all the property values for gases that are necessary for heat transfer calculations, the heat conductivity is known with
the least accuracy especially in the range of higher temperatures. Even for air data found in the literature a t temperatures around 2000” F. differ by as much as 5 2 0 % (4-4). The heat conduction process and heat conductivity values in solid materials are the subject of a number of papers (5A, QA, I I A , I S A ) . Heat conduction in insulating materials in the form of ponders or fibers has been investigated by calculation and experimentation ( f A , 7 A , 16A, 1TA), with special ?ttention directed toward the reduction in the conductivity value which arises as soon as the free molecular path length is of the same order of magnitude as the size of the air spaces within the insulating material. The temperature field generated in rods by a heat source moving 15 ith uniform velocity was measured and used to determine the thermal diffusivity of solid materials (15A). Calculations were presented for the unsteady heat conduction process in composite slabs with different boundary conditions and assumptions on property values (ZA, SA). Other transient heat conduction problems are discussed in (IOA, IZA, 14A), and an airflow analog to the one dimensional heat conduction process is described (6A). The thermal conductivity of unisotropic materials-laminated plastics-was investigated by use of an unsteady state method. The heat conductivities in the different directions were found to vary by as much as a factor of six (8A).
Channel Flow New applications often utilize the heat transfer between fluids with very large temperature differences. This necessitates investigations into the influence of the variation of the property values with temperature on the heat transfer. Calculations of this influence in laminar fully developed tube flow are reported (8B) and experimental and analytical investigations for developed turbulent tube flow (SB). It %asfound that introducing the properties a t a properly defined reference temperature
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INDUSTRIAL AND ENGINEERING CHEMISTRY
accounts with sufficient accuracy for the variation of the property values. The complete temperature field in the heated region of a tube through which water flon-s turbulently was calculated with the help of an electric analog computer using values for the eddy diffusivity and eddy conductivity proposed by K&rmLn (17I3, 26B). In an extensive investigation, temperature and velocity profiles were measured in rectangular channels, the two walls of which were kept a t constant but different temperatures .and through which air flowed turbulently. From the results the values of eddy viscosity and eddy conductivity were determined and were found to depend upoil local position as well as upon flow velocity (TB). Det,ails of the trarisition process from laminar to turbulent flow of water in a tube were studied b y Aoiv visualizat'ion methods (85B). Other papers deal with turbulent heat transfer in pipes (3R, 6 B ) and annuli (22B, 23B). A number ol investigations dealt with the turbulent f l o ~ through a tube of unusual liquids like mercury or mercury sodium mixtures ( 6 B , 1OB, I S B , 15B, 16B, 28B), lead bismuth eutectic (18B, d l B ) without or with the addition of magnesium, water a t pressures up to 2000 pounds per square inch in the nonboiling region (19B),heat transfer to nitric acid under heat flux conditions similar to those encountered in rocket engines (d@), and heat, transfer to slurries of chalk in water (223). The investigations on liquid metals are still not in agreement as to the influence of 71-etting on heat transfcr and usually resulted in heat transfer values lower than the ones predicted by Martinelli's theoret,ical relationship. Heat transfer to water a t high pressures in t,he noriboiling region could be predicted by the usual Susselt number correlations for turbulent flow. Average heat transfer coefficients for fully developed laminar flow in rectangular tubes of different side length ratio were c a l c u l a t e d (AB) and investigated experimentally for turbulent flow of air in trapezoidal and rectangular passages ( I B ) . Local wall s h e a r i n g s t r e s s e s around the periphery of polygonal passages determined from flow measurements by Kikuradse were used to calculate the wall temperature d i s t r i b u t i o n around such passages for t u r b u l e n t flow of fluids n i t h a Prandtl near one (11B) and for fluids with a very low Prandtl num-
Vol. 45. No. 5
the flow to drop in avial direction in the same way as in a Lnval nozzle. A Russian paper investigates this possibility (30B). It is concluded that only heat transfer without simultaneous friction-for instance by radiation---could lead to such a type of flow. Measurements on recovery factors for supersonic flov of air in a tube are summarized (2OB).
