INDUSTRIAL A N D ENGINEERING CHEMISTRY
26
VOl. 22,
KO.
1
Heat Transfer from a Gas Stream to a Bed of Broken Solids’v2 C. C. F u r n a s NORTH CENTRAL EXPERIMENT STATION, U.
s. BUREAUOF MINES,MINNEAPOLIS, MI“.
The B u r e a u of Mines is m a k i n g a s t u d y of h e a t transfer from a noncompressible f e r f r o m gas s t r e a m s to beds of broken solids. T h i s many industrial procfluid to a bed of small partipaper gives t h e experimental results of o n e section of esses d e p e n d s u p o n cles. the work-namely, the t r a n s f e r of h e a t f r o m a s t r e a m efficient contact between a At least one empirical study of air t o a bed of i r o n balls covered w i t h a t h i n coating fluid stream and a bed of solid has been made of heat transof iron oxide. T h r e e different sizes of iron balls were particles. This fluid stream fer within particles in which used-1.85, 3.17, a n d 4.86 cm. in diameter. Temperais called upon to t r a n s f e r there is a heat of reaction ( 6 ) , t u r e s up to 750” C. were used. The r a t e s of gas flow either heat or material or, in but in this instance no study were varied approximately f r o m 0.01 to 0.06 s t a n d a r d most instances, both of these was made of the transfer from liter per second per s q u a r e c e n t i m e t e r of cross-sece n t i t i e s ; yet there is little the gas stream. tional a r e a of the bed. Two coefficients of h e a t transfundamental knowledge that N u m e r o u s studies have fer were computed, the first for a u n i t volume of the bed is directly applicable to this been made of heat transfer of solids, t h e o t h e r for unit surface area of the particles particular system. from gas flowing through conin the bed. B o t h coefficients were f o u n d t o vary a p Information concerning the d u i t s t o t h e conduit walls. proximately as the first power of the absolute temperalaws of heat transfer from a This information h a s been ture a n d as the 0.75 power of the gas velocity. The gas stream to a bed of broken summarized carefully in varicoefficient of h e a t t r a n s f e r per u n i t of volume of the solids should be of particular ous places (1,9,11). bed varies inversely as the 0.9 power of t h e d i a m e t e r of value to those interested in H e a t Transfer i n Conduits the particle. The coefficient per u n i t of surface area fuel beds, gas producers, lime of particles is practically independent of the particle kilns, blast furnaces, heat reThe d a t a from v a r i o u s generators, and similar pieces size. sources on the heat transfer of equipment. T h i s p a p e r from a gas stream to conduit deals with heat transfer from a stream of air to iron balls. walls are often erratic and contradictory. The correlators, The data are necessarily of limited character, but the general however, have found certain definite valuable relations beprinciples formulated should be applicable to a wide variety tween variables. Weber ( I C ) collected data from various sources and found that they were best interpreted by the of systems. equation Division of General Problem 0.88 (V)O.*c p 2 T0.6 K1 (1) As the class of systems under consideration is not one in m0.3 which a “steady state” may be studied, a number of difficulties where K I = coefficient of heat transfer measured in B. t. u. per square foot per second per degree Fahrenheit and special considerations arise that are not encountered in temperature difference the simpler cases. The general problem divides itself natuTi = velocity in pounds per square foot per hour rally into the following heads: C, = average specific heat at constant pressure of gas
HE operation of a great
T
A-Heat transfer from liquids to small particles B-Heat transfer from liquids to large particles C-Heat transfer from gas to small particles D-Heat transfer from gas to large particles E-Heat transfer from gas to small particles when there is a heat of reaction F-Heat transfer from gas to large particles when there is a heat of reaction
A division has been made between large and small particles. The small particles are of such a size that the temperature throughout the entire piece at any given time is practically constant. This condition has a great deal to do with the laws of heat transfer, and large particles may be expected to complicate the situation. Obviously, heats of reaction within the particle itself form another complicating factor. This paper deals only with system C, a gas stream and small particles, but these are conditions of quite wide application.
in B. t. u. per pound S = surface factor in reciprocal feet T = arithmetic mean temperature of the gas in degrees Fahrenheit absolute m = molecular weight of the gas
The equation is applicable to metric units with an appropriate change of the value of the constant term. A more recent summary (11) of the data for gas flowing inside of conduits is
vo.
