ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT
E. R. G. ECKERB
University of Minnesota, Minneapolis, Minn.
This review covers work i n the field of heat transfer that has been published during the year 1953 i n book form or i n generally available magazines. I n addition, N A C A reports, which find a wide distribution, have been included. An attempt was made to include foreign literature, although the coverage is not complete i n this respect. The cooling problems encountered i n aeronautics i n the effort to increase the velocity of aircraft and missiles created interest i n heat transfer under special conditions Bike supersonic velocities, rarefied gas flow, boundary layer flow, and very large temperature differences. Atomic power created interest i n processes that result in specially large heat transfer coefficients. Research is continued on classical heat transfer processes that are still poorly wnderstoodsuch as heat transfer i n separated flow regions, evaporation, and two-phase heat transfer. There is increased interest i n heat exchangers for more than two fluids and regenerative (periodic flow) exchangers.
TIVITY in the field of heat transfer was demonstrated by the number of papers presented at the different meetings of engineering. societies, and also by the special seasions and symposia that were devoted to this subject. The American Institute of Chemical Engineers held a symposium 0 1 1 heat transfer in Atlantic City in December 1953 in which 15 subjects were discussed. The American Society of Mechanical Engineers devoted seven sessions of its annual meeting a t New Yorlc to the field of heat transfer. Two of the sessions consisted of a symposium on physical properties. In addition, 0. A. Saunders from the Imperial College of London, a e l l known in the field of heat transfer, surveyed the recent advances in this field. (Papers discussed in the seven sessions t o be published during the present year in the magazines of this society are not included in this survey.) B meeting of the Heat Transfer and Fluid Mechanics Institute was held a t Los Angeles, Calif., in June 1953. (Preprints of the papers submitted to this institute are available through Stanford University, Palo Alto, Calif. Since they will be published in various engineering magazines, they are not yet included in this year’s survey.) With the Third Midwestern Conference on Fluid Mechanics held in March in Xnneapolis, Minn., was connected a symposium on transport processes that was sponsored by the Office of Ordnance Research. Three lectures in this symposium presented surveys on different aspects in the field of heat transfer. I n the past year the Univeisity of hfichigan published the lectures covering the whole field of heat transfer given during a heat transfer symposium in summer, 1952. Two books became available late in 1952 that treat the field of heat transfer from two completely different viewpoints. The book by F. TV. Hutchinson, “Industrial Heat Transfer,” Kew York, Industrial Press, simplifies the routine calculations which the designer of heat transfer equipment has t o do by presenting a large number of graphs from which heat flow by conduction, radiation, convection, and combined processes can be determined without any calculations for various geometric configurations and fluids. The book by R. 6.L. Bosworth, “Heat Transfer Phenomena,” Kew York, John Wiley & Sons, is a treatise on the basic physical concepts in the field of heat transfer and is interesting and stimulating in that i t develops many unusual aspects of the different processep in this field, especially in heat conduction. Aeronautics has recently joined the group of engineering branches with a strong interest in heat transfer. There is a n increasing number of reports from the National Advisory Committee for Aeronautics (N$CA) and of papers published by the Journal of Aeronautical Sciences in this field. Applications that
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932
are discussed frequently are deicing problems and thermal stresses.
eat
arction
It has been pointed out in a sur-
vey(QA)by Hirschfelder on transport properties of gases and liquids that the one property which can be calculated by means of statistical mechanics with the least accuracy is heat conductivity. This emphasizes the importance of an experimental investigation ( S A )in which the heat conductivity for air has been measured t o a temperature of 1300” F. The paper contains extrapolated values of heat conductivity and Prandtl number to temperatures of 4000” B. which are correct within approximately 10%. Physical properties for concentrated nitric acid, including heat conductivity and Prandtl number, are contained in a NACA Technical Report (9‘4). Xew solutions of the heat conduction equation obtained with the help of the Laplace transformation for periodically varying surface temperatures ( 5 A , 6 A ) and for temperature dependent thermal properties ( l a )813 well as new applications of the relaxation method ( 7 A ) have been published. The similarity rules applying to heat conduction processes were reviewed ($A).