Boundary Layer Flow
Boundary layers develop on the surfaces of all objects placed into an unlimited flow or along the walls of channels whose width is not too small as compared to the length. The question of hona variation of the wall temperature in flow direction influences heat transfer found considerable interest recently. Calcdations for laminar boundary layers with and without pressure gradient in flow direction were published (8C). Heat transfer and skin friction in laminar boundary layers on cylinders in axial incompressible flow are investigated ( d G ) , and the development of the laminar boundary laver and local heat transfer values as obtained from approximate calculations were compared with experimental results for a cylinder with an axis ratio of 1:4 in an air flow normal to its axis (12C). Measurements of local heat transfer and skin friction values on circular cylinders in air streams of different turbulence level normal to the cylinder axis indicate that the turbulence level influences heat transfer even in the region where the boundary layer is laminar (5C). An exact solution of the Navier-Stokes equations was presented by KArm&n in 1921 for the laminar boundary layer which develops on a rotating plate. The corresponding heat transfri problem has now been solved (QC). Theoretical relations for heat transfer and fluid friction 15 ere derived for turbulent incompressible and compressible boundary layers along a flat plate from P r a n d t l ' s mixing length theory and the assumption that the total temperature variation across t h e boundary layer is similar to the velocity variation ( 3 C ) . The effect of a surface temperature variation along a flat plate on the convective heat transfer in turbulent boundary lavers was investigated ( l O C ) . H e a t transfer measurements on a flat plate determined the influence of surface roughness ( I C . 1 l C ) . The high speeds obtainin the flight Of Figure 1. Interference Photo Showing isotherms Around Heated Cylinder in Airflow Normal to Its Axis (Reynolds Number P I 8) stage rockets i n s t i g a t e d
ber (12s). The need of t h e k n o w l e d g e of such local temperatures arises in applications where the nalls are subject to high heat temperatures' Photo reveals boundary layer around forward portion of cylinder surface and sepatransfer coefficients were reted flow regime in rearward portion the friction and heat measured on straight fins transfer process in laminar (I@). It was found that boundary layers a t Mach numbers up to ten (6C, 7C, ISC). The results of such calcupulsations in flow of water through a tube increased in the lations depend on what variation of the property values with turbulent range the heat transfer coefficients by as much as 60 to 70% (27B). temperature is assumed. Experimental investigations in heat The calculation of a gas flow through tubes a t velocities near transfer through laminar and turbulent boundary layers on it the sonic speed becomes considerably difficult even for a onecooled flat plate in an air stream a t Mach number 2,4 redimensional treatment in which the gas state is considered to sulted in heat transfer values which agree essentially with available correlations ( 1 S C ) . Also, the temperature recover!. vary only along the tube axis. Such calculations for a onefactors checked values available in the literature (4c, 14C). atomic gas are presented (29B). Thc friction in a gas flow a t supersonic velocities through a tube with constant cross-sectional Unexpected high values (up to 0.95) were measured in some area causes the pressure to rise in flow direction where no heat investigations, but only in the transition region from laminar to turbulent flow. transfer occurs. Simultaneous cooling, however, may cause
May 1953
INDUSTRIAL AND ENGINEERING CHEMISTRY
Flow w i t h Separated Regions The optical Zehnder-Mach interferometer was used as a tool to investigate local heat transfer coefficients around circular cylinders in air flow normal to their axes a t Reynolds numbers between 20 and 500 (7D). Average coefficients on cylinders were measured a t low air speeds ( l l D ) . Additional information is available on the temperature and velocity field in the wake behind a heated cylinder in an air stream a t Reynolds numbers between 100 and 5000 (ID). Heat transfer values which check equations based on the kinetic theory of gases and temperature recovery factors which exceed the value one were obtained in experiments on high speed flow of rarefied air normal to the axis of a circular cylinder with Mach numbers between 2 and 3, Reynolds numbers between 0.28 and 203, and Knudsen numbers (ratio of mean molecular path to cylinder diameter) between 0.025 and 12 (l7D, 18D),and for flow around spheres (6D). Heat loss from a plate in a compressible viscous and heatconducting gas was investigated with a linearized theory (4D). D a t a on average heat transfer coefficients to a single heated tube in an unheated tube bank were obtained experimentally ( 1 6 0 ) . D a t a on heat transfer and fluid friction encountered in the flow across banks of tubes resulting from an extensive investigation were published in continuation of previous papers (20). Additional information on heat transfer in tube banks is contained in (160, 190). The influence of turbulence on heat transfer can be studied from an experimental investigation on a duct consisting of a flat and a wave-shaped plate through which air is flowing ( 3 0 ) . Local heat transfer coefficients on a finned cylinder were measured ( 2 2 0 ) . Heat flow through a packed bed system consisting of spherical particles in a direction normal to the flow of air (bD, 8D) and heat transfer between beds of fluidized solids and the container walls were investigated (lOD, 1 2 0 , l S D , $OD). An attempt was made t o predict the pressure drop and heat transfer to packed beds from data obtained on a simple isolated sphere ( 1 4 0 ) . Gas solid film heat transfer coefficients in fluidized coal beds have been studied experimentally (210). Cooling effectiveness of a water jet directed normally against a surface was measured (9D).
Transfer Mechanism Studies are continued with the aim to obtain better understanding of the turbulent transfer mechanism for momentum and heat. Reynolds analogy theorem for this process is critically reviewed (6E). Local transfer of heat is studied in anisotropic turbulence (2E). The concept of “friction temperature” is introduced to correlate heat transfer data in analogy to the friction velocity used in fluid mechanics (4E). Turbulent transfer parameters are obtained from measurements on air flowing through a heated pipe (SE). New information on the transition process from laminar to turbulent free convection flow is obtained with the aid of a Zehnder-Mach interferometer (1E).
953
thermal resistance a t the surface was studied. Natural convection heat transfer becomes very intense in centrifugal fields (48’).
Film and Transpiration Cooling Effective cooling of a wall against the influence of a high temperature gas stream can be obtained by ejecting through a slot in a downstream direction a liquid film which evaporates into the gas stream (4G). Heat transfer coefficients connected with transpiration cooling of a porous wall through which air is ejected into a high temperature gas stream were obtained by exact solutions of the laminar boundary layer equations considering the fluid properties to be dependent on temperature (1G). Such solutions were used to calculate local heat transfer coefficients in the laminar region of an air flow around cylinders of arbitrary cross section (2G, 5G). Heat transfer to air passing through a porous, heated wall was measured (3G).