3
K I = 0.22 CpTj2’3 0O.z
(2) where. T, = mean temperature of gas film in degrees Fahrenheit absolute D _=:equivalent diameter of the passage in inches
Further work has been done on summarizing data for flow at right angles to pipes (3). For a single pipe, Vm
K1 = 0.8 Tj”3 ~ 0 . 5 ~
Previous Investigations
As far as is known, a paper by Schumann (10) is the only one that is directly applicable to this study. Schumann developed a complete and comprehensive theory for heat transPresented before the Division of Gas and 1 Received Atlgust 19, 1929. Fuel Chemistry at the 78th Meeting of the American Chemical Society, Minneapolis, Minn., September 9 to 13, 1929. S. Bureau of Mines. f Published by permission of the Director, U. (Not subject to copyright.)
where
+ 0.08logioD D = outside diameter of pipe in inches n = 0.60
For air flow at right angles to a group of staggered pipes, 0.8 TY’’~ W“ D J Ki =
where w
=
Do.53
(1 + -
(3)
(4)
(5)
pounds of air per second per square foot of minimum free area between pipes in a plane a t right angles to air flow
INDUSTRIAL A N D ENGINEERING CHEMISTRY
28
mocouple wires were brought out through a gas-tight stuEng box packed with asbestos cord. Gas coming out through the shield passed through a tee and valve placed immediately in front of the stuffing box. All connections were made gastight. When the valve a t the end of the thermocouple shield was closed, no gas flowed by the thermocouple and the couple measured the temperature of the surrounding solids. When the valve was opened, gas passed through the shield over the bead, and the couple read practically the true gas temperature.
VOl. 22, No. 1
and Northrup recording potentiometer. The other couples were read with a portable potentiometer, Heat Losses
The apparatus was calibrated for heat losses by heating it with a gas stream and then allowing it to cool, the rate of cooling being observed. The author believed that most of the resistance to heat flow through the walls of the apparatus was in the insulation and that it was practically immaterial whether or not gas was flowing. After the apparatus had cooled for a short time, the rates became erratic, undoubtedly because of convection currents within the column. Hence, for heat-loss curves only the first few temperature readings were used, the curve being extrapolated to lower temperatures by means of the published relation between the thermal conductivity of Sil-0-Cel powder and temperature (3). Experimental Difficulties
&tail of thennocouple shield
Figure 3-Detail
The difficulties in this form of experimentation are numerous, and most of them are not encountered in “steady state” measurements. Care must be taken that the tip of the thermocouple shield is sufficiently well insulated from the outside of the apparatus to prevent erroneous readings of the solid temperature. The gas velocity through the shield must be maintained sufficiently high to insure the correct reading of the gas temperature. The heat losses often amount to more than half of the total heat transferred and easily lead to incorrect results. Even with a bed of solids which apparently is uniform, it is practically impossible to maintain a uniform gas flow over the entire cross section, and this often results in erratic data. The apparatus described undoubtedly can be improved, but the author believes that the principle of operation is sound and that the method is probably the best that can be used on this type of work.
Mv
of Heat Transfer Apparatus
The gas flowing through the shield passed out from the valves v 4 , V S , or v6 (Figure 1) through orifice 02, through valve v7, and back into the circulating gas system.
