0
Evaporation of liquids into Their
Superheated Vapors
0
JU CHIN CHU, A. M. LANE1,
AND
D. CONKLIN2
Polyfechnk lnsfifufe of Brooklyn, Brooklyn, N. Y.
D
RYING solids by direct contact with the superheated vapors
of its own moisture, especially superheated steam, has t~een recommended as a highly efficient method of drying by several authors. Walker, Lewis, WcAdamns, and Gilliland (19) mention briefly the advantages of superheated steam drying. Superheated vapor has had limited application in the past. Wenzel and White (20, 21) summai,ized the past applications on drying brown coal, lignite, wood, and vegetables with superheated steam. Wenzel (20) mentioned some recent superheated st,eani installations for drying silica gel and insulating material. Super:heated hexane vapor drying is being employed to remove hexane from extracted soybean flakes. Most recently, pilot plant equipiment is being built for drying calcium silicate with superheated st,eam. Serious consideration has rec,ently been given to drying of activated carbon, petroleum catalysts. and coal with superheated steam. Superheated vapor operation, although endowed wit'h many advantages, thermal and otherwise. has certain limitations. First, it is limited to drying solids which have an allowable temperature limit above the saturation temperature of its moisture and probably above the opemting temperature of t'he superheated vapor, depending on the degree of dryness required. Another disadvantage is that it is difficult to obtain low moist,uw contents. It was the purpose of this investigation to determine t8heevaporation rates from a liquid surface when in direct contact with its superheated vapor. Liquid surfaces were chosen sincc they present kuown surface areas xvith which accurate values of the rate of evaporation or heat transfer coefficientscan be d&mninerl. The data obtained from this investigatiori is direvtly c.ompi~ral~lc to the constant rate period when drying solids. In the evaporation of liquicls with air, vapors from the liquid interface must diffuse through - an air film to reach t'he mniii air stream. The vapor in the air film is at a higher partial pressure than the vapor in the main air stream. The difference in the partial pressures is a measure of the driving force for mass transfer. I n superheated vapor evaporation partial pressure differences do not occur. Wenzel and White (20, 21) have postulated that the temperature a t the interface is higher than the saturation temperature corresponding to the operating pressure of the equipment. In other words, the liquid is superheated with respect to the operating pressure of the equipment. A degree of liquid superheat of t'he order of a few hundredths of a degree Fahrenheit would be sufficient to provide adequate vapor pressure increase to account for the mass transfer. Technical difficulties make it, difficult, however, to measure such small temperature increases in a fluid film.
The investigations of \Venae1 et a [ . (80. 21) were limited t,o high pressure operation which would find very limited application because of the more expensive equipment required, the higher operating temperatures, and because operation would necessarily have to be hatchwise. The final correlatiou on the basis of the dimensionless equation flowing parallel to single planes WIS given as (20):
This cortelation of his data gave him results that had a maximum deviation of &40% and a standaid loot-mean-squ:tre deviation of 5 2 0 % .
Equipment The experimental equipment consisted essentially of an electrically heated boiler, an electyically heated superheater, a n evaporating chamber, and a condenser, as shown in Figure 1. The superheater raised the saturated vapor to the desired temperature. The superheated vapor next entered the evaporating chamber where saturated liquid was evaporated. The superheated vapor containing evaporated liquid was then conderlsd and the condensate collected and measured. Boiler. The boiler was constructed from 6-inch standard steel pipe, 33 inches long, and placed in a vertical position. The bottom plate was drilled and tapped t'o receive four Chromalox Type TX-1415B copper immersion heat'ers, each of' which was rated a t 1500 watts operating on 115 volts, giving a total boiler capacity of 6 kw. The rate of liquid feed to t,he boiler was maintained constant hy means of a constant level regulator, as indicated in Figure 1. During actual operation of the boiler it was observed that the
.
1
Present address, Wyssniont Co., Long Island City,
N. Y. 1
Figure I. Experimental Equipment
Present address, Merck & Co., Rahway. N. J.