Change of Phase Mass transfer connected with evaporation of water into an air jet blown tangentially along a plane plate from which evaporation takes place was studied experimentally ( 2 2 H ) . The tests provided information also on the influence of a dry starting section between the exit nozzle of the jet and the wet surface. Evaporation from drops into a gas was studied ( 9 H , l S H , 14H, 18H, 20H) and condensation of steam or water drops (SH). Measurements on heat transfer in a boiling liquid flowing by forced circulation through short vertical tubes revealed a dependence of the heat transfer coefficient on the difference between the wall temperature and liquid temperature even a t very large flow velocities (16H). Heat transfer coefficients in the nonboiling region approached boiling heat transfer values with much lower pressure drop. It is therefore recommended t h a t boiling be suppressed in the heated sections of forced circulation evaporators as far as possible (16H). Outside heat transfer coefficients on horizontal tubes to different boiling liquids were measured (11H) and inside tubes ( d 4 H ) . Higher heat transfer coefficients were observed on finned tubes a t a given temperature difference than on plain tubes per unit of outside surface. A new method of correlating heat transfer data for surface boiling of liquid was proposed (15H). Heat transfer coefficients of vapors condensing on horizontal tubes (12H, 17H), in tubes (dH, 5H, 19H),and on a metal surface ( 6 H ) were investigated. Heat transfer connected with combustion of liquid fuels ( d l H ) , n i t h two-phase flow ( 2 S H ) , and heat exchange a t the cylinder walls of a refrigerating compressor ( 4 H ) are covered. Circulation in boilers was studied (8H). New tests on supersaturation of steam expanding through a nozzle are described (10H). A calculation procedure for one-dimensional two-phase flow is developed (7H) and applied to the flow in vertical evaporator tubes. Heat transfer and pressure drop for turbulent flow of air-water mixtures in a horizontal pipe were investigated experimentally ( 1 H ) .
Natural Convection The integrated momentum and heat flow equations were used to obtain approximate relationships for free convection heat transfer on a vertical flat plate in the laminar region ( 6 F ) , and exact solutions for the same problem were obtained in a large range of Prandtl numbers ( S F ) . These investigations show that the usual procedure to correlate Nusselt numbers as a function of the product, Grashof times Prandtl number, does not agree with real conditions in a large Prandtl number range. The results of an experimental investigation concerning heat transfer from liquid metals and nonmetals to horizontal cylinders were compared with available correlations ( 1 F ) . Heat transfer from horizontal and vertical wires to gases a t low pressures were measured (SF), and the effect of the molecular structure on the
Radiation Emissivity values for refractory materials and molten steels are reported (21). Heat radiation from luminous flames is a factor which can be predicted only very unsatisfactorily and is accordingly under investigation (41, 81). The contribution of chemiluminescence to the heat transfer by radiation in internal combustion engines was found to be very small ( S I ) . On the other hand, extremely high heat transfer rates must occur in the combustion chambers of big rockets to evaporate the injected fuel. They are ascribed to the contribution of chemiluminescence to the radiative heat transfer from the flames (91). Infrared radiation was used to determine the temperature of nonluminous flames (51),and the line reversal technique served as a
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INDUSTRIAL AND ENGINEERING CHEMISTRY
means to measure temperatures of rapid transient processes ( I Z ) . The contribution of thermal radiation to the heat transfer in high temperature gas turbines was found to be small (71). The use of glass mat surfaces as radiant heaters in ovens and dryers is described (61).
Measurement Techniques A new method was described for determining the static temperature in high velocity gas streams by measurement of static and total pressure and mass flow rate (6Kj. Thermometers for measurement of the total temperature in a high velocity gas stieam which may be inserted transversely into the flow were described ( I K ) . Nusselt numbers describing the heat transfer to circular cylinders in cross flow of an air stream in the subsonic range and a t Reynolds numbers betneeri 260 and 30,000 weie determined and used to calculate the time constant of thermocouples in high velocity air streams (7Zi). Conductio11 errors arising in measurements of the surface temperature were studied (Qi), and electrical techniques were developed to compensate €or the thermal time lag of thermoelements and resistance thermometers (8K).The hot wire anemometer and its use for measuring turbulent fluctuations esperially in compressible flons nere investigated ( 2 K , 3K. 6 K , Q K ) . Instruments for measuring heat flux in furnaces (1OZi) and in rocket motors (11K) are described.