Interpretation of Results
Procedure
By definition the coefficient of heat transfer is the rate of heat acquisition, measured in calories per second, divided by the temperature difference between the gas stream and the solid. It is common practice to limit the coefficient to the heat transferred per unit of surface area. I n the study under
When a run was started, the gas w&s by-passed around the column through valve v1 until the temperature was constant. At a given time the gas was started through the column by opening vp and closing V I . Repeated readings were taken on the three shielded thermocouples. The lower
velocity past the couple of at least 7 meters per sec-
the-surface of the thermocouple bead were silverplated to minimize radiation and to aid in the measurement of gas temperatures (5). After the gas temperature was obtained, the valve was closed again, and a little later the couple again read the solid temperature. Thus, by alternating the opening and closing of the valves on the thermocouple shield a single couple could be used to give a double record of solid temperature and gas temperature. Each record was necessarily intermittent, but the points were near enough together to permit satisfactory interpolation. A typical plot of the time record of such a couple is shown in Figure 4. The record of one of the couples was kept on a Leeds
I consideration the area exposed to the gas stream depends upon the size, shape, and degree of packing of the particles in the bed. Since all these variables are involved, it is more convenient to determine the coefficient for a given volume of apparatus and then to compute the coefficient for unit surface area. Formulas for both quantities are given in a later section. The rate of heat absorption is directly proportional to the weight of the solid material, its specific heat, and the rate of temperature change. I n addition to the heat actually absorbed by the solids, a further quantity is transferred but lost by conduction through the walls of the apparatus. To
January, 1930
INDUSTRIAL AND ENGIXEERING CHEMISTRY
evaluate the coefficient of heat transfer it is necessary to determine each of these quantities. The weight of metal per centimeter of length of apparatus was determined at the time the apparatus was set up. The specific heat of iron was taken from the literature (8). The data for rate of temperature change and temperature difference between gas and solid are obtained from the record of the gas and solid temperatures (potentiometer reading) plotted against time (Figure 4). The slope of the curve at any time is the rate of temperature change of the apparatus at the given point and time under consideration. The slope can easily be translated into degrees Centigrade per second. This quantity is multiplied by the specific heat of iron at that temperature and by the weight of iron per centimeter of apparatus. To it is added the rate of heat loss, which is determined by the difference between the temperature of the column and the room. The sum is divided by the gas and solid temperatures at this particular time (Figure 4). The quotient is the coefficient of heat transfer measured in calories per second per degree Centigrade difference of temperature per centimeter of length of apparatus ( h ~ ) .To obtain the coefficient for each cubic centimeter of apparatus (hv) the above coefficient is divided by the cross-sectional area of the apparatus. If, in turn, this last coefficient is divided by the surface area of particles and container per cubic centimeter of apparatus, the quotient is the usual coefficient measured in calories per second per square centimeter of surface per degree Centigrade difference (ha). A sample computation is given below.
29
Effect of G a s Velocity
The data on the effect of changing gas velocity, the temperature remaining constant, for the three sizes of balls are plotted in Figure 5 as straight lines on logarithmic paper. This means that hv = KV" (7) where hv =coefficient of heat transfer from gas to solid, in calories per second per degree Centigrade difference per cubic centimeter of apparatus K = constant V = velocity measured in standard liters per second per square centimeter cross-sectional area of the bed, and n is a constant
The slope of the plotted line is the value of n. According to Figure 5, for balls 1.85 cm. in diameter the coefficient varies approximately as the 0.74 power of the velocity; for balls 3.17 cm. in diameter, as the 0.76 power; and for balls 4.86 cm. in diameter, as the 0.78 power. I n general, the coefficient is approximately proportional to the 0.75 power of the gas Velocity. Therefore hv = KVo.75
(8)
Increasing gas velocity increases the coefficient of heat transfer, probably because the stagnant gas film surrounding the particles becomes thinner as the gas velocity increases. Most of the resistance to heat transfer is in this film, so decreasing the thickness of the film may be expected to increase the heat transfer.
SAMPLECOMPUTATION Diameter of balls, 3.17 cm. Flow = 0.01875 standard liter per second per square centimeter Weight of iron per centimeter of length of apparatus = 1150 grams Cross-sectional area of bed = 167.5 sq. cm. Room temperature = 30' C. From Figure 4: Gas temperature (potentiometer) = 17.10 millivolts Gas temperature (from calibration curve, not given) = 400" C. Solid temperature (potentiometer) = 15.34 millivolts Solid temperature = 358.6' C. Temperature of gas - temperature of solid = 41.4' C. Slope of solid temperature curve on chart = 0.238 On chart, 1 cm. on ordinate = 2.25 millivolts = 53" C.; on calibrated couple: 1 cm. on abscissa = 250 seconds 0.238 X 53 Rate of change of temperature of solid = 250 0.0504' C. per second Specific heat of iron (8) a t 359' C. = 0.140 Heat capacity of 1 cm. of apparatus = 161 calories per ' C. Heat acquired by metal = 161 X 0.0504 = 8.1 calories per second Heat loss: Solid temperature - room temperature = 330" C. Coefficient of heat loss a t 360' C. (curve not shown) = 0.006 calories per second per cm. length of apparatus per degree Centigrade difference Heat loss = 330 X 0.006 = 2.0 calories per second Total heat transferred from gas stream -= 8.1 2.0 = 10.1 calories per second Coefficient of heat transfer = 10.1/41.4 = 0.244 calorie per second per centimeter of apparatus per degree Centigrade difference Coefficient of heat transfer = 0.244/167.5 = 0.00146 calorie per second per degree Centigrade difference per cubic centimeter of apparatus
+
D a t a Obtained
Data have been obtained on balls 1.85, 3.17, and 4.86 cm. in diameter. The rate of air flow ranged from 0.01 to 0.053 standard liter per second per square centimeter of crosssectional area of the bed. Temperatures up to 700" C. were obtained. The voids in the different beds of material ranged from 39.5 to 50.6 per cent.
