HEATTRANSFER mg
GEORGE T. SKAPERDAS
THE M. W. KELLOGG COMPANY, NEW YORK 7, N. Y.
FLUIDIZED SYSTEMS
I E L D S of heat transfer in which substantially more work was reported for the year ending September 1949 than for any previous periods covered in this series of reviews include surface boiling, fluidized systems, and compressible flow of air in the sonic velocity range. Additional data, however, became available in many other fields.
The past year was marked by the appearance of heat transfer data in the industrially important field of fluidized beds of particles. Mickley and Trilling (58) measured heat transfer coefficients for beds of spherical glass beads fluidized by air in two types of apparatus. I n one, heat was supplied by an axial Calrod to a bed 2.875 inches in diarncter and 50 inches high and in the other heat was supplied through the outer circumferential surface of beds 4 X 100 inches and 1 X 75 inches. In all cases only part of the bed received heat. In general, the presence of solids greatly increased the heat transfer coefficient possible a t the same superficial gas velocity, the increase being as much as seventyfold in some cases. Data from the internally heated bed could be correlated by solid concentration and particle diameter, but the superficial gas velocity was needed as an additional factor in order to correlate the data from thc externally heated system. No explanation of this functional difference was offered and the authors pointed out that many more variables remain to be studied. Leva, Weintraub, and Grummer ( 4 7 ) heated air, carbon dioxide, and helium flowing through fluidized beds of round sand, sharp sand, and an iron catalyst in steam-jacketed tubes. The large increase in coefficient due to solids was again reported, and correlation of these data led to the conclusion that the coefficient varied with mass velocity but was independent of solids concentration and solids density. Levenspiel and Walton ( 4 8 ) reported data on heat transfer between the container wall and air-fluidized coal, extending the gas velocity downward t o values well below those required for fluidization. Though the heat transfer coefficient increased with gas rate a t low gas rates, the coefficients increased but, slightly t o a maximum and thcn decreased as gas velocity increased in the range of fluidization velocities. A fluid bed, the lower part of which was cooled while the upper part was heated, was studied by Gilliland and Mason (28). The lower section dissipated almost all the heat absorbed in the upper part, indicating very rapid solid mixing vertically. The bed exhibited very small axial temperature gradients, but somewhat greater radial gradientr. An abstract of Russian worh on heat transfer in fluidized systems published by Chukhanov ( I O ) was noted.
GENERAL
h selective review of developments in heat transfer since 1942 !vas presented in some published lectures of McAdams (5.8); these covered analytical and numerical methods of solution of conduction problems of increasing complexity; boiling, including surface boiling phenomena and the effect of pressure up to the critical; analogies between transfer of momentum and heat; mean temperature difference definitions; and heat transfer to air flowing a t velocities in the sonic region. The first volume of a heat transfer book by Jakob (SI) appeared. This book placed great emphasis on the theoretical concepts of convection, boiling, condensation, and particularly conduction, but included empirical correlations of data that are useful in equipment design. SURFACE BOILING
The teini “surface boiling” has been used to describe the very high heat transfer rates observed when subcooled liquids are heateci by surfaces above the boiling point. This phenomenon was specifically investigated by Knowles (4g,43) a few years ago. lIcAdams et al. (53) studied this field further by heating degassed distilled water rising through an annular space heated by a stainless steel tube 0.25-inch in outside diameter. The observed heat fluxes rose from normal values to 2,000,000 B.t.u./ (hour)(sq. foot) when the surface was raised above the boiling point of water. Photographic observation showed cyclical formation of bubbles on the surface and subsequent condensation a t regular intervals. Regardless of water velocity, pressure, degree of subcooling, and system dimensions, d l flux data were correlated against the difference between surface temperature and saturation temperature of the water as long as the water had been degassed. Aeration of the wa‘ter gave higher heat fluxes a t a given temperature difference. Another investigation of surface boiling JT as rrported by Kreith and Summerfield (45) who determined heat transfer for flow of aniline, n-butyl alcohol, and water through a tube 0.5 inch in inside diameter and 17.5 inches long. The beneficial effect of surface boiling, with at,tendant fluxes up t o 1,600,000 B.t.u./(hour) (sq.foot), was observed when the surface was above the bubble point of saturated aqueous aniline, though below the boiling point of dry aniline. These investigators concluded that addition of a small amount of a volatile component should be helpful in achieving the very high rates characteristic of surface boiling. I n these tests, the difference in temperature from the surface to the bulk of the liquid appeared t o be one of the correlating variables, and pressure drop data were obtained for n-butyl alcohol. Gunther and Kreith (94) heated stagnant, subcooled water using a small, flat, horizontal, electrically heated strip above the boiling point, and took pictures a t the high heat fluxes. From these observations it was concluded that the high transfer rates resulted from disturbance of the surface film by periodic formation and collapse of bubbles.
COMPRESSIBLE FLOW OF AIR
Interest in gas turbines and high speed flight has led to studies of heat transfer to air flowing a t sonic velocities. Heat transfer coefficients and pressure drop were measured by Kaye, Keenan, and McAdams ( 3 8 )for air flowing a t supersonic velocities through a 0.5-inch tube of brass, Textolite, or Lucite, and low values of heat transfer and friction loss weie observed. It was found that Stanton numbers varied between values characteristic of laminar flow and values characteristic of turbulent f l o in ~ &heboundnry layer, rising to approach the latter values toward the end of the supersonic test section where the bouiidary layer had become more fully established. Humble, Lowdermilli, and Grele (50) measured heat transfer and pressure drop for air flowing in a heated tube at temperatures up to 1600” F. and Mach numbers up to unity. Temperature was found to be a separate variable in correlating the data using Nusselt, Prandtl, and Reynolds numbers evaluated a t the bulk temperature, but all data could be brought to one line using mixed temperatures in evaluating the 62
lanuary 1950
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INDUSTRIAL AND ENGINEERING CHEMISTRY
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moduli. A summary of available information on convection coefficients for plates, wedges, cones, cylinders, and pipes a t high velocities was presented by Johnson and Rubesin (34) and test data on heat transfer t o the nose of a'rocket were reported by Fischer and Norris ( I ? ) , who found the stability of the boundary layer t o be influenced by Mach number and surface temperature rather than by Reynolds number. An analytical study by Kalikhman (35) of heat transfer and flow in the sonic range was translated, and Goldstein and Scherrer (23)presented test results of a total temperature probe in which recovery, at supersonic velocities, of the velocity temperature component was almost complete. Teniperature distribution work for high velocity, parallel flow past a flat plate was reviewed by Rubesin and Johnson ( 6 9 ) .
correlations, and over-all coefficients$of 17 to 44 B.t.u./(hour) (sq. foot)( O F.) were observed. Hall and Smith ($6)determined reaction rate, radial temperature distribution, and effective thermal conductivity in a 1.5-inch differential reactor during catalytic oxidation of sulfur dioxide, One of the conclusions from this work was that the radial mixing of gas was slight. Ledoux ( 4 6 ) presented a graphical solution, using dimensionless quptities, of the unsteady state cooling of a bed of broken solids by means of a gas stream, as employed in regeneration of adsorption beds. A nomograph on transient heat flow in packed beds was presented by Klinkenberg (41), and data on heat transfer between air and sand in a rotary dryer were presented by Friedman and Marshall (18).
CONVECTION
DIRECT CONTACT CONVECTION
Omohundro, Bergelin , and Colburn ( 6 0 ) presented preliminary results of a comprehensive program on cross-flsw heat transfer of interest in shell and tube exchangers. The measurements, in which oil was cooled in a bank of seventy tubes on staggered equilateral spacing, indicated t h a t the heat transfer data showed general but not complete agreement with previous correlations. The available viscosity correction ratio and the correlations on the effect of tube size or pitch were found, however, not to represent these recent results in pressure drop. I n a further report from this program, Bergelin, Davis, and Hull ( 4 ) reported more heat transfer and pressure drop data for in-line and square and triangular staggered banks of tubes. The pressure drop data were correlated by a viscosity ratio of varying index in the viscous range of Reynolds numbers, but a constant index on the viscosity ratio was satisfactory for the correlation of heat transfer data. The heat transfer coefficient a t a given oil velocity was the same for the staggered tube arrangements but somewhat lower for the in-line banks. The j-factor a t a given Reynolds number was different for each of the three banks, but at a given unit power loss the staggered arrangements gave higher coefficients, the differences decreasing at higher velocities. Pressure drop and heat transfer test results useful for comparing 16 exchangers for possible service as aircraft heaters were compared by Boelter et (11. ( 5 ) , and London and Ferg presented summarized test results for seven types louvered fin units considered for use in gas turbine regenerators. It was reported that none of the various finning arrangements tested gave as high a coefficient a t a given power 103s per unit surface as do pin fins. Heat transfer coefficients for fatty acids flowing through tubes in the transition region were measured by Kern and Van Nostrand (39),who found the values to be lower than could be predicted from some of the available correlations. Giedt ( 2 1 ) measured the variation in the local coefficient as air was heated flowing across a &inch cylinder. Starting from the forward stagnation point, the coefficient decreased to a minimum and then increased to a maximum, but a t high Reynolds numbers the local coefficient decreased again toward the rear stagnation point. Properties required in the design of'systems usirig chlorinated biphenyl as a heat transfer fluid were presented by McArdle et al. (55), while papers on convection were presented by Drake ( 1 4 ) for an inclined plate in the laminar flow region, by Wagner (7'4) for a disk rotating in ambient air, and by Elenbaas (16)for vertical and horizontal cylinders. Eckert (16) presented a photographic study of laminar layer turbulence. I n the field of heat transfer in packed beds, Bunnell et al. (8)passed hot air through a 2-inch reactor packed with alumina cylinders in a bed cooled by boiling water. Gas and solid temperatures were measured at various levels and the results were reported as effective thermal conductivities which increased with gas velocity. Tasker (72) presented test data on heat transfer in a phthalic anhydride pilot plant catalytic reactor made of 1.5-inch tubes; his results were compared with previous
A careful theoretical analysis and experimental results for heat and mass transfer between air and water in a packed column were presented by McAdams, Pohlenz, and St. John *(64).It was found that the familiar equality between humid heat and the ratio of volumetric heat transfer and diffusion coefficients is not generally valid in packed towers, particularly a t low gas velocities, and this effect was attributed to incomplete wetting of the packing a t the lower gas velocities. By taking data on the same equipment for adiabatic, isothermal water conditions and adiabatic, water-cooling conditions, it was possiblc to estimate the liquid film resistance in cooling runs to be about 27 to 46% of the total resistance. The importance of allowing for liquid film resistance in these systems was pointed out. Taecker and Hougen (71) measured heat transfer coefficients for air cooled by evaporation of water at its wet-bulb temperature from porous rings and Berl saddles wetted thoroughly with water but not irrigated, The results show t h a t rings have lower heat transfer factors than solid spheres (which were studied previously) and that Berl saddles give higher heat transfer factors than rings, the difference increasing with Reynolds number. Peck and Ryant (65) studied the water-cooling performance of an automobile radiator core for operation when dry, or when sprayed with water or lithium chloride solution. Heat transfer by direct contact of two liquid phases was studied in the case of water and hydrocarbon oil3 by YablonskiI and Yablonskaya (80),who correlated their results in terms of the Nusselt, Grashof, and Prandtl numbers, using a calculated interfacial temperature. CONDENSATION AND BOILING
Condensation of Freon 12, n-butane, acetone, and water outside a single vertical row of 6 tubm with 16 cross fins per inch was studied by Kat2 and Geist (36). Over-all coefficients were measured and condensing film codTicients were calculated using the Wilson plot. Visual observation showed that condensate flowed from tube to tube only a t certain points but not uniformly along the tube length, and splashed away from lower tubes more and more as the condensation rate was increased. This effect and the tiansition to a condensate film Reynolds number greater than 2100 were reported to bt: the reason for the much smaller decrease in condensing coefficient for the lower tubes than predicted by the Nusselt theory, and it was observed that the average coefficient for six tubes was only 10% lower than the coefficient for the top tube. These results may have been due in part to the fact that the second tube was bowed and, furthermore, bypassing p u l d be minimized in a tube bank. Coefficients for the top tube were, on the average, 14% below the value predicted by the Nusselt equation, and acetone, which has high static retention on the fins, gave at least as good coefficients as Freon 12 which has low retention, indicating t h a t retention of condensate on the fine is a n unimportant factor for these condensing film coefficients.
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I N D U STR I A L A N D EN G IN EER IN G CM EM I STR Y
Chu et (11. (9) preezntrd ,data on condensing benzene, toluene, and ethyl acetate on a horizontal tube. Film coefficients were derived from over-all coefficients using a Wilson plot modified to pIot points a t constant heat flux, and, therefore, constant condensing coefficient. These data were in fair agreement with the Nusselt, theory. Film coefficients for Freon 12 boiling inside a single, horizontal tube heated electrically were reported by Geigcl et al. (70), and Lukomsld (51) studied the effect of pressure on boiling of carbon dioxide, noting that increased pressure led to lower coeficients near the critical. Kirschbaum (40) presented a paper on evaporation of water from graphite and porcelain tubes, and Hildebrandt and Warren ( 2 7 ) reported results of scaling in boiling calciuni sulfate solutions and fermentatioii mash stillagz CONDUCTION
’Thermal conductivity data were presented by Bates ( 2 ) for ailicunes,.and by Boelter and Sharp ( 6 ) for air and exhaust gases between 50” and 900” F. A previous correlation of t,hermal conductivity of metals was discussed by Powell (66). Some data a t room temperature on the thermal conducthity of packed cottonseed hulls were presented by Long (50). Data on constitution and properties of various high temperature insulating materials were reported (1, 80,62, 67, 68, 7s). Thermal resistance data on laminated and machined joints were reported by Brunot and Buckland ( 7 ) and on joints between stationary metal surfaces by Weills and Ryder (77). I n the solution of complex conductLon problems the relaxatioii method was applied by Nickerson and Dusinberre (59) to the numerical solution of heat transfer through thick insulation on cylindrical enclosures, and McCann and Wilts ( 6 6 ) presented data on the second resistor-capacitor analog computer now zvailable in the United States for solution of complex problems. Kayan (37)solved the case of heat flow through a two-dimensional corner composed of two different materials, taking into account resistance on both sides of the corner. He used three methodsgeometric analogy, electric analogy, and arithmetical iterationand compared the results. Solutions of heat conduction problems specifically involved in sliding friction between solid bodies m-ere presented by Holm (dB), Oosterkamp (61), and Wannier (75). SERVKE AND DESIGN DATA
Fouling Coefficients were determined by Watzinger and Lyderaen ( 7 6 ) for sodium chloride brine in steel pipes, and the results were found to be slightly higher than data previously available for sea water. Hall and Weston (26) presented extensive test data on the effect of treating cooling water high in organic matter by means of phenolic compounds and chlorine; the beneficial effect of such treatment on industrial hydrocarbon condensers was illustrated. Deposits found on the flue gas side of boilers fired with English coals were described by Crossley ( l a ) ,who also outlined methods of alleviation. A semitheoretical method €or design of circular tube sheets was presented by Gardner (19). MISCELLANEOUS
Dah1 and Fiock ( I S ) discussed the use of noble metal shields for thermocouples used on gas turbines, and Hornfeck (29) presented test data comparing the response characteristics of several designs of thermometer elements. A method of measuring film heat transfer coefficient without measuring surface temperature was described by Bell and Kat2 (3). The method is based on flow of fluid with cyclically varying temperature past the surface and observation of the resulting change in amplitude and phase of the fluid temperature. Sweat cooling refers to cooling a porous materia1 exposed to high temperature by passage of a cool gas through the porous
Vol. 42, No. 1
body. Weinbaum and Wheeler (78) presented a mathematical analysis for this system and Jakob and Fieldhouse (39)presrnted test results for a 1-inch porous disk. 13ielectric heating of gFanular silica was investigated by Jelinek et al. (SS),who found that the heating rate for silica was much smaller than for alumina, which had bcen tested earlier. Heating rates of foods in glass and other containers were studied by Mcrrill (57). Heat transfer through glass panes simulating windows was determined by Parmelee and Aubele (6S), who also reported on solar energy transmission through hollow glass blocks ( 6 4 ) . Thermal conditions in rooms were discussed by Korsgaard ( 4 4 ) , a i d the heat absorption of a horizontal coil buried in the ground was measured by Coogan (11) to supply data for heat pump design. Tribus et al. ( 7 3 ) reported analytical determinations of heat transfer from a small Calrod to air containing water vapor or water dropleis, and ronyidered both icing and nonicing condition? LITERATURE CIKD
Baldwin, W.J., Chem. .Eng. Progress, 44, 875 (1948) Bates, 0. IC., ISD. EKG.CHEM.,41, 1966 (1949). Bell, J. C., and Kats, E. F., “Heat Transfer and Fluid Mechanics Institule,” p. 243, New York, Am. Soc. Mech. Engrs., 1949.
Bergelin, 0. P., Davis, E. S., and Hull, €1. L., Trans. Am,. SOC. Mech. Engrs., 71, 369 (1949).
Boelter, L. M. I