Heat Transfer Applications Heat exchangers involving three fluids whose properties vary >Tit11 temperature were calculated n 3 h the help of an analog computer (25L). Analogous investigation on a two-fluid heat exchanger is contained in (1615). The results of a specific example showed t h a t a simplified calculation, which int,roduced constant properties at mean temperatures, underestimated the required heat exchanging surface considerably. Equations describing the temperature-time history for liquids in a tank heated by external heat exchangers TT-vere presented (2SL). Charts have been published which are useful for a calculation of heat exchangers working with parallel flow, counterfloli-, cross flow, or combinations of these types. As a common basis for all these calculations the effectiveness of the heat exchanger is used (5L). The performance of small heat exchangers working with liquid metals is studied (34L). Ext,erisive investigation of a shell-and-tube heat exchanger (ZbL), comparison ol high performance heat exchangers (IYL),data on heat exchangers in chemical industry (2L, 18L, SOL), aircraft radiators (SWL), and water coolers (S7L) are found in literature. Several papers are of regenerators (8L, 15L, 27L, 2QL). devoted to the cal~ulat~ion h-umerous investigations are devoted to the problem of increasing the efficiency of gas turbines by introducing a heat exchanger which preheats the air by the combustion gases (SL, W4L). A difficult problem, especially in aircraft applications of gas turbines, is posed bj- the fact that the hot combustion gases and the compressed air before entering the combustion chamber niust both be ducted through the heat exchanger. Use of a liquid as a heat-transferring medium for a gas-turbine heat' exchanger is proposed in order to alleviate this difficulty (22L). A mathematical formulation of the problem to predict the surface temperature of the skin of missiles under the influence of aerodynamic heating and transient conditions results in a partial integrodifferent,ial equation as soon as the effect of a nonuniform surface temperature on the heat transfer is included. For the range of laminar boundary layers this problem was t.reated in (6L). An analytical method for determining the performance of turbojet tail-pipe heat exchangers is outlined in (4L). An important field of applicat,ion of heat transfer to the gas turbines engine is the cooling of the turbine blades (1015). The temperature distribution in liquid-cooled turbine blades was
Vol. 45, No. 5
determined ( 2 I L ) . I n the field of supersonic flow of gases, heat transfer is intimately connected with the flow. Problem.; arising by the condensation of air in wind tunnels operating IT ith extremely high supersonic (hypersonic) velocities are outlined (91L, 38L). Film heat transfer coefficients a t the surface of tubes arrangcd as vertical baffles in mixing vessels were determined. The vessel was filled with water or different oils, and a rotational movement was imparted by a mixing device ( Q L ) . Heat transfer in internal combustion engines ( I L , 33Lj and in gun barrels (I@,, 28L) arc applications with unsteady state conditions. Other engineering applications investigated were heat transfer in furnaces ( d O L , 26L), to a liquid metal stream in a mold (11L), and in journal bearings (7L). A number of investigations were devoted to the study of the deicing process of an air foil. Cyclic deicing obtained by intermittent heating of the airfoil surface, either by electric or gas heaters, was studied (13L, IQL, d6L, SQL). The question of hoafar the icing conditions as occuring on an airplanc in flight can be simulated by investigations in an icing wind tunnel was studied (IWL).
Literature Cited Heat Conduction (1A) Allcu't, A. A., General Discussion on Heat Transfer, Inst. Mech. Engrs. (London) and Am. Soc. Mech. Engrs., 12. 232 (1951). (2A) Anthony, M. L., Ibid., p. 236. (3A) Beutler, John A4.,and Xnudsen, James G., Heat Transfez, Symposium, 351 (1951) (Reprints available, Am. Inst. Chem. Engrs.). (4A) Bonilla, Charles F., and Glassman, Irvin, Ibid., p. 458. (5A) Cetinkale, T. Pi.,and Fishenden, M., General Discussion on Heat Transfer, Inst. Meoh. Engrs. (London) and Am. Soo. hlech. Engrs., p. 271 (1951). (6A) Coyle, 11.B., Ihid., p. 265. (7A) Deissler, R. G., and Eian, C. El., ,Vatl. Advisory Comm. Aeronaut., Research M e m o . E52C05 (1952). (SA) Eckert, Roger E., and Freiling, Jerome, IWD. ENG.CHEX, 44, 906 (1952). (9-4) Eshelby, J. D., General Discussion on Heat Transfer, Inst,. Mech. Engrs. (London) and Am. Inst. Mech. Engrs., p. 271 (195 1). (108) Griffith, M. V., and Hutchings, E. E., Ibid., p. 285. (11A) Griffiths, Eser, and Hickman, 31. J., Ibid., p. 289. (12A) Heerden, C. van, Ibid., p. 283. (13A) Powell, R. W., I b i d . , p. 290. (14A) Price, P. H., and Sarjant, R. J., Ibid., p. 281. (15A) Rosenthal, D., and Ambrosio, A., Trans. Am. SOC.Mech. Engrs., 73, 971 (1951). (16d) Rowley, F. B., Jordan, R. C., Lund, C. E., and Lander, R. 1'1,. Heating, P i p i n g A i r Conditioning, 23, 103 (1951). (17.1) Verschoor, J. D., and Greebler, Paul, Trans. Ani. Sac. Mech. E?igrs., 74, 961 (1952). Channel Flow (1B) Boelter, L. &,I.K., Sanders, V. D., and Romie, P'. E., LVa,tl. Advisory C o m m . Aeronaut., Tech. Note 2524 (1951). (2B) Bonilla, Charles F., Cervi, Armando, Jr., Colven, Thomas ,J,, and Wang, S. J., Heat Transfer Symposium, 390 (1951)
(Reprints available, Am. Inst. Chem. Engrs.). (3R) Bosanquet, C. €I., General Discussion on Heat Transfer,
(4B) (5B)
'
(6B) (7B)
(8B) (9B)
Inst. Mech. Engrs. (London) and Am. Soc, Mech. Engrs., p. 175 (1951). Clark, S. H., and Kays, W. M., 1952 Heat Transfer gS Fluid Mechanics Inst., 159 (1952) (Reprints available, University of California, Los Angeles, Calif.). Codegone, Cesare, General Discussion on Heat Transfer, Inst. Mech. Engrs. (London) and Am. SOC.Meoh. Engrs., p. 183 (1951). Cope, W. F., Ibid., p. 436. Corcoxn, W. H., Page, F., Jr., Sohlinger, W. G., and Sage, B. H., IXD.EXG.CHEY.,44, 410 (1952). Deissler, R. G., Natl. Adoisory Comm. Aeronnut., Tech. ;Vote 2410 (1951). Deissler, R. G.. and Eian, C. S.,Ihid., 2629 (1962).