Figure 5-Relation
between Rate of Gas Flow and Coefficient of Heat Transfer
Effect of T e m p e r a t u r e
A typical set of data for the variation of the coefficient of heat transfer with the logarithm of the temperature for a constant rate of flow is plotted in Figure 6. The slope of the line is appproximately 1.0, so the coefficient of heat transfer may be said to be directly proportional to the temperature. Increasing temperature increases the thermal conductivity, the specific heat, and the linear velocity a t constant mass rate of flow of a gas. All these changes tend to increase the coefficient of heat transfer. On the other hand, an increase in temperature increases the viscosity of the gas, which tends to decrease the heat transfer. However, in all cases that have been studied the first three changes have had a greater effect than the last one; so the coefficient increases with temperature.
INDUSTRIAL AND ENGINEERING CHEMISTRY
30
Effect of Particle Size
The data on the effect of changing particle size on the coefficient of heat transfer if the rate of flow is constant are given in Table I. Table I-Effect
of Variation of Particle Size and of Voids on the Coefficient of Heat Transfer
SURFACE
AREAPER
TEMPERATURE
FLOW
Liter/sec./ cm.2 0.06 0.06 0.06
OC.
500 500 500
DIAMETER
Cm. 1.85 3.17 4.86
VOIDS
Vol. 22, No. 1
power of the effect on the resistance to gas flow. Using this relation and Equation 9, it is possible to compute the value the coefficient oflheat transfer would have if the voids were the same in all the beds considered. Thus, A log h = +l.68 ( U P - D i ) - 3.56 (Uz2 - s ') (10) The results of the computation on effect of voids are given in Table 11.
CM.
LENGTH
I N B E D APPARATUS h L
T ."o
Sa. cm.
39.5 45.0 50.6
370 224 149
h
Table 11-Effect
of Varying Particle Size on Coefficients of Heat Transfer
(Voids constant, flow = 0.06 standard liter per second per square
centimeter)
1.55 0.80 0.39
0,00925 0,0048 0.0023
Effect of Voids
The increase in voids with increase in size of particle, as shown by column 4,Table I, is caused by the relative smallness of the container. The wall of the container prevents the spheres from settling into their normal positions in the bed. The effect is greater for the larger particles. I n large containers, in which the wall effect is negligible, the voids in the bed are independent of the size of the particle. 0 v1
52
% 0. a 0 n
B
t >O
d
DIAMETER
A logio A P
OF
FOR
PAR- OBSD. VOIDS= TICLE hr, VOIDS39.5%" A Cm. 70
SURPACE AREA hL
PER C X .
LERGTH
WITH
VOIDS=
l o g h ~ b 39.5%
APPA-
hvc
1.85 1.55 39.5 0 0 0.0 1.55 0,00925 3 17 0.80 45.0 0.19 0.076 0.95 0.00567 4.86 0.39 50.6 0.42 0.168 0.58 0.00346 a See Equation 9. b See Equation 10. c Cross-sectionalarea of apparatus = 167 5 sq cm.