1586
July 1953
INDUSTRIAL AND ENGINEERING CHEMISTRY
level controller was sensitive to small changes in level of the boiler, ensuring a uniform, steady flow of liquid make-up into the boiler. Sufficient vapor space was maintained above the boiling liquid to knock out entrainment. A vapor outlet from the boiler to bhe superheater was provided on the side of the boiler near the top. The outlet connection was made by weldin a 11/2-inch International Pipe Standard nipple to the boiler. #he entire boiler was insulated with 4 inches of glass wool. Evaporating Chamber. The evaporating chamber which was constructed of 16-gage sheet steel consisted essentially of a duct to carry the superheated vapors and a pan containing the liquid under investigation. The vapor duct was comprised of a transition section from 2 X 2 inch opening of the superheater t o a 2 X 4 inch cross section above the pan where the evaporation took place. The over-all length of the evaporating chamber was 241/2 inches. The evaporator pan had an area of 4 X 4 inches and was l l / r inches deep. It was flanged to the vapor duct and was therefore removable for cleaning. I t was thermally insulated from the duct. A liquid level gage was constructed to detect liquid level changes of less than l / 4 0 inch. An observation opening in the side of the vapor duct afforded a visual check on the liquid level, as well as providing a means to align the equipment before operation. Tempcratures of the superheated vapor before and after the pan were measured by means of mercury thermometers graduated from 100" to 200" C. at intervals of 0.1" C. The entire evaporating chamber, including the pan, was insulated with 4 inches of glass wool. The details of superheater and condenser have been published (8).
Experimental Fluids. The liquids investigated in this study were water, 1-butanol, and benzene. The I-butanol and benzene were technical grade, having a minimum purity of 99%. Distillcd water was used in both the boiler and thr rvaporator.
Experimental Procedure
rl
After the boiler and evaporating pan were filled with cpld liquid to the predetermined levels, the electrical immersion heaters in the boiler and the condenser cooling water were turned on. When the liquid began to boil, the boiler feed level controller was adjusted to maintain the proper level in the boiler and the neparatory funnel was filled with liquid. The superheater was turned on and the Powerstat adjusted to give the proper degree of superheat. When dealing with flammable vapors, it is important that the superheater be turned on after boiling has started in order to preclude the possibility of autoignition before the system is purged of air. The equipment was then allowed to come to equilibrium. The time required to come to equilibrium was usually 2 to 3 hours, depending on the temperature of the ,superheated vapor and the flow rate. The liquid level in the evaporator pan was kept constant during the period of attainment of equilibrium. The equipment was considered to be in equilibrium when the thermometers upstream and downstream of the evaporator pan did not vary more than 0.2' C. during a period of a t least 20 minutes. After equilibrium had been established, the flow rates to the boiler and to the evaporator and of the condensate were determined by measuring the times required to deliver or collect measured volumes of the liquid. For the condensate rate and the boiler feed rate, each 1000- or 2000-ml. batch was timed. For the evaporator feed, each 25 ml. was timed, although where the evaporation rat@ was high 100-ml. increments were used. An average of 500 ml. of liquid were evaporated for each run.
Table 1.
1587
The temperatures of the superheated vapors, as well as the temperatures of the boiler feed and evaporator feed, were recorded a t frequent intervals, along with the boiler temperature and pressure, The liquid level in the evaporator pan was checked continuously. For those runs which immediately foilowed the preceding run, the firsf three steps were not required. I n the fourth step, the Powerstat was merely adjusted to give a new superheat temperature. The last two steps were then followed, as outlined above. The radiation effect of the comparatively cool liquid surface on the thermometers is to cause these thermometers to give temperature readings lower than the true gas temperature. To investigate this effect, a run was chosen where the vapor temperatures are a t a maximum and the true gas temperatures were calculated. The calculations were based on the assumption that all the surfaces seen by the thermometers, including the walls of the duct, were a t the saturation temperature of the liquid. The maximum possible error calculated is about ITo,which is within ex-perimental error.
Results The experimental data and calculated heat transfer coefficients are summarized in Tables I, 11, and 111, for the three liquids investigated-1-butanol, water, and benzene, respectively. The conditions chosen for the tests are in the range of those normally encountered in commercial applications involving the drying of granular or powdery solids. The enthalpy data of the
Experimental Conditions and Heat Transfer Coefficients for 1-Butanol
Vapor Temp., F. Upstream Downstream
Condensate Rate, T z m c , g./hr.
Evaporator Feed Rate Temp., g./h;. F.
6240 5910 5980 6300 6210 12700 12600 12500 19000 18800 19500 19020
221 156.2 88.5 300 208 202 297 380
' F.
("
F.)