M a y 1953
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INDUSTRIAL A N D ENGINEERING CHEMISTRY
(10B) Doody, T. C., and Younger, B . H., Heat Transfer Symposium, 77 (1951) (Reprints available, Am. Inst. Chem. Engrs.). (11B) Eckert, E. R. G., 1952 Heat Transfer & Fluid Mechanics Inst., 175 (1952) (Reprints available, University of California, Los Angeles, Calif.). (12B) Eckert, E. R. G., and Low, George M., Natl. Advisory Comm. Aeronaut., Tech. Note 2401 (1951). (13B) English, D., and Barrett, T., General Discussion on Heat Transfer, Inst. Mech. Engrs. (London) and Am. SOC.Mech. Enus., p. 548 (1951). (14B) Ghai, M. L., Ibid., p. 120. (15B) Gilliland, E. R., Musser, R. J., and Page, W. R., Ibid., p. 402. (16B) Isakoff, Sheldon E., and Drew, Thomas B., Ibid., p. 405. ENO. (17B) Jenkins, Rodman, Brough, H. W., and Sage, B. H., IND. CHEM.,43, 2483 (1951). (18B) Johnson, H. A., Hartnett, J. P., and Clabaugh, W. J., 1952 Heat Transfer and Fluid Mechanics Inst., 5 (1952) (Reprints available, University of California, Los Angeles, Calif .) . (19B) Kaufman, S. J., and Henderson, R. W., Natl. Advisory Comm. Aeronaut., Research M e m o . E51118 (1951). (20B) Kaye, Joseph, Keenan, Joseph H., and Shoulberg, Robert H., General Discussion on Heat Transfer, Inst. Mech. Engrs. (London) and Am. SOC.Mech. Engrs., p. 133 (1951). (21B) Lubarsky, Bernard, N a t l . Advisory Comm. Aeronaut., Research Memo. E51G02 (1951). (22B) Mizushina, Tokuro, General Discussion on Heat Transfer, Inst. Mech. Engrs. (London) and Am. SOC.Mech. Engrs., p. 191 (1951). (23B) Peregrine, E. P., and Rowland, G., Ibid., p. 197. (24B) Reese, Bruce A., and Graham, Robert W., Natl. Advisoru Comm. Aeronaut., Research Memo. 52D03 (1952). (25B) Rothtus, R. R., and Prengle, R. S., IND.ENG. CHEM.,44, 1683 (1952). (26B) Schlinger, W. G., Berry, V. J., Mason, J. L., and Sage, B. H., General Discussion on Heat Transfer, Inst. Mech. Engrs. (London) and Am. SOC.Mech. Engrs., p. 150 (1951). (27B) Taylor, A. T., and West, F. B., Chem. Eng. Progr., 48, 39 (1952). (28B) Trefethen, L. M., General Discussion on Heat Transfer, Inst. Mech. Engrs. (London) and Am. SOC.Mech. Engrs., p. 436 (1951). (29B) Valerino, M. F., and Doyle, R. B., Natl. Advisory Comm. Aeronaut., Tech, Note 2328 (1951). (30B) Varshavsky, G. A., Ibid., Tech. Memo. 1274 (1951).
955
(4D) Cole, J. D., and Wu, T. Y . , 1952 Heat Transfer and Fluid Mechanics Inst., 139 (1952) (Reprints available, University of California, Los Angeles, Calif.). (5D) Denton, W. H., General Discussion on Heat Transfer, Inst. Mech. Engrs. (London) and Am. SOC.Mech. Engrs., P. 370 (1951). (6D) Drake, R. M., Jr., and Kane, E. D., Ibid., p. 117. (7D) Eckert, E. R. G., and Soehngen, E., Trans. Am. SOC.Mech. Engrs., 74, 343 (1952). (8D) Felix, J. R., and Neill, W. K., Heat Transfer Symposium, 123 (1951) (Reprints available, Am. Inst. Chem. Engrs.). (9D) Friedman, S. J., and Mueller, A. C., General Discussion on Heat Transfer, Inst. Mech. Engrs. (London) and Am. Soc. Mech. Engrs., p. 138 (1951). (10D) Heerden, C. van, Nobel, P., and van Krevelen, D. W., Zbid., p. 358. (11D) Hutchings, E. E., Ibid., p. 287. (12D) Johnstone, H. F., Toomey, Robert D., Heat Transfer Symposium. 171 (1951) (Reprints available, Am. Inst. Chem. Engrs.). (13D) heva, Max, General Discussion on Heat Transfer, Inst. Mech. Engrs. (London) and Am. SOC.Mech. Engrs., p. 421 (1951). (14D) Rans, W. E., Chem. Eng. Progr., 48, 147 (1952). (15D) Schmidt, T. E., General Discussion on Heat Transfer, Inst. Mech. Engrs. (London) and Am. SOC.Mech. Engrs., P. 186 (1951). (l6D) Snyder, N. W., Heat Transfer Symposium, 31 (1951) (Reprints available, Am. Inst. Chem. Engrs.). (17D) Stalder, Jackson R., Goodwin, Glen, and Creager, Marcus O., General Discussion on Heat Transfer, Inst. Mech. Engrs. (London) and Am. SOC.Mech. Engrs., p. 143 (1951). (18D) Stalder, Jackson R., Goodwin, Glen, and Crettger, Marcus O., Natl. Advisory Comm. Aeronaut., Tech. Note 2438 (1951). (19D) Thomson, A. S. T., Scott, A. W., Laird, A. McK., and Holden, H. S., General Discussion on Heat Transfer, Inst. Mech. Engrs. (London) and Am. SOC,Mech. Engrs., p. 177 (1951). (20D) Vreedenberg, H. A., Ibid., p. 373. ENG. (21D) Walton, J. S., Olson, R. L., and Levenspiel, Octave, IND. CHEM.,44, 1474 (1952). (22D) Weiner, J. H., Gross, D., and Paschkis, V., General Discussion on Heat Transfer, Inst. Mech. Engrs. (London) and Am. SOC.Mech. Engrs., p. 154 (1951). Transfer M e c h a n i s m