RATUS
370 224 149
ha 0,0042 0.0043 0.0039
The data of column 7 are plotted in Figure 7. The coefficient of heat transfer per cubic centimeter of apparatus (h,) varies inversely as the 0.9 power of the diameter of the particle. If the values of h ~the , coefficient per unit length of apparatus, are divided by the total metal surface per unit of length, the value of ha,the coefficient per unit of area, is practically constant (column 9, Table 11)-that is, it is practically independent of the size of particle. It would seem that the small particles have proportionately more "dead" area-that is, area in which the gas stream does not strike the surface.
'd
10
3Y x
$0
m
E 2
cl
t
2 0
0 LOG10 ABSOLUTE TEMPERATURE
Figure 6-Relation between Absolute Temperature and Coefficient of Heat Transfer
That those factors which increase resistance to fluid flow alsa increase the coefficient of heat transfer is a reasonable hypothesis. With the aid of dimensional analysis this assumption has been shown to be in agreement with experimental facts ( 7 ) . If one assumes that the different factors enter in the relation to the same order, one can evaluate the effect of the voids on the coefficient of heat transfer. A study has been made of the factors that affect the flow of gases through beds such as those now being considered (4). Two of the variables considered are rate of gas flow and voids in the bed. With particles of the size under consideration in this paper the resistance to gas flow is approximately proportional to the square of the velocity. The voids were found to affect the resistance according to the equation log10 AP = K 4.2~ 8.89 v 2 (9)
+
where AP = resistance measured in pressure drop v = fractional voids in the bed
Consider the relative effect of gas velocity on heat transfer and resistance to flow. Resistance is proportional to the square of the velocity, while heat transfer is proportional to the 0.75 power (Equation 8). The effect of heat transfer, then, is proportional to the 0.75/2 = 0.375 power of the resistance effect. Give this figure the value 0.4 as a first a p proximation. Now extend the hypothesis to a consideration of the effect of voids; if the voids are changed the effect on the coefficient of heat transfer is proportional to the 0.4
-
< 0 n
Eo8 /
0
/ 0
3
L;O
i
5 2 2 SO 6
s+
n
05
n 2s
0 35 LOG10 DIAMETER
Ji)
0 G>
OF BALLS,CX
Figure 7-Relation between Coefficient of Heat Transfer and Particle Size with Voids Constant
Equations for Coefficients of H e a t T r a n s f e r
The empirical equations of the relations just discussed are as follows: (11) h, 0.000034u~~76 T X 101.689 - 3 . 6 0 ~ 2 (12) where h, = coefficient of heat transfer in calories per second per cubic centimeter of volume of bed per degree difference between gas and solid h, = coefficient of heat transfer in calories per second per degree Centigrade difference between gas and liquid per square centimeter of surface u = gas velocity measured in standard liters per second per square centimeter cross-sectional area of bed
January, 1930 T
INDUSTRIAL AND ENGIATEERINGCHEMISTRY
d
= absolute temperature in degrees Centigrade = diameter of particles in centimeters
u
=
fractional voids in the bed
Expressing the equations in English units,
h, = 0,0000028~0.15T X 101.68~- 3.5602 (14) h, = coefficient of heat transfer in B. t. u. per second per cubic foot of volume of bed per degree Fahrenheit difference between gas and solid h, = coefficient of heat transfer in B. t. u. per second per square foot of surface per degree Fahrenheit difference between gas and solid u = rate of flow in standard cubic feet of gas per second per square foot of cross-sectional area of bed T = temperature in degrees Fahrenheit absolute d = diameter of particle in inches
Temperature History of a System A coefficient of heat transfer is a differential quantity. A system that is changing its heat content continuously has a temperature history that can be determined only by integration of equations involving the coefficients of heat transfer. The integration of these equations for a fluid flowing through a bed of solid particles has been very cleverly accomplished by Schumann ( I O ) .
