GOSS, 11.J., Turner, G. A., AIChE J., 17, 590, 592 (1971). Gunn, I). J., England, R., Chem. Eng. Sci., 26, 1413 (1971). Gunn, I). J., Pryce, C., Trans. Inst. Cheni. Enq., 47, T341 (1969). Hutchins, J. lI.,-III, Harrington, R . V., “Encjdopedia of Chemical Technology,” Yo]. 10, 2nd ed, Wiley-Interscience, S e w York, N . Y., 1966, p 598. “International Critical Tables,” Vol. 5, 1IcGraw-Hill, S e w York, K.Y., 1929. D 232. KuFera,’E., J.’ ?hrornatogr., 19, 237 (1965). Lanczos, C., “Applied .halysis,” Prentice Hall, Englewood Cliffs, K.J., 1956, Chapter 2 . Leva, 11.)Ind. Eng. Cheni., 39, 857 (1947). LIcHenry, K. FV.,Jr., Kilhelm, R. H., AIChE J . , 3, 83 (1957): Perry, J. H., Chilton, C. H., Kirkpatrick, S. I>., Ed, “Chemical Engineers Handbook,” 4th ed, IIcGraw Hill, Sew York, K.Y.. 1963. Kosen, j. B., Winsche, W. E., Jr., J . Chem. Phys., 18, 1387 (1950).
Touloukian, Y. e., Ho, C. Y., “Thermophysical Properties of Matter,” Vol. 2, T.P.R.C., Purdue University, Lafayette, Ind., pp 154-156. Turner, G. il., Chem. Eng. Sci., 18, 553 (1963). Turner, G. A,, AICh,E J., 13, 678 (1967). Ind. Eng. Chcm., Fundam., 10, 400 (1071). Turner, G. -4., Turner, G. A,, “Heat and Concentration Waves,” Academic Press, Sew York, N . Y., l972a, Chapter 9. Turner, G. A , , “Heat and Concentration Waves,” Academic Press, Yew York, S . Y., 1972b, pp 98, 109-110. Turner, G. .4.,“Heat and Concentration Waves,” Academic Press, New York, ?J. Y., 1972c, p 127. Turner, G. A,, “Heat and Concentration Waves,’’ Academic Press, Sew York, N. Y., 1972d, pp 313-218. Wakao, S.,Vortmeyer, D., Cheni. Eng. Sci., 2 6 , 1753 (1971). Wakao, N.,private communication (1973). RECEIVED for review June 12, 1972 ACCEPTED June 18, 1973
Heat Transfer to Dry Milk Powder during Pneumatic Transport through an Entrance Region P. Y. Wang and D. R. Heldman* Agricultural Engineering Department and Department of Food Science and Human Yutrition, Jlichigan State Cniversity, East Lansing, Michigan 48823
The rate of heat transfer between a tube wall with uniform temperature and a gas-solid mixture being conveyed through the entrance region of the tube has been measured. The influence of loading ratio expressed as a convective capacity parameter on heat transfer rate has been described for loading ratios greater than one. The heat transfer relationship has been expressed in terms of a mixture Nusselt number as a function of Reynolds number and the convective capacity parameter. The results reveal that the heat transfer rate in the entrance region of a tube increases with an increase in convective capacity parameter and Reynolds number. The influence of introducing powder particles into the air stream at a temperature different than the air was not significant.
T h e application of a gas-solids mixture as a heat transfer aiid transport media \!-as first used in petroleum-cracking plants. I t was determined experiment’allythat the use of solids in gaseous heat transfer tem increased the heat transfer rate. Farbar and Norley 5 i ) were the first iiivestigat’ors in t’his field. Due t o the limited number of investigations and the complexity of the f l o mechanism, ~ most’available information is based on experinieiit’alresults. Heat trawfer data are limited t o (a) equal inlet teniperatures for the gas and particles and (b) aerodynamically fully del-eloped regioiio. I n practical sit,uations such ab the food industry, cooling of spray-dried food products begiiis immediately after mixing with the coiiveyiiig medium and a temperature gradient should be maiiitaiiied betiveeii the two phases t o ensure rapid cooling. Heldmaii. et al. ( 1 9 i l ) , indicated that’ gas and particles will :attain ail ecpilibriurn teniperature very rapidly after particle injection t o the air stream. I n order t,o reduce the temperature of spray-dried food products more rapidly during pneumatic transport, it is necessary to gain additioiial knowledge about the lieat’ trniisfer characteristics during pneumatic t,raiisport. ; Irecent revie17 by Sadek (1972) indicated that heat transfer coefficimts i n ail air-solid stem are dependent 424
Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 4, 1973
primarily 011 the particle area per unit gas volume. There is little or 110 information t o assist in predicting surface heat transfer coefficient for gas-solids mixtures in the entrance region t o a conveying tube. The objective of this inr-estigatioii was to develop a suitable expression to describe heat transfer between the tube \Tall and a gas-solids mixture during pneumatic tranyiort in the region near the location a t which solids are injected into the conveying tube. Experimental
System and Instrumentation. T h e system utilized for esperimeiital phases of the investigation is described by X a n g tern coiitaiiied three separate conipoiients including particle feed and recovery! air metering and flow measurement, and lieat exchange. I n this iiivestigatioii, the ~ r a l of l the tubular heat exchanger was maintaiiied a t a uniform temperature. .Idetailed vie\r of the lieat exchanger and closely related portions of the experimental syatem are illustrated in Figure 1. The 12 locations a t which temperature measurements irere taken using col)per-coii~taiitarithermocouples are iiidicated.