Boundary Layer Flow (1C) Boelter, L. M. K., Young, G., Greenfield, M. L., Sanders, V. D., and Morgan, M., Natl. Advisory Comm. Aeronaut., Tech. Note 2517 (1951). (ZC) Bond, R., and Seban, R. A,, J . Aeronaut. Sci., 18,671 (1951). (3C) Donaldson, Coleman Dupont, 1952 Heat Transfer & Fluid Mechanics Inat., 19 (1952) (Reprints available, University of California, Los Angeles, Calif.). (4C) Eber, G. R., J . Aeronaut. Sci., 1 9 , l (1952). (5C) Giedt, W. H., Ibid., 18, 725 (1951). (6C) Janssen, Earl, and Young, George B. W., Ibid., 19,229 (1952). (7C) Klunker, E. B., and McLean, F. Edward, Natl. Advisory Comm. Aeronaut., Tech. Note 2499 (1951). (SC) Levy, Solomon, J . Aeronaut. Sci., 19, 341 (1952). (9C) Millsaps, Knox, and Pohlhausen, Karl, Zbid., 19,120 (1952). (1OC) Rubesin, Morris W., Natl. Advisory Comm. Aeronaut., Tech. Note 2345 (1951). (11C) Sato, Takashi, and Sugawara, Sugao, M e m . Fac. Eng., Kyoto Univ., 14, No. 1 (1952). (12C) Seban, R. A,, and Drake, R. M., Am. SOC. Mech. Engrs., Paper 52-SA-11 (1952). (13C) Slack, Ellis G., NatE. Advisory Comm. Aeronaut., Tech. Note 2686 (1952). (14C) Stine, Howard A., and Scherrer, Richard, Zbid., 2664 (1952). (15C) Van Driest, E. R., Ibid., 2497 (1952).
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Flow w i t h Separated Regions (1D) Berry, V. J., Mason, D. M., and Sage, B. H., Heat Transfer Symposium, 1 (1951) (Reprints available, Am. Inst. Chem. Engrs.). (2D) Bergelin, 0. P., Brown, G. A., and Doberstein, S. C., Trans. Am. SOC. Mech. Engrs., 74, 953 (1952). (3D) Boelter, L. M. K., Sanders, V. D., Young, G., Morgan, M., and Morrin, E. H., NatE. Advisory Comm. Aeronaut., Tech. Note, 2426 (1951).
(1E) Eckert, E. R. G., and Soehngen, E., General Discussion on Heat. Transfer. Inst. Mech. Engrs. (London) and Am. Soc.-Mech. E n b s , p. 321 (1951). (2E) Hinze, J. O., and van der Hegge Zijnen, B. G., Ibid., p. 188. (3E) Seban, R. A., and Shimazaki, T. T., Ibid., p. 122. (4E) Squire, H. B., Zbid., p. 185. (5E) Taylor, Geoffrey I., Ibid., p. 193. I
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N a t u r a I Convection (1F) Hyman, Seymour C., Bonilla, Charles F., and Ehrlich, Stanley W., Heat Transfer Symposium, 55 (1951) (Reprints available, Am. Inst. Chem. Engrs.). (2F) Madden, Arthur J., Jr., and Piret, Edgar L., General Discussion on Heat Transfer, Inst. Mech. Engrs. (London) and Am. SOC.Mech. Engrs., p. 328 (1951). (3F) Ostrach, Simon, Natl. Advisory Comm. Aeronuut., Tech. Note 2635 (1952). (4F) Schmidt, Ernst H. W., General Discussion on Heat Transfer, Inst. Mech. Engrs. (London) and Am. SOC.Mech. Engrs., p. 361 (1951). (5F) Sugawara, Sugao, and ,Michiyoshi, Itaru, M e m . Fac. Eng., Kyoto Univ., 13, No. 4 (1951). Film a n d T r a n s p i r a t i o n Cooling
(IG) Brown, Byron W., and Donoughe, Patrick L., Natl. Advisory Comm. Aeronaut., Tech. Note 2479 (1951). (2G) Eckert, E. R. G., and Livingood, John N. B., Zbid., 2733 (1952). (3G) Grootenhuis, P., Mackworth, R. C. A., and Saunders, 0. A., General Discussion on Heat Transfer, Inst. Mech. Engrs. (London) and Am. SOC.Mech. Engrs., p. 363 (1951). (4G) Kinney, George R., Natl. Advisory Comm. Aeronaut., Ibesearch Memo. E52B20 (1952). (5G) Staniforth, R., General Discussion on Heat Transfer, Inst. Mech. Engrs. (London) and Am. SOC.Mech. Engrs., p. 446 (1951).
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INDUSTRIAL AND ENGINEERING CHEMISTRY
956 '
Change of Phase (1H) Abou-Sabe, A. H., and Johnson, H. A,, Trans. Am. SOC.Mech. Engrs., 74, 977 (1952). (2H) Beatty, K. O., Jr., Finch, E. B., and Schoenborn, E. M., General Discussion on Heat Transfer, Inst. Mech. Engrs. (London) and Am. SOC.Mech. Engrs., p. 32 (1951). (3H) Brown, G., Ibid., p. 49. (4H) Brown, James, Ibid., p. 55. (5H) Carpenter, F. G., and Colburn, A. P., Ibid., p. 20. (6H) Hampson, H., Ibid., p. 58. (7H) Harvey, Bruce F., and Foust, Alan S., Heat Transfer Symposium, 292 (1951) (Reprints available, Am. Inst. Chem. Engrs) . (8H) Haywood, R. W., General Discussion on Heat Transfer, Inst. Mech. Engrs. (London) and Am. SOC. Mech. Engrs., p. 63 (1951). (9H) Ingebo, R. D., Chem. Eng. Progr., 48, 403 (1952). (10H) Kerr, W., Scott, A. W., and Sorour, M., General Discussion on Heat Transfer. Inst. Mech. Enars. - .(London) and Am. Soc. Mech. Engrs., p. 69 (1951). (11H) Myers, John E., and Kats, Donald L., Heat Transfer Symposium, 330 (1951) (Reprints available, Am. Inst. Chem. Engrs.). (12H) Peck, R. E., and Reddie, W.A,, IND.EPTG.CHEM.,43, 2926 (1951). (13H) Ranz, W. E., and Marshall, W.R., Jr., Chem. Eng. Progr., 48, 141, 173 (1952). (14H) Richardson, E. G., General Discussion on Heat Transfer, Inst. Mech. Engrs. (London) and Am. Soc. hIech. Engrs., p. 66 (1951). (15H) Rohsenow, W. M.,T r a n s . Am. SOC.Mech. Engrs., 74, 969 (1952). (16H) Schweppe, Joseph L., and Foust, Alan S., Heat Transfer Symposium, 242 (1951) (Reprints available, Am. Inst. Chem. Engrs.). (17H) Short, Byron E., and Brown, Howard E., General Discussion on Heat Transfer, Inst. Mech. Engrs. (London) and Am. SOC.Mech. Engrs., p. 27 (1951). (18H) Sjenitzer, F., Ibid., p. 61. (19H) Smith, Julian C., and Robson, Horace T., Ibid., p. 38. (20H) Snyder, R. W., Ibid., p. 160. (21H) Spalding, D. B., Ibid., p. 345. (22H) Spielman, Maurice, and Jakob, Max, Am. SOC.Mech. Engrs., Paper 52-SA-1 (1952). (23H) Verschoor, H., and Stemerding, S.,General Discussion on Heat Transfer, Inst. Mech. Engrs. (London) and Am. SOC. Mech. Engrs., p. 201 (1951). (24H) Yoder, Richard J., and Dodge, Barnett F., Ibid., p. 15. Radiation Agnew, J. T., T r a n s . Am. SOC.Mech. Engrs., 74, 219 (1952). Bacon, J. E., and James, J. W., General Discussion on Heat Transfer, Inst. Mech. Engrs. (London) and Am. SOC. Mech. Engrs., p. 354 (1951). Baker, H. Dean, and Laserson, Gregory L., Ibid., p. 334. Berenblut, I. I., Ibid., p. 349. Bernath, L., Powell, H . N., Robison, A. G., Welty, F., and Wohl, K., Ibid., p. 315. Broughton, Geoffrey, Ibid., p. 324. Brown, T. W.F., Ibid., p. 431. Ribaud, G. M.,Saunders, 0. A., and de Graaf, J. E., Ibid., p. 352. Sanger, E., Goercke, P., and Bredt, I., N a t l . Advisory Comm. Aeronaut., Tech. M e m o . 1305 (1951). M e a s u r e m e n t Techniques (1K) Beede, H. M . , and Droms, C. R., Instruments, 24, 3 (1951). (2K) Betchov, R., N a t l . Advisory Comm. Aeronaut., Tech. M e m o . 1346 (1852). (3K) Betchov, R., and Welling, W., Ibid., 1223 (1952). (4K) Boelter, L. M. K., and Lockhart, R. W., Ibid., Tech. Note 2427 (1951). (5K) Clark, J. A., and Rohsenow, W. M., Trans. Am. SOC.Mech. Engrs., 74, 219 (1952). (6K) Reichardt, H., Natl. Advisory Comm. Aeronaut., Tech. M e m o . 1313 (1951). (7K) Scadron, iMarvin D., and Warshawsky, Isidore, Ibid., Tech. Note 2599 (1952).
Vol. 45, No. 5
(8K) Shepard, Charles E., and Warshawsky, Isidore, Ibid., 2703 (1952). (9K) Tchen, Chan-Mou, Ibid., 2436 (1951). (10K) Thring, M. W., General Discussion on Heat Transfer, Inst. Mech. Engrs. (London) and Am. SOC.Mech. Engrs., p. 342 (1951). (11K) Ziebland, H., Ibid., p. 368. H e a t T r a n s f e r Applications (1L) Alcock, J. F., General Discussion on Heat Transfer, Inst. Mech. Engrs. (London) and Am. SOC. Mech. Engrs., p. 438 (1951). (2L) Altena, P. H. van, and de Haas, T. K., Ibid., p. 451. (3L) Aronson, D., T r a n s . Am. Soc. Mech. Engrs., 74, 675 (1952). (4L) Behun, Michael, Harrison C., and Chandler, Jr., Natl. A d visory Comm. Aeronuat., Tech. Note 2456 (1951). (5L) Bosnjakovic, F., Vilicic, M., and Sliepcevich, B., VDI-Forschungsheft No. 432 (1951). (6L) Bryson, A. E., and Edwards, R. H., Inst. Aeronaut. Sei., Sherman M. Fairchild Preprint, No. 365 (1952). (7L) Cameron, A., General Discussion on Heat Transfer, Inst. Mech. Engrs. (London) and Am. SOC.Mech. Engrs., p. 194 (1951). (SL) Davies, S. J., and Singham, J. R., Ibid., p. 434. (9L) Dunlap, I. R., Jr., and Rushton, J. H., Heat Transfer Symposium, 411 (1951) (Reprints available, Am. Inst. Chem. Engrs.). ( 1 O L ) Ellerbrock, Herman H., Jr., General Discussion on Heat Transfer, Inst. Mech. Engrs. (London) and Am. SOC. Rilcch. Enars.. u. 410 (19511, (11L) Fell, E. W.,?bid.; p. 194. (12L) Gclder, Thomas F., and Lewis, James P., N a t l . Advisory Comm. Aeronaut., Tech. Note 2480 (1961). (13L) Gray, V. H., Bowden, D. T., and Glahn. U. Ton, Ibid., Research M e m o . E51J29 (1952). (14L) Hicks, E. P.,General Discussion on Heat Transfer, Inst. Mech. Engrs. (London) and Am. SOLMech. Engrs., p. 279 (1951). (15L) Hrynissak, W., Ibid., p. 460. (16L) Kayan, Carl F., Ibid., p. 227. (17L) Kays, W. M., and London, A. L., Ibid., p. 127. (18L) Kayser, H. G., Ibid., p. 464. (19L) Lewis, James '1 , and Bowden, Dean T., Null. Advisory C o m m . Aeronaut., Research M e m o . E51J30 (1962). (20L) Linden, A. J. ter, General Discussion on Heat Transfer, Inst. Mech. Engrs. (London) and Am. 800. Mech. Engrs., p. 276 (1951). (21L) Livingood, John N . B., and Brown, W. Byion, N a t l . Advisory C o m m . Aeronaut., Tech. Note 2321 (1951). (22L) London, A. L., and Kays, W. N., Aeronaut. Eng. Rev., 11, 42 (1952). (23L) Lynch, E. P., Heat Transfer Symposium, 367 (1951) (Reprints available, Am. Inst. Chcm. Engrs.). (24L) Manson, S. V., Natl. Advisory C o m m . Aeronaut., Tech. Note 2254 (1951). (25L) Paschkis, V., and Heisler, M. P., Heat Transfer Symposium, 211 (1951) (Reprints available, Am. Inst. Chem. Engrs.). (26L) Sarjant, R. J., and Smith, D., General Discussion o n Heat Transfer, Inst. Mech. Engrs. (London) and Am. SOC.Mech. Engrs., p. 356 (1951). (27L) Saunders, 0. A,, and Smoleniec, S., Ibid., p. 443. (28L) Schmidt, Ernst H. W., Ibid., p. 263. (29L) Schults, B. H., Ibid., p. 440. (30L) Smith, R. A., Ibid., p. 52. (3lL) Stever, H. Guyford, Ibid., p. 393. (32L) Still, E. W., Ibid., p. 448. (33L) Taylor, C. Fayette, Ibid., p. 397. (34L) Tidball, R. A., Heat Transfer Symposium, 99 (1951) (Reprints available, Am. Inst. Chem. Engrs.). (35L) Tinker, Townsend, General Discussion on Heat Transfer, Inst. Mech. Engrs. (London) and Am. Soc. Mech. Engrs., p. 89 (1951). (36L) Tribus, Myron, Trans. Am. Soc. Mech. Engrs., 73, 1117 (1951). (37L) Walker, G. H., General Discussion on Heat Transfer, Inat. Mech. Engrs. (London) and Am. SOC.Mech. Engrs., p. 434 (1951). (38L) Wegener, Peter P., J . Aeronaut. Sci., 18, 665 (1951). (39L) Weiner, Frederick, Trans. Am. SOC.Mech. Engrs., 73, 1131 (1951). RECEIVED for review November 3. 1952.
ACCEPTED March 23, 1953.