31
Acknowledgment The author Fishes to express thanks to S. P. Burke and T. E. R. Schumann, of the Combustion Utilities Corporation, to W. H. McAdams of the Massachusetts Institute of Technology, and to W. L. Badger, of the University of Michigan, for numerous helpful suggestions a t the beginning of this work. Literature Cited (1) Badger, “Heat Transfer and Evaporation,” p. 40, Chemical Catalog, New York, 1926. (2) Celite Products Co., “Heat Insulation,” p. 10 (1924). (3) Chappell and h k h d a m s , Trans. A m . SOL.M e c h . Eng., 48, 1201 (1926); see also Walker, Lewis, and filchdams, 09. c i t . , (12), p. 131. (4) Furnas, Bur. Mines Bull. 307 (1929). (6) Haslam and Chappell, IKD. Exc. CxEm., 17, 402 (1925). (6) Haslam and Smith, Ibid., 20, 170 (1928). (7) McAdams and Frost. Ibid., 14, 1101 (1922). (8) Ralston, Bur. Mines, Bull. 296, 188 (1929). (9) Royds, “Heat Transmission by Radiation, Conduction, and Convection,” p. 106, Constable, 1921. (10) Schumann, J . Franklin I n s t . , 208, 405 (19291. (11) Walker, Lewis, and McXdams, “Principles of Chemical Engineering,” p. 146, McGraw-Hill, 1923. (12) Ibid., p. 149 (1927). (13) Ibid., p. 151 (1927). (14) Weber, Undergraduate thesis, M . I. T., 1919; see also Badger, 00.cit., p. 45, and n’alker, Lewis, and McAdams, o p . cit., ( l l ) , p. 149.
Syntheses in the Diphenyl Series’” Russell L. Jenkins, Rogers McCullough, and C. F. Booth FEDERAL PHOSPHORUS COMPANY, ANNISTON, ALA.
r
r
HE very high cost of Simple methods which give excellent yields are den i t r o c h l o r o d i p h e n y l s , ald i p h e n y l has heretoscribed for the preparation of the following monosubthough they are not described fore permitted relastituted derivatives of diphenyl: ortho and para, chloro-, in this paper. ti\,ely little research on this nitro-, and amino-diphenyls. The melting points and Raw Material material with the idea of deboiling points of these materials are given. The reloping practical UFes for its methods for four of these derivatives have been applied T h e t e c h n i c a l diphenyl derivatives. Recently a conion a semi-plant scale. The commercial production of which is now available in mercial process has been deany of them awaits only the developmentofa sufficient large quantities is a l i g h t veloped which makm possible demand. yellow, crystalline solid. Its freezing point is 68” C. This the sale of diphenyl a t 40 to 50 cents a pound, or approximately 1 per cent of its former material is approximately 97 per cent diphenyl, the remainder price. This development has made diphenyl easily available consisting of higher boiling hydrocarbons, boiling mostly above t o investigators and has stimulated research to find uses for 380” C. For the preparation of most derivatives the technical this hydrocarbon. An extensive program of research in the field of chemi- diphenyl is sufficiently pure as a starting material. If higher cals derivable from diphenyl was begun by this laboratory purity is desired, the technical material may be recrystallized during the past year. I n the course of this program it was from alcohol or distilled a t atmospheric pressure. For necessary to prepare considerable quantities of the simpler recrystallization 4 cc. of alcohol are recommended for each derivatives as starting points for more complex syntheses. gram of material. The product is pure white and in the The literature reveals the comparative ease by which form of plates. For distillation an efficient fractionating diphenyl undergoes substitution, but though many of. the column is recommended, by the use of which it has been simpler derivatives have been described there is lacking any possible to obtain, in one distillation, diphenyl boiling within general procedure that gave promise of commercial adapta- a range of 0.3” C. in over 95 per cent yield. The technical tion. It was therefore necessary for the writers to develop diphenyl contains a small amount of volatile coloring matter practical methods of nitration, reduction, and chlorination which is difficult to separate by distillation, and the distilled as applied to diphenyl. The purpose of this paper is to pre- product is therefore slightly yellow. Repeated distillation sent the best methods for the preparation of the ortho and a t atmospheric pressure, however, removes the color. para isomers of the chloro-, nitro-, and amino-diphenyls. Monochlorination Methods have also been developed for the preparation of several disubstituted and mixed derivatires, such as the Monochlorination has been carried out bv Drevious workers Received September 27, 1929. Presented before the Division of in the presence of catalysts, notably antimony pentachloride Organic Chemistry at the 77th Meeting of the American Chemical Society, (IO,$1). The use of iron as a catalyst for this reaction apColumbus, Ohio, April 29 to May 3, 1929. * Contribution No. 1 from the Organic Research Laboratory of the pears to have been Monochlorination leads to the production mainly of 2Federal Phosphorus Company.