312.8 314.8 282.0 352.0 353.3 305.2 333.0 351.0 320.2 351.1 299.7 272.1
Table II.
Experimental Conditions and Heat Transfer Coefficients for Water
Table 111.
Condensate Rate, Temp.: g./hr. F.
Evaporator Feed Rate, Temp., g./hr. O F.
6610 6480 6420 4390 4290 4380 3540 3650 3620 6450 2140
80.4 85.6 103.0 77.5 51.6 51.2 62.4 33.4 50.3 76.4 26.4
64 63 62
130
61 63 63 66 66 80 80
80 82 80 75 78 83 82 82 72 78 80
243.9 243.9 243.9 243.9 243.9 243.9 243.9 243.9 243.9 243.9 243.9 243.9
20.4 14.7 14.0 18.1 12.6 21.8 22.4 24.0 39.8 37.8 35.8 31.0
B.t.u./ihr.) hc ta.
' F. 212.0 212.0 212.0 212.0 212.0 212.0 212.0 212.0 212.0
. .. ...
ft.) (OF.)
(aq.
13.8 13.3 14.9 13.1 11.1 12.3 10.5 9.06 10.9 12.3 6.56
Experimental Conditions and Heat Transfer Coefficients for Benzene
Vapor Temp., F. Upstream Downsbream 274.8 353 3 310.5 276.3 311.7 351.9 334.7
435 603 284 125
61 65 78 61 66 77 67 74 71 68 64 67
B.t.u./(hr.) (sq. ft.)
341.2 336.0 297.1 386.2 384.6 322.0 356.5 373.6 332.4 a72. 6 308.7 276.8
Vapor Temp.. F. Upstream Downstream
56 57 60 55 56 64 61 64 73 73 70 69
hot
ts
258.6 327.6 291.4 266.4 298.2 330.1 305.2
Condensate Rate, Temp.,
g./hr. 11180 11620 11630 22500 22700 22800 10810
F. 64
..
67 68 68 68 79
Bvaporator Feed Rate Temp., g./hr: 295 576 380 373 541 705 481
F.
74 76 76 65 73 75 78
hc,
ta,
F.
176.2 176.2 176.2 176.2 176.2 176.2
...
B.t.u./(hr.) laq. ft.) F.) 14.4 15.0 13.4 17.2 18.4 18.8 14.5
("
INDUSTRIAL AND E N G I N E E R I N G CHEMISTRY
1588 IO00
Vol. 45, No. 7
the Reynolds number. By the theory of least squares, the equation of the line that best fits the data is:
600
Instead of the equivalent diameter, the previous investigators (10, 20, 21) used the length of evaporation surface parallel to the direction of flow. On this basis the data TYas correlated as curve A in Figure 3. The equation of this curve was represented by:
300 -4
g
@
.-x
(7) 100
70
600
330
1000
2000
Repold's
Figure 2.
0
6000
KKX,
b000
Number, Re:?
Correlation of Heat Trader Coefficient
Butyl alcohol
0
Water
@
j{ =
Benzene
liquids and saturated vapor were calculated from the data given (11, 12, 16). The heat transfer coefficients were calculated from experimental data using the following equations:
ti - tz A ~ L X= ___ tl - t,
In tz - te h,
Cuive B represents the line that best fits the data of Wenzel et al. (20, 21). Curve L" represents the line that best fits both the data of Wenzel and the data of this investigation. Although the author of this paper does not recommend the use of this curve, its use for calculation purposes will yield a conservative design. The equation of this line is:
=
AtLM
(4)
= 26.6
($)($)2'3
(--) LG
-0.00
The standard deviation of the experimental data obtained during this investigation was =t21%.
Discussion The results obtained in this investigation have been shown to correlate well with methods to be found in the literature based on the physical proprrties of the fluid in addition to the operating characteristics. The experimental data have a standard rootmean-square deviation of =t11%, and a maximum deviation of rtr21%. Although the possible advantages of using superheated vapors have Iong been recognized, only recently (20, $1) has any
The heat transfer coefficients are correlated on the basis of the following j-factor equation: (5)
Tables IV, V, and VI present the values of the physical properties of the three fluids studied, as well as the mass velocities, from which the values of the various dimensionless groups can be calculated. The values of the physical properties for the superheated vapors were evaluated a t the arithmetic mean temperature, t A M , of the upstream temperature, t ~ and , the downstream temperature, t2. Colburn ( 2 , 1 5 )recommends that the caloric temperature be used in evaluating the properties of the superheated vapor. It was found that in this mor k Then the heat transfer coefficients do not differ greatly a t the hot end and the cold end, the difference between the caloric temperature and the arithinrtic mean temperature was negligibly small. The viscosity of 1-butanol vapor was calculated from the generalized chart as presented by Hougen and Watson ( 5 ) The thermal conductivity of I-butanol vapor was calculated from the equation of Shushpanov (17'). The specific heat of 1-butanol vapor was calculated by the method of Dobratz (3). Dobratz compared the value for the specific heat of 1-butanol calculated by his method with experimental data within the temperature range employed in this investigation and found agreement within 1%of the experimental value. The viscosity, specific heat, theimal conductivity, and Prandtl number of superheated steam were obtained from the critical study of Govier (4). The specific volume of superheated steam was obtained from Keenan and Keyes (6). The viscosity and thermal Conductivity of benzene vapor was obtained from Perry (IS, 14). The specific heat of benzene vapor was obtained from Clarke ( 1 ) . Figure 2 is a logarithmic plot of heat transfer factor, J H ,versus
Table IV. G
Dimensionless Heat Transfer Groups for Superheated 1-Butanol Vapor Ir
Table V. G 431 438 446 878 577 874 416
P
G 259 254 251 171 167 172 138 143 142 253
83.8
k 0.0164 0.0154 0.0140 0.0171 0.0171 0.0149 0.0160 0.0169 0.0154 0.0168 0.0145 0.0135
Pr-lJa 1,090 1,090 1.082 1.093 1.093 1,090 1,090 1.093 1,090 1.092 1.086 1,082
Nu
Nu'
Dimensionless Heat Transfer Groups Cor Superheated Benzene Vapor CP $ Pr-lIa Xu h-u'
0.0247 0.0273 0.0259 0.024R 0.0260
0.0273 0.0267
Table VI.
CP
0.461 0.461 0.445 0.481 0.481 0.455 0.470 0.478 0.461 0.478 0.481 0.438
0.349 0.373 0.360 0.380
0.361 0 373 o 3x0
0 0119 0,0144 0.0130 0,0121 0,0131 0.0144 0.0137
1.113
1.121 1.118 1.114 1.118 1.111
1.083
242 209 206 285 280
260 212
403 348 343 475 466 434 330
Dimensionless Heat Transfer Groups for Superheated .Steam B
CP
0.0352 0.0333 0.0364 0.0357 0.0339 0.0324 0.0354 0.0328 0.0340 0.0357 0.0332
0.471 0.474 0.470 0.471 0.473 0.476 0.471 0.475 0.473 0.471 0.474
ic 0.01735 0.01621 0.01807 0.01760 0.01655 0.01573 0.01743 0.01593 0.01659 0.01760 0.01613
Pr-l'a 1 014 1.000 1.107 1.015 1,010 1.007 1.014 1.008 1,010 1.015 1.009
NU 158 164 165 134 135 156 120 114 131 140 81
XU' 264 274 274 223 224 260 200 190 217 230 135
I N D U S T R I A L AND E N G I N E E R I N G CHEMISTRY
July 1953
R#ynold I
Figure
Nu&,
Re's
9
3. Correlation of Heat Transfer Coefficient
0 Butyl Alcohol 0 Water
8
Benzene
0 Water Data of Wenzel (20, 21)
work been done to develop the quantitative information. The equation recommended by Wenzel does not fit well with the data obtained in this investigation, Wenzel (20) stated qualitatively that, as the degree of confinement of the vapor flow over the liquid surface becomes greater, the effect of mass velocity becomes smaller. Previously published d a t a by Shepherd, Hadlock, and Brewer (16) for air drying indicates that h =f
(G)o.76
(9)
whereas Wenzel's d a t a yields the relation h = f
(G)@.36
(10)
This work indicates that
h = f (G)o.s"
1*
1589
those solids where the surface roughness effect is appreciable, the use of Equation 6 will yield a conservative design and an allowance for this can be made if desired. The illustrative problem which follows indicates how the equation can be applied to a drying problem. The advantage that could be realized when using superheated vapor as a drying medium is illustrated in Figure 4, which presents a comparison between the rate of evaporation of water with superheated steam and the rate of evaporation of water with air, both at atmospheric pressure ( 7 ) . The data for the evaporation of water with air was calculated from the data of Shepherd, Hadlock, and Brewer (16) on the basis that the air is a t an absolute humidity of 0.0 pound of water per pound of dry air. The decided advantage of superheated steam is readily apparent. The results of Maisel and Sherwood (IO)for the evaporation of water into air from plane surfaces were examined and were considered inapplicable for comparison with the data obtained from this investigation. The rates of evaporation into suDerheated steam were calculated from Equation 6. Figure 5 shows graphically the rates of evaporation of benzene into superheated benzene vapor and into air a t various temperatures and mass velocities. The data for the evaporation of benzene into air was calculated from the equation of Wade (18), assuming the humidity of the air is 0.0 pound of benzene vapor per pound of benzene-free air in order to calculate maximum rates. The rates of evaporation into superheated benzene vapor were calculated from Equation 6. Examination of Figures 4 and 5 clearly indicates the greatly increased rates of evaporation obtainable with superheated vapors except when the superheated vapor temperature is relatively close to the saturation temperature. With superheated vapor operation the rate of evaporation approaches zero a t the satura-
(11)
The weighing technique employed by Wenzel could be a possible source of error which increases as the mass velocity increases. The suspension wires for his pans could bind in the weight transmitter standpipes, causing the weight recorder to be slugzish. The scatter of his weight readings during the runs would seem to bear this out. His technique of allowing the liquid sample to evaporate without maintaining the level would tend to minimize the effect of mass velocity. The magnitude of the Reynolds number used in Wenzel's experimental work was considerably higher than employed in this study. Wenzel was primarily interested in pressure operation and, consequently, was able to attain high Reynolds numbers a t comparatively low linear velocities. The present work was undertaken primarily for atmospheric pressure operation. An advantage of lower pressure operation is that a greater number of materials could be dried in this manner because of the lower temperatures that can be employed, with the consequent better thermal economy. Another advantage is that less expensive equipment can be employed for the same end result. The working equation recommended for design purposes is Equation 6. This equation was selected as the recommended working equation since, in the cases where the equation is applicable, which is the majority of industrial applications, an effective diameter can be calculated. The effect of the length of the sample can be accounted for by material and heat balances. This equation can be used d&ectly for establishing drying rates in the constant rate period for those solids where the surface roughness effect on the heat transfer coefficient is small. For
Figure
4. Retes of Eveporation of Water into Superheated Steam end Air
1590
INDUSTRIAL AND ENGINEERING CHEMISTRY
16
caws the dust-bearing exhaust steam can be totally condensed and insoluble dust can be easily separated from the condensate by filtration. If desired, the exhaust steam can be used for process heating and the over-all thermal efficiency can be increased further. Operation with superheated vapor provides a nonoxidizing atmosphere, thereby making it possible to process efficiently materials \vhich are normally sensitive to oxidation a t somewhat elevated temperatures. The thermal efficiency of superheated vapor operation is more strikingly illustrated when operating with flammable liquids. Insurance regulations often require that for air drying applications the concentration of the vapor be maintained a t 25% of the lower explosive limit. This requiies that a large excess of air be employed. For example, the lower explosive limit of 1-butanol is 0.044 pound of 1-butanol vapor per pound of butanolfree air. At 25y0 of the explosive limit the permissible concentration is 0.011 pound of 1-butanol per pound of butanolfree air. This means that 90 pounds of air are required for each pound of 1-butanol evaporated. By calculation of the heat consumption for air operation at 25% of the lower explosive limit and for superheated 1-butanol vapor operation, the following comparison is obtained:
14
z
G
le
3
a
5 10 0
2 u- 8
a (L
z 0
F 6 c P
a
w
4
2
0 MASS V E L O C I T Y , pounds pcr(hour)(rq. foot)
Figure 5.
Vol. 45, No. 7
Rates of Evaporation of Benzene into Superhested Benzene Vapor and Air
tion temperature. The air evaporation rate, on the ot,her hand, with the air a t the saturation temperature for the pure liquid, is a definite quantity. h critical evaporation temperature can be determined a t which the rate of evaporation into superheated vapor is equal to t'he rate of evaporation into air. It can also be seen in Figures 4 and 5 that constant temperature evaporation curves for superheated vapor and for air will intersect at some critical mass velocity. This is possible because of the greater effect of mass velocity on the rate of evaporation into air. In most practical operating cases this m u l d not, occur, since the rate of evaporation into air would exceed the rate of evaporation into superheated vapors only a t very high mass velocities. Operation with superheated vapor also has a large thermal advantage. Figure 6 shows a comparison between the amount of heat required for superheated steam operation and the amount of heat required for adiabatic operation using air as a drying medium. The curves are based on an incoming aksolute humidity of 0.00 pound of water vapor per pound of bone-dry air, and a n initial air temperature of 70" F. In adiabatic operation all heat required for evaporation of water is introduced with the hot air entering the dryer. KOexternal heat is supplied. Figure 7 shows the decided saving in heat consumption when operating with superheated steam. Figure 7 shows a comparison between the amount of heat required for superheated steam operation and the amount of heat required for isothermal air operation. The curves are based on an initial absolute humidity of 0.00 pound of water vapor per pound of air and an initial air temperature of 70" F. The air is first. preheated to the dryer operating temperature and then introduced into the dryer. Continuous reheating of the air maintains the constant dryer temperature. The curves readily show the thermal advantage of superheated steam operation. In superheated steam operation. the thermal economy remains the same whether the operation is adiabatic or isothermal. In the former, the quantity of steam flow through the dryer is large. With isothermal operation employing internal reheating of the steam, the quantity of steam exhausted from the dryer is exactly equal to the quantity of water evaporated. This is of great importance when drying very powdery materials. In these
Dryer Exhaust Temp., ' F. 250 300 350
Heat Consumption, B.t.u./Lb. 1-Butanol Evapd. -4ir drying Superheated vapor drying 4500 375 5600 400 6700 425
This clearly indicates the thermal efficiency superiority of superheated vapor operation compared to air operation.
Conclusions This investigation of the evaporation of a liquid by direct cnntact a i t h its superheated vapors has shown the feasibility of such operation and its application to drying problems. Definite limitations exist for superheated vapor drying which must be considered. Superheated vapor operation is limited to relatively temperature-stable materials. Batch operation is not desirable because of large start-up and shutdown losses unless special precautions are taken and additional equipment installed.
INDUSTRIAL AND ENGINEERING CHEMISTRY
July 1953
1591
h, ho = heat transfer coefficient of convection, B.t.u./(hr.) (sq. ft.)(’ F.) = heat transfer coefficient of radiation. B.t.u./(hr.) hr . , (sq. ft.) ( F.) = enthalpy of evaporator liquid feed, B.t.u./lb. HL H s = enthalpy of va or leaving boiler, B.t.u./lb. 3.y = j-factor, (Nu)&r) -1 ’8, dimensionless = j-factor, (Nu) (Pr) /a, dimensionless J.: = j-factor, (St)(Pr)2/3,dimensionless .1H k = thermal conductivity, B.t.u./(hr.)(sq. ft.)(’ F.)(ft.) L = length of evaporation surface parallel to the direction of flow, ft. m = constant n = constant N u = Nusselt number, hD/k, dimensionless NU‘ = Nusselt number, h L / k , dimensionless P r = Prandtl number, c / k , dimensionless Q = total heat transferred to liquid surface, B.t.u./hr. Q’ = total heat transferred, B.t.u./hr. Re = Reynolds number, D G / p , dimensionless Re’ = Reynolds number, L G / p , dimensionless St = Stanton number, h/cG, dimensionless = upstream temperature of superheated vapor, ’F. tl = downstream temperature of superheated vapor, O F. tZ = caloric temperature, O F. to = temperature of evaporator feed liquid, O F. tE = teyperature of the gas film around the thermometer, tr
F.
’
= true gas temperature, F. = saturation temperature of liquid,
= arithmetic mean temperature of
tl
’ F.
and tP, O F.
= log-mean temperature difference, = temperature difference of cold end,
= temperature difference of hot end, tl Figure 7.
Heat Consumption for Superheated Steam Drying and Isothermal Air Drying
The thermal advantages of superheated vapor operation are very decidedly in favor of such operation. The rates of evaporation with superheated vapor are greater than for a4r except when the operating temperature is near the saturation temperature of the liquid. The heat transfer coefficients obtained in this investigation varied from 9.06 t o 39.8 B.t.u. per (hour)(square foot)(’ F.). The operating temperatures varied from 275 to 385” F. and mass velocities from 138 to 878 Ib. per (hour)(square foot). The heat transfer coefficients are correlated with physical properties by the eauation:
jH =
(T)(x)-1’3 hD c p = 4.56 (?)o‘so
with a maximum deviation of f 2 1 % and a standard root-meansquare deviation of i11 %. Further studies should be made to investigate the effect of the degree of confinement of the vapor on the influence of mass velocity on the heat transfer coefficient. The correlation developed from this study can be applied to drying problems in the constant rate period, -provided due allowance is made for the effect of surface roughness on the heat transfer coefficient.
Acknowledgment Grateful acknowledgment is made t o the Wyssmont Co., which made this study financially possible, t o Arnold Weisselberg, consulting engineer for Wyssmont Co., for his helpful suggestions, and to D. F. Othmer, head of the Department of Chemical Engineering a t the Polytechnic Institute of Brooklyn, for his encouragement and interest.
Nomenclature
a, a’ = constants A = area of evaporating surface, sq. ft. A‘ = cross-sectional area of vapor duct, sq. f t . b, b’, b” = constants c , CP = specific heat, B.t.u./(lb.)(” F.) D = eauivalent diameter, ft. Do = o;tside diameter of thermometer, f t . E = evaporation rate with superheated vapor, Ib./hr. E’ = evaporation rate with air, Ib./hr. F, = caloric fraction, dimensionless G = massvelocity, lb./(hr.) (sq. ft.)
linear velocity, ft./min.
ZL
=
v
= specific volume, cu. ft./lb.
e p
= emissivity = viscosity, lb./(ft.)(hr.)
F. tz - t:,
- t,,
’ F.
F.
Subscripts 1 = upstream condition of the superheated vapor 2 = downstream condition of the superheated vapor f = gas film surrounding the thermometer
literature Cited (1) Clarke, L., “Manual for Process Engineering Calculations,” p. 103, New York, McGraw-Hill Book Co., 1947. (2) Colburn, A. P., Trans. Am. Inst. Chem. Engrs., 29, 174 (1933). (3) Dobratr, C. J., IND.ENG.CHEM.,3 3 , 7 5 9 (1941). (4) Govier. G. W.. Sc.R. thesis. Universitv of Michigan. 1948:
Govier, G. W., and White,’R. R., presented before the Am: SOC.Mech. Engrs., New York, 1950. Hougen, 0. A., and Watson, K. &I.,“Chemical Process Principles,” Pt. 111, p. 870-1, New York, John Wiley & Sons, 1947.
Keenan, J. H., and Keyes, D. B., “Thermodynamic Properties of Steam,” New York, John Wiley & Sons, 1947. Kern, D. Q., “Process Heat Transfer,” Chap. 3, New York, McGraw-Hill Book Co., 1950. Lane, A. M., and Conklin, D., thesis, Polytechnic Institute of Brooklyn, 1952. McAdams, W. H., “Heat Transmission,” 2nd ed., p. 223, New York, McGraw-Hill Book Co., 1942. Maisel, D. S., and Sherwood, T. K., Chem. Eng..Progr.,46, 131 (1950).
Perry, J. H., ed., “Chemical Engineers Handbook”, 3rd Ed., p. 215-16. New York. McGraw-Hill Book Co.. 1950. Ibid., p. 228. Ibid., p. 371. Ibid., p. 461. Ibid., p. 473.
Shepherd, C. B., Hadlock, C., and Brewer, R. C., IND.ENG CHEM., 30,388 (1938). Shushpanov, P. I., J . Exptl. Theoret. P h w . (U.S.S.R.), 9, 875 (1939).
Wade, S. H., Trans. I n s t . Chem. Engrs. (London), 20, 1 (1942). Walker, Lewis, McAdams, W. H., and Gilliland, E. R., “Principles of Chemical Engineering,” 3rd ed., p. 635, New York, McGraw-Hill Book Co., 1937. Wenzel, L., Sc.D. thesis, University of Michigan, 1949. Wenzel, L., and White, R. R., IND. ENG.CHEM.,43, 1829 (1951). RBCEIVED for review, October 1, 1952. ACCEPTED March 9, 19.53. Presented before the Division of Industrial and Engineering Chemistry at the CHEMICAL SOCIBTY, Atlantic City, 122nd Annual Meeting of the AMERICAN N. J.