Tbe mathematical solutions by Graetz and Nusselt for laminar heat transfer to a Ruid flowing through a circular tube have been extended ( I @ ) to the case in which a hot liquid passes in laminar flow from a section with isothermal conditions into a section which is loccited in an environment of constant but different temperature. The calculation takes into accounl a finite heat resistance through the tube wall and on the outside of the tube. The results are presented in graph form. Calculations by the relaxation procedure have been made for heat transfer in laminar flow through rectangular and triangular tubps with different ratios of length to height and for constant wall temperature or heat flow to determine heat transfer coefficients averaged over the circumference of such passages. The results have been partially checked by experiments ( S B ) A method was presented (7Bj for calculating the temperature distribution that exists in thc wall of heat exchangers with polygonal flow passages around the circumference of the channel when the flow through the passage is turbulent and when the heat input through the walls or the internal heat geneiation within the walls is prescribed. The results of this calculation agreed with measurements for passage shapes that contain only large angles. ??or channels with sinall included angles, the measured temperature difference~tend to be larger than the calculated ones ( 7 B ) . One uf the few existing exact solutions of the Navier-Stokes equation had been obtained by Harmel in 1916 for laminar two-dimensional flow through divergent and convergent passages. ,4 solution of the corresponding energy equation has now been published (11B). This solution includes the effect of internal friction and provides information on the temperature profiles and on heat transfer to the walls of such
INDUSTRIAL AND ENGINEERING CHEMISTRY
Mol. 46, No. 5
FUNDAMENTALS REVIEW passages. A method for calculating heat transfer in turbulent flow through tubes or in boundary layers without pressure gradients from friction data had been initiated by Reynolds and later on developed by Prandtl and Taylor as well as by von KBrm&n. This method proved very useful in many recent investigations. Deissler used it to calculate the influence of large temperature differences on heat transfer. In a recent paper (4B), Deissler extended his calculations to the entrance regions of smooth passages. Approximately fully developed heat transfer was in general obtained in an entrance length of less than 10 diameters. The variation of Nusselt number with tube lengths for air which enters a tube with uniform wall temperature agreed with experimental results previously obtained by Boelter and coworkers. The reference temperature a t which the property values should be introduced into the dimensionless heat transfer correlation in order to eliminate the influence of temperature difference was also determined in this investigation. Another paper (6B) extends the calculations to heat transfer in a fully developed turbulent flow of supercritical water through circular tubes. Figure 1 summarizes the results of this investigation for water under a pressure of 5000 pounds per square inch. From the diagram in this figure the reference temperature, t*, can be determined. Introduction of the property values a t this temperature into the well-known dimensionless relations for heat transfer in turbulent flow through tubes-for instance, the equation by Dittus and Boelter-results in the correct answer for the investigated situation. Experimental investigations for heat transfer in turbulent flow of air through a tube with a length to diameter ratio of 15 and a t high surface temperatures (18B)adds to our information on the situation in the entrance region. Again relationships for the reference temperatures are developed from the results of this investigation. A summary of NACA research (fSB)on turbulent heat transfer and friction for air flowing through tubes with large temperature differences is especially interesting for the correlation presented on heat transfer in tubes with rough surfaces. These correlations have been obtained on the basis of experiments with different roughncsses created artificially by milling circular grooves into the inner tube wall. The results indicate that the effect of roughness on heat transfer is less pronounced than on friction. A number of papers deal with heat transfer from liquid metals to the walls of circular tubes (OB, 9B, 13B, 15B). Whether and how much this heat transfer is influenced by surface wetting remains to be decided. Heat transfer to a non-Newtonian fluid (polyvinyl alcohol) has been measured (1B). The well-known relationship for turbulent flow of ordinary fluids through a tube presents the results of this investigation with sufficient accuracy when an apparent viscosity is introduced into the Reynolds number. In a survey (17B)on heat transfer in turbulent flow through ring-shaped passages between two concentric tubes the conclusion is reached that heat transfer coefficients to the inner wall are always larger than the corresponding values to the outer wall and that the well-known rule of the hydraulic diameter does not apply. Correlations for these heat transfer coefficients are given. A method by which heat transfer for laminar and turbulent flow through tubes and along surfaces can be calculated for the special condition that the wall temperature varies arbitrarily along the tube length which has been developed by Bond and Rubesin is surveyed (16B). The paper extends this method also to the case when the heat flow through the tube wall instead of the wall temperature is prescribed. Comparisons with experiments show generally good agreement and indicate that a considerable influence of such a temperature variation on the heat transfer exists under special conditions. An analytic study has been made on the effect of variable viscosity and thermal conductivity on high speed slip flow of a rarefied gas between two rotating concentric cylinders. Corrections are given that can be applied to a previously published solution by Scherberg for constant viscosity and thermal con-
May 1954
ductivity to take into account the effect of property value variation, An experimental check of the investigated flow type should be possible and would provide a check on the assumptions made in slip flow calculations.
Boundary Layer FIQW Heat transfer in laminar boundary layer flow is of special interest for aeronautical applications where the Reynolds number in high altitude flight becomes sufficiently small to make the flow laminar. Accordingly, a considerable number of papers were published that attack the difficult problem of calculating heat transfer to bodies of arbitrary shape in either two-dimensional ( I C , WC)or rotationally symmetrical flow (3C) and under the condition of a wall temperature varying along the surface ( 1 7 C ) and of arbitrary pressure distribution along the objects (SC, 1OC). Only approximate procedures are available under those conditions. A set of experiments on elliptic cylinders with an axis
10
OB
I
HEAT TRANSFER t*-t, t*-t,
t0--tb
1
0 . 4 ~ 1
0.4
P
0 O
-2
i
-1-I
"0
=
5000
lb/in2
I
2
m 'b to-tb
Figure 1. Reference Temperature for Friction and H e a t Transfer to Supercritical Water Flowing Turbulently Through a Circular Tube (58) t* = reference temperature f b = bulk tem erature of fluid to tm
= tube walftemperature = temperature at which specific heat of water reaches its maximum
ratio 1to 3 (4C)and 1to 4 (18C) showed that reasonable accuracy can be obtained by such calculation methods. A graphical solution for turbulent boundary layers in compressible fluids (9C) and an extension of Reynolds analogy ( 1 3 2 ) to determine heat transfer from friction data for high velocity flow have been presented. Two papers (5C, 6 C ) surveyed the present-day knowledge on convective heat transfer a t high velocities. At Mach numbers as they will be reached by missiles in a foreseeable future, extreme temperature variation throughout the boundary layers has to be expected. This will cause a large variation of the property values of air with temperature and have a pronounced effect on heat transfer. Accordingly, several papers have investigated this influence (7C). Since high velocity flight will occur a t large altitudes, the effect of slip of the flow along surfaces in rarefied air on heat transfer has also t o be explained (1%'). Gas radiation may influence the heat transfer because of the high temperatures expected in such boundary layers a t high supersonic velocities (WOC). Experimental information on heat transfer in supersonic flow becomes gradually available for Mach numbers to 7 (SSC). A calculation of laminar boundary layer flow over the surface of spinning axisymmetric bodies (a&') located in a stream
INDUSTRIAL AND ENGINEERING CHEMISTRY
933
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT veyed critically (@), and new correlations have been proposed. In experiments on heat transfer between beds of fluidized solids and the m d s of the container, irregular fluctuations of the particle velocities with a period of the order 1 second were observed and were attributed to large scale eddies set up in this type of flow ( 7 D ) . Similar eddies have been observed in mixed, forced, and natural convection under the condition that the natural convection flow tends to move near the surface in opposite direction to the forced flow ( I F ) . Generally conditions appear very involved in fluidized beds and extensive fundamental research is needed to clarify this process. Interesting measurements of heat transfer from droplets of benzene rising through a mater column have been reported ( 3 0 ) .
Transfer Mechanism
104
105
106
107
108
109
1010
1011
6Fg
Figure 2. Different Flow Regimes Connected with Convective Heat Transfer in a Fluid Flowing Through a Vertical Tube (IF) Free convection Row is generated by the gravitational field and tends to create flow that near the tube surface is parallel to forced flow Pr = Prandtl number Red = Reynolds number based an tube diameter Crii = Crashaf number L/d = Length to diameter ratio of tube
parallel to the body axis indicates that heat transfer on the surface of such bodies is usually proportional to t,he spinning torque when the Prandtl number of the fluid is of the order of unity. An experiment,al investigation of laminar and t,urbulent heat transfer under the same condit,ions (d5C) determined t,he increase in heat transfer rates with rotation. The increase in turbulent flow was found to be more pronounced than in laminar floiv. The temperature increase caused by the internal friction within a flowing fluid is an important factor, not only in aeronautical applications (aerodynamic heating), but also in the oil film of fast running bearings (21C). It determines decidedly the bearing qualit'ies. Heat transfer from cylinders to a rarefied gas flowing with high velocity normal to the cylindw axis has been measured ( 1 4 C ) ,and the calculations of heat transfer t u different object,s in gas flows at extreme rarefaction (free molecule flow) have been summarized on a general basis ( 1 f C ) . Tm-o papers ( I S C , 26C) survey the present-day knowledge in rarefied gas flow heat transfer as far as theoretical consideration and experimental results are concerned.
Flow with Separated Heat transfer in air from a single tube heated electrically and arranged in an unheated tube bundle has been investigated experimentally (SD). The average heat transfer to the tube increased gradually when the heated tube was placed in the first, second, or third row. Further downstream the heat transfer did not change any more. Velocity and temperzture profiles were measured ( 2 0 ) 15 to 120 diameters downstream of a cylinder, and correlations were presented in an effort to study local conditions for transfer processes. Heat transfer to a spherical particle moving in an air stream has been measured ( 6 D ) in a Reynolds number range 50 to 1000. Correlations for the Ptanton number as a function of Reynolds number and of the skin friction coefficient are presented. A method ( 2 D ) has been proposed to calculate the radial transport of heat in packed beds through which a fluid flows in axial direction by summing up the different contributions as conduction, convection in the flowing gas, and radiation. The large number of parameters on which heat transfer in fluidized beds depends makes a satisfactory correlation of experimental results very difEcult. Present-day correlations are sur-
934
A summarizing report on present-day knowledge of transport processes in turbulent shear flow has been presented at the Third Midwestern Conference ( 2 2 3 ) . The method to calculate heat transfer in turbulent flow from information on the friction process as initiated by Reynolds (Reynolds analogy) and extended by Prandtl, Taylor, and von KArmBn has served as basis of a considerable number of recent papers. These are summarized ( $ E ) with special reference to high temperature application. I n alp attempt to further the understanding of the transition from laminar to turbulent flow in straight pipes, a study was undertaken in which the motion of a single vortex system generated near the wall on its path through the fluid has been observed (SE).
NatWrai CQnVectiQn Information on the temperature and velocity field in laminar free convection flow on a vertical plate obtained by a numerical solution oC the boundary layer differential equations is now available in a wide range of Prandtl numbers between 0.01 and 1000 ( 5 F ) . The Nusselt number can in a large range of Prandtl numbers not be expressed satisfactorily as a function of the product Grashof times Prandtl number. Approvimate solutions with integrated boundary layer equations, on the other hand, agree with the results of the exact solutions. Heat transfer t o an inclined flat plate has been investigated with the help of the Zehner-Mach interferometer ( 8 F ) . Natural convection heat transfer from horizontal cylinders to liquid metals has been measured (46'). d careful investigation of free convection heat transfer in air enclosed between two plane walls revealed the existence of different flow regimes, a laminar and a turbulent regime, and a transition regime in which, under certain circumstances, a peculiar type of cellular flow is set up ( $ F ) . Considerable free convection flow can be obtained in fluid layers by the presence of an electric field ( Q F ) . In this case Coulomb forces act as body forces in place of the gravitational force, Internal friction in natural convection flom has the interesting effect that i t tends to increase the temperature differences and in this way the free convection flow itself (OF). Local heat transfer coefficients have been measured in turbulent flow through a short tube under the condition that appreciable free convection flow is superimposed to the forced flow and that the free convection effect tends t o generate a flow which near the tube wall is directed either parallel or opposite t o the forced flow. I n the mixed flow region a considerable increase of the heat transfer coefficient is caused especially when free and forced flow are directed in opposite directions. The different flow regimes in the Reynolds-Grashof number field for parallel flow conditions are indicated in Figure 2.
~ r a ~ s and ~ ~ ~ a ~ ~ Q ~ I n the Heat Transfer Symposium a t the University of Xichigan the basic physical processes have been discussed which underly
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
Vol. 46, No. 5
FUNDAMENTALS REVIEW transpiration cooling, whereby a surface manufactured from a porous material is cooled in such a way that the coolant is pressed through the porous wall or in the film cooling process in which the coolant is blown through slots parallel to the surface to insulate it by establishing a coolant film ( I G ) . The cooling effectiveness of these methods can be increased by evaporating a liquid coolant film from the surface. A comparison of the effectiveness of the transpiration and film cooling methods with the conventional convection cooling showed (ZG) that from the viewpoint of consumption of coolant, the transpiration cooling method is the best, even when the effectiveness of convection cooling is increased by the application of extended surfaces. Film cooling has advantages over the convection cooling only when the necessity arises to cool special parts of the surface extensively. A method for a calculation of the temperature increase of a fluid flowing through a porous medium with internal heat sources has been presented (SG).
Change of Phase The large number of physical parameters on which heat transfer with evaporation and condensation depends are responsible for the fact that even the dimensionless parameters for this process have not yet been established. Rohsenow discussed the similarity laws for heat transfer with evaporation ( 6 H ) and Traupel the similarity rules for film condensation ( 8 H ) . In special cases like forced flow film boiling on horizontal tubes, it is possible to set up a theory from which heat transfer can be calculated and t o approximate experimental results ( 2 H ) . Experimental investigations in this field deal with a determination of boiling coefficients outside horizontal tubes ( 6 H ) . No general correlation for all fluids could be obtained for the reasons mentioned a t the beginning of this chapter and because probably unknown surface effects influence the heat transfer. Film heat transfer coefficients for refrigerants boiling inside tubes ( I H ) and the effect of the forced circulation rate on boiling heat transfer and pressure drop in short vertical tubes ( 7 H ) were measured. A study of the evaporation of a liquid into its own superheated vapor from the surface of short tubes ( S H ) , revealed that the Nusselt number is proportional to the square root of the Reynolds number indicating that laminar flow conditions prevail in this investigation. The two-phase one-dimensional flow equations and their application to the flow in evaporator tubes was treated in a paper at the Heat Transfer Symposium in Atlantic City ( 4 H ) . The paper covered a determination of the maximum velocity a t the evaporator tube exit.
Radiation Considerable attention has been given recently to the possibility of using solar radiation for the heating of buildings. As a basis for engineering calculations, information is necessary on the amount of heat available during the winter months ( I J ) . The amount of solar energy received by a south-facing vertical surface is of special interest. Since few direct measurements of this value exist, estimates were made on the basis of extended measurements a t one station in the United States and on information available on the amount of radiation received by horizontal surfaces ( S J ) . The localities in the United States that during winter months receive the largest amount of radiation on vertical south-facing surfaces are Colorado and New Mexico with approximately 1500 B.t.u. per square foot per day. The middle western states are generally fairly well supplied with solar heat. Washington and the northeastern states are less favored in this respect. Southern Minnesota, for instance, receives on a vertical area during February the same average amount of sun radiation as South Carolina. Collection of sun radiation a t comparatively low temperatures and its utilization for heating purposes in connection with a heat pump look especially promising. An interMay 1954
COURTESY OF T H E T R I h E CO
,
LA CROSSE, W I S .
Figure 3. Brazed Aluminum Heat Exchanger for Five Stream Operation (Above) Exploded View of Heat Exchanger (Below)
esting paper (2J) calculates the contribution of radiation to the heat conduction process in insulating material.
Measurement Techniques Special difficulties arise in the measurement of temperatures with thermocouples when a determination in high velocity high temperature gas streams has to be made. A probe measuring the total gas temperature has been described which very carefully balances and minimizes errors caused by radiation and conduction ( 6 K ) . A survey discusses the different instruments that have been developed for a measurement of total temperature in high velocity gas streams ( 4 K ) . A thermocouple has been described ( 1 K )that is able to measure transient temperatures with an extremely small time lag and that is based on an idea developed in Germany during the war. It consists of a layer of nickel with a thickness of one micron plated on top of a thin steel rod. The diameter of the complete temperature probe is approximately 1/10 of an inch and its length 3 / ~of an inch. It has been used to measure surface temperatures in gun barrels. The time required for the probe to reach 36.2% of the amplitude of a stepwise temperature change m-as found to be in the order of '/4 microsecond. A thermocouple psychrometer with a very small time lag due to the use of very fine wircs has been described ( S K ) . Interesting studies of heat transfer problems with a Zehnder-Mach interferometer are contained in a paper by Coulbert ( 2 K ) . Among those is the study of a transient boundary layer arising on a metal wall that has been heated temporarily by a flash bulb, the study of the heat flow through riveted junctions, and heat transfer studies for superimposed free and forced convection.
INDUSTRIAL AND ENGINEERING CHEMISTRY
935
eat Transfer Ap Interest in developing methods for the calculation of special type heat exchangers has continued-for instance, for heat exchangers involving more than two fluids (20L) or in unsteady state systems (15L) (Figure 3). A survey deals with design procedures for periodic flow regenerators (4L). A hydraulic analog for steady state heat exchangers is discussed ( i 8 L ) . A thorough study of the influence of heat conduction along the passage Talk parallel to the flow direction on heat exchange has been made (IOL). Heat transfer coefficients in liquid mixing using vertical tube baffles have been measured (5L). Design information on heat exchanger systems used in nuclear pori-er plants gradually is becoming available. Two papers describe liquid metal heat exchangers ( 1L, 21L ) . Transpiration cooling is considered as an effective means of cooling the blades of gas turbines, and accordingly, calculation procedures t o determine the blade wall temperatures have been developed ( l 4 L ) . The use of electric analogs for the calculation of the temperature distribution in air or liquid cooled turbine blades is described (6L). Deicing of airplanes by a heating of the critical surfaces, like leading edges of wings and ailerons, is still under intensive study (SL, 8L, 18L). The method of cyclic deicing by the application of hot gas seems especially promising (9L). Calculations indicate that icing of airplane wings may still occur in supersonic flight to Mach numbers of 1.4 in spite of the fact that a t larger velocities the wing surface is heated by aerodynamic heating (gL). Aerodynamic heating of the skin of aircraft a t high supersonic velocities causes considerable thermal stresses; accordingly heat transfer conditions and temperature distributions as well as their effect on stresses has been studied (YL,l i L , 16L, 17L, i 9 L ) .
References H e a t Conduction ( l a ) Beutler, J. A,, Jr., and Knudsen, J. G., Chem. Eng. Prop. Svmmsium Ser.. 5 (1953). (2A) Chu&ill, R, V., “Heat Transfer Symposium,” Univ. Michigan, Ann Arbor, p. 283 (1953). (3-4) Glassman, I., and Bonilla, C. F., Chem. Eng. Progr. Symposium Ser., 5 (1953). (4-4) Hirschfelder, J. O., Proc. Third Midwestern Conference on Fluid Mechanics, Univ. of Minnesota, Minneapolis, p. 3 (1953). (5A) Jaeger, 3. C., Proc. Cambridge PhiE. SOC.,49, pt. 2, 355 (1953). ( 6 4 Jaeger, J. C., Quart. Appl. Mech., 11, 132 (1953). (711) Sarukhanian, G., Forsch. Gebiete Ingenieurw., 19, 101 (1953). (8A) Sibbitt, W. L., St. Clair, C. R., Bump, T. R., Pagerey, P. F., Kern, J. P., and Fyfe, D. W., Natl. Advisory Comm. Aeronaut., Tech. Note2970 (1953). C h a n n e l Flow (IB) Bonilla, C. F., Cervi, A., Jr., Colven, T. J.,and Wang, S.J., Chem. Eng. Progr. Sumposium Ser., 5, 127 (1953). (2B) Chu, J. Chin, Brown, F., Burridge, K. G., IND.ENCI.CHEM., 45, 1686 (1953). Trans. Am. SOC.Mech. Engrs., (3B) Clark, S. H., and Kays, W. IM., 75, 1191 (1953). (4B) Deissler. R. G.. Natl. Advisory Comm. Aeronaut., Tech. Note 3016 (1953). (5B) Deissler, R. G., and Taylor, M.F., Ibid., Res. illem. E53B17 (1953). (6B) Doody, T. C., and Younger, A. H., Chem. Eng. Progr. Sumposium Ser., 5,33 (1953). (7B) Eckert, E. R. G., Proc. Third fixidwestern Conference on Fluid Xerhanics, University of Minnesota, Minneapolis, p. 703 (1953). (8B) Grele, bI. D., and Gedeon, L., Natl. Advisory Comm. Aeronaut., Res. Men. E52L09 (1953). (9B) Johnson, H. A., Hartnett, J. P., and Clabaugh, TV. T., Trans. Am. SOC.iMech. Engrs., 75,1191 (1953). (10B) Lin, T. C., and Street, R. E., Satl. Advisory Comm. Aeronaut., Tech. Note 2895 (1953). (11B) hIillsaps, K., and Pohlhausen, IC., J . Aeronaut. Sci., 20, 187 (1953).
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(l2B) Pinkel, B., Ant. SOC.iMech. Engrs.. paper 53-SA-34 (1953). (13B) Poppondiek, 13. F., Heat Transfer Symposium, Univ. Michigan, Ann Arbor, p. 77 (1953). (14B) Schenk, ,J,, and Dumore, J. ill., Appl. Sei. Research, 4 (A), 39 (1953). (I5B) Ticlball, R. A., Chem. Eng. Progr. Symposium Ser., 5,43 (1953). (16B) Tribus, M., and Klein, J., Heat Transfer Symposium, Univ. of Michigan, Minneapolis, p. 211 (1953). (17B) Walger, O., Chem.-lng.-Tech,., 25, 474 (1953). (18B) Wciland, W. F., and Lowdermilk, W. H., Natl. Advisory Comm. Aeronaut., Res. Mem. E53E04 (1953). Boundary Layer Flow
(IC) Beckwith, Ivan E., Natl. Advisory Comm. Aeronaut., Tech, Note 3005 (1953). (2C) Dienemann, W., Z. angew. Math. illech., 33, 89 (1953). (3C) Drake, R. >I., Jr., J . Aeronaut. Sci., 20, 309 (1953). (4C) Drake, R. RI., Jr., Seban, R. A., Doughty, D. L., and Levy, S., Trans. Am. SOC.Mech. Engrs., 75,1191 (1953). (5C) Eber, G. R., Proc. Third Midwestern Conference on Fluid Mechanics, University of Minnesota, Minneapolis, p. 161 (1953). (6C) Eckert, E. R. G., Heat Transfer Symposium, Univ. of Michigan, Ann Arbor, p. 173 (1953). (7C) Klunker, E. B., and LIcLean, F. E., Ibid., Tech. Note 2916 (1953). Ibid., Tech. Note 3028 (1953). (8C) Low, G. M., (9C) Martin, J. J.,J . Aeronaut. Sei., 20, 147 (1953). (1OC) Morris, D. K.,and Smith, J. W., Ibid., 20,805 (1953). (11C) Oppenheim, A. K., Ibid., 20,49 (1953). (12C) Probstein, R, F., and Lees, L., Ibid., 20,291 (1953). (13C) Rubesin, &I. W., Natl. Advisory Comm. Aeronaut., Tech. Note 2917 (1953). (14C) Sauer, F. RI., and Drake, R. X, Jr., J . Aeronaut. Sei., 20, 175 (1953). (15C) Schaaf, 8. A., Heat Transfer Symposium, Univ. of Michigan,
.._
Ann Arbor n. _. 237 - ~ ~ . ...,.. ~ ~ . (19.53). \ - - - - I
(l6C) Schaaf, S. A., Ibid., p. 261 (1953). (17C) Schuh, H., Royal Inst. Technology, Div. Aeroanutics, Stockholm, Sweden, K T H Aero TN 33 (1953). (18C) Seban, R. A,, and Drake, R. M., Trans. Am. SOC.Mech. Engrs., 75, 1191 (1953). (19’2) Sibulkin, M., and Eber, G. R., J . Aeronaut. Sci., 20, 288 (1953). \----,-
(20C) Smith, J. W., Ibid., 20,679 (1953). (21C) Stephan, H., Forsch. Gebiete Ingenieurw., B , 430 (1953). (22C) Tessin, W., and Jakob, M., Trans. Am. SOC.Mech. Engrs., 75, 1191 (1953). (23C) Tifford, A. N., and Chu, S. T., J. Aeronaut. Sci., 20, 643 (1953). (24C) Tifford. A. N.. and Chu. S. T.. Proc. Third Midwestern Conference on ’ Fluid Mechanics, University of Minnesota, Minneapolis, p. 579 (1963). (25C) Von Glahn, U., Katl. Advisory Comm. Aeronaut. Res. Mem. E53F02 (1953). (26C) Wegener, P. P., Winkter, Eva &I., and Sibulkin. AI., J . Aeronaut. sei.,20,221 (1953).
. ,
Flow w i t h Separated Regions (1D) Argo, W. B., andsmith, J. M.,Chem. Eng. Progr., 49,443 (1953). (2D) Berry, J V., Mason, D. M., and Sage, I3. II., Ibzd., Symposium Ser., 5, p. 1 (1953). (3D) Garwin, L., and Smith, B. D., Ibid., 49,591 (1953). (4D) Heerden, C. van, Nobel, A. P. P., Krevelen, D. W.van, IKD. EKG.CHEW,45, 1337 (1953). (5D) Snyder, N. W., Chem. Eng. Progr. Symposium Ser., 5 , l l (1953). (6D) Tang, Y . S.,Duncan, J. M., and Sohweyer, €I. E., Natl. d d visory Comm. Aeronaut., Tech. Note 2867 (1953). (5D) Toomey, R. D., and Johnstone, H. F., Chem. Eng. Progr. Symposium Ser., 5, 51 (1953). T r a SB sfer Mecha n ism
(1E) Kuethe, A. AI., Proc. Third Midwestern Conference on Fluid Mechanics, University of Minnesota, hIinneapolis, p. 85 (19.53. \ _ _ _ .
(2E) Summerfield, M.,Heat Transfer Symposium, Univ. of ;IIichigan, Ann Arbor, p. 151 (1953). (3E) Weske, J. R., and Plantholt, A. H., J . Aeronaut. Sci., 20, 717 (1953). N a t u r a l Conwection (1F) Eckert, E. R. G., Diaguila, A. J., and Curren, A. N., Xatl. Advisory Comm. Aeronaut., Tech. Sote 2974 (1953).
INDUSTRIAL A N D ENGINEERING CHEMISTRY
Vol. 46,No. 5
FUNDAMENTALS REVIEW (2F) Graaf, J. G. A. de, and Held, E. F. M. van der, A p p l . Sci. Research (A), 3, 393 (1953). (3F) Hahnemann, H. W., Allgem. Wdrmetech., 4,240 (1953). (4F) Hyman, S. C., Bonilla, C. F., and Ehrlich, S. W., Chem. Eng. Progr. Symposium Ser., 5 , p. 21 (1953). (5F) Ostrach, S.,Natl. Advisory Comm. Aeronaut., Rept. 1111 (1953). (6F) Ostrach, S., Trans. Am. Soc. Mech. Engrs., 75, 1191 (1953). (7F) Poppendiek, H. F., Ibid., 75, 1191 (1953). (8F) Rich, B. R.,Ibid., 75,1191 (1953). (9F) Schmidt, E., and Leidenfrost, W., Forsch. Gebiete Ingenieurw., 19, 65 (1953).
Film a n d Transpiration Cooling (1G) Eckert, E. R. G., Heat Transfer Symposium, Univ. of Michigan, Ann Arbor, p. 195 (1953). (2G) Eckert, E. R. G., and Livingood, J. N. B., Natl. Advisory Comm. Aeronaut., Tech. Note 3010 (1953). (3G) Schneider, P. J., J . AppZ. Phys., 24, 271 (1953).
Change of Phase (1H) Baker, M., Touloukian, Y. S., and Hawkins, G. A,, Refrig. Eng., 61, 986 (1953). (2H) Bromley, L. A., Leroy, N. R., Robbers, J. A,, IND.ENG. CHEM.,45, 2639 (1953). (3H) Chu, J. Chin, Lange, A. M., Conklin, D., Ibid., 45,1586 (1953). (4H) Harvey, B. F., and Foust, A. S., Chem. Eng. Progr. Symposium Ser., 5, 91 (1953). (5H) Myers, J. E., and Katr, D. L., Ibid., p. 107. (6H) Rohsenow. W. M., Heat Transfer Symposium, Univ. of Michigan, Ann Arbor, p. 101 (1953). (7H) Schweppe, J. S., and Foust, A. S., Chem. Eng. Progr. Symposium Ser., 5, 77 (1953). (SH) Traupel, W., Allgem. Wdrmetechnik, 4, 105 (1953). 1
.
Radiation (1J) Hand, I. F., Heating and VentiZating, 50,73 (1953). (25) Held, E. F. M.van der, Allgem. Warmetechnilc, 4, 236 (1953). (35) Jordan, R. C., and Threlkeld, J. L., Heating, Piping, Air Conditioning, 25,111 (1953). M e a s u r e m e n t Techniques (1K) Benderskey, D., Mech. Eng., 75, 117 (1953). (2K) Coulbert, C. D., Ibid., 74, 1005 (1952).
(3K) (4K) (5X) (6K)
Kawata, S., and Omori, Y., b. Phys. Sac. Japan, 8, 768 (1953). Kraus, W., A1Zgem. Wdrmetechnik,4,113 (1953). Lowell, H. H., J . Appl. Phys., 24, 1473 (1953). Werner, F. D., and Keppel, R. E., Proo. Third Midwestern Conference on Fluid Mechanics, University of Minnesota, Minneapolis, p. 463 (1953).
H e a t Transfer Applications Brooks, R. D., and Rosenblatt, A. L., Mech. Eng., 75, 363 (1953). Callaghan, E. E., and Serafini, J. S., Natl. Advisory Comm. Aeronaut., Tech. Note 2861 (1953). Callaghan, E. E., and Serafini, J. S., Ihid.. 2914 (1953). Coppage, J. E., and London, A. L., Trans. Am. SOC.Mech. Engrs., 75,1191 (1953). Dunlap, I. R., Jr., and Rushton, J. H., Chem. Eng. Progr. Symposium Ser., 5 , p. 137 (1953). Ellerbrock, H. H., Jr., Schum, E. F., and Nachtigall, A. J., Natl. Advisory Comm. Aeronaut., Tech. Note 3060 (1953). Foust, A. S.,Heat Transfer Symposium, Univ. of Michigan, Ann Arbor, p, 1 (1953). Gelder, T. F., Lewis, J. P., and Koutz, S. L., Natl. Advisory Comm. Aeronaut.. Tech. Note 2866 (1953). Gray, V. H., and 'Bowden, D. T., 'Ibid.', Research Mem. E53C27 (1953). Hahnemann, H. W.,Forsch. Gebiete Ingenieurw., 19, 81. 105 (1953). Huth, J. H., J . AeTonaut. Sei., 20, 613 (1953). Juhasz, I. S., and Hooper, F. C., IND.ENO.CHEW,45, 1359 (1953). Linden. A. J.. Alloem. Warmetechnik. 4. 107 (1953). . , Livingood, J,' N."B., and Eckert, E. R. G., Trans. Am. Sac. Mech. Engrs., 75, 1271 (1953). Lynch, E. P., Chem. Eng. Prom. Symposium Ser., 5. p. 121 (1953). Manson, S. V., Natl. Advisory Comm. Aeronaut., Tech. Note 2988 (1953). Manson, S. V., Heat Transfer Symposium, Univ. of Michigan, Ann Arbor, p. 9 (1953). h'lessinger, B. L., J . Aeronaut. Sci., 20,29 (1953). Parker, H. M., Natl, Advisory Comm. Aeronaut., Tech. Note 3058 (1953). Paschkis, V., and Heisler, M. P., Chem. Eng. Progr. Symposium Ser., 5 , p. 65 (1953). Trocki, T., and Nelson, D. B., Mech. Eng., 75,472 (1953).
MASS TRANSFER f@! R O B E R T L. P I G F O R D University of Delaware, Newark, Del.
The most interesting developments during the past year have been In the field of ion exchange kinetics, including both new experiments and calculation methods. Other important developments have taken place in calculational methods for diffusion and in experimental studies of thermal and molecular diffusion rates.
LTHOUGH a large volume of information is already avail-
A
able on the resistance to mass transfer from a geometrically simple surface to a fluid that flonv past it there is still a need for additional data of this kind, especially if the experiments are carried out carefully. By comparing various hypotheses about mass transfer mechanism with such data more may be learned about the processes by which turbulent exchange and other mass transfer phenomena take place.
Mass Transfer Rate Measurements a t Surfaces Evaporation of water into a turbulent air jet from a porous flat surface parallel to the direction of air flow was investigated experimentally by Spielman and Jakob (8.5). The jet was formed by a rectangular nozzle located about 3 inches from the first May 1954
of 11 porous plates, each 3 inches long in the direction of flow. The best of the data obtained on local mass transfer coefficients was found to be correlated by the empirical equation
(hcx/Du)(pBlv/l') = 0.031 ( z u l p / p ) o . * [ l
-
(2s1/2)o.*]-o.11
(1)
where k, = local mass transfer coefficient, pound-mole per (hour) (square foot) (Pol1nd-mole Per cubic foot), based on the d r ~ i t = i g ~ ~evaporating ~ n ~ strip ~ o from ~ cnozzle ~ ~outlet, ~ ~ ~ ~ feet x8t E distance of leading edge of first active mass transfer area from nozzle, feet D o= diffusion coefficient in gas, square feet per hour P B M = logarithmic mean partial pressure of air, atmospheres
z
~ ~ ~ ~ $ in air ? jet~passing~ Over~evapo~ rating strip, feetper hour p / p = kinematic viscosity of gas, square feet per hour
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
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