Experimental Procedures. There were tn-o types of experimeiits conducted in this iiivestigatioii. One type was with equal iiilet temperatures for air aiid particles. The second type was coiiductetl with the air and product at' different temperatures at the inlet. For the latter case, the inlet air temperature \vas varied. In the case of equal inlet temperature, nonfat dry milk 1)nrticles were exposed to tlie room air for 24 hr in order to obtnin the equal temperatures. For experiments n i t h diff ereiit inlet tenii)erai:ures, the air was preheated bh- the electrical heater. Since the temperature of the gas-solids mixture a t the heat exchanger inlet could not be measured accurately using the thermocouple at location 3, the mixture temperature was predicted using an e n t h d p y balance
where T I and T.. are air and product temperatures (before mixiiig) a t locations 1 ai. d 2 , respectively. The outlet temperature of the mixture was measured using thermocouples 9 and 10 a t a locxtion :ipproximately i ft from the exit of the heat eschaiiger. 13y allotviiig this distance (7 it) for flow of the gassolids mixture, in an insulated tube, measurement of a n equilibrium temperaturi> was assured. The distance to reach the ec~iiilil~riuiii teii1per:iture i n an iiisulated tube rvab deterriiiiietl :ipprosimatel\ 4 Ct from the mixing by Heldmaii, el al. (1971). The temperature of xir or particles a t location 3 could not, be tletected. Tlir linrticle redistributor illustrated in Figure 1 was iiecessary to provide uiiiform particle distribution nithiri the heat, excliaiiqer. 111 atltlitioii, .:his iiistallatioii reduced the influence of ilon- cliaracateridcs iip'treain iron2 the heat exchanger on llow c1i:mcteristic.s in tl. e heat exchanger. T7iiiforni wall temperature \vas iiiaiiitained in the heat escliaiiger by circulatinp; uniform temperature m t e r through tlie :iiind:ir space of tlie heat exchaiiger. 13y maiiitaiiiing a higher 1ie:it transfer coefficient on the water side of the heat excliuiiger :I> com])ared t o tlie mixture d e , a uniform n-a11 teiiil)eratui'e \vas assured. I-sing a rvnter fioX7- rate of 3460 lb lir corre,qioiidiiip to a Keyiiolds nuniber of 1.23 X lo1, a temperature differeiire b e t ~ e e i iinlet, and outlet of less than 2'F )vas iiiaintained. Particle Characteristics. Soiifat d r y milk part'icles were used i i i :ill experinieiits coiiducted. The mean particle diameter \va5 :i-iimecl t o be 60 p based on data reported by Hayashi, et nl. ( 1 9 6 i ) .-1particle density of 1.46 was used based on data reportetl 1)y llall mid H'drick (1966). -1specific heat of 0.36 I3tu 111 "1: \vas usecl in .:)rediction equations. This value n-as l)retlicted based oil product composition mid was verified by experinieiital deteriniliatimi iii a diff ereiitial tliernial analyzer. Computation Proced.ures. H e a t t'rarisfer rate in a shella d - t i h e h w t excliaiigei is usually defined by
(2)
q, = LXDLAT,,,
where ATnlis tlie loguitl-imic mean temperature difference aiid call lie espreqsed as AT,,, = (ATmi
-
ATmo)/111
(ATnii/ATnio)
where ATnli = T,,i - T,,. and AT,no = T,, - T,. Heat trail-fer rate (q\v) can also be determined by t,he enthalpy increase of t h e gas-solids mixture. 9 , = (GaC:,
+
GpCp)(Z'mo
- Tmi)
(3)
Conibiiiatioii of eq 2 aiid 3 gives =
(GaCa
+ G'pCp)(Tnlo- TIni)/'IIDLATm
(4)
t
ir.ixture t o separator
Figure 1. Location of thermocouples
Oii the right-hand side of eq 4, the parameters caii lie either measured or obtained from the information available. The overall heat transfer coefficient C is also defined by
For 18-8 (chromenickel) stainless steel the thermal coiiductivity ( k t ) is equal t o 9.4 ]%tu;lir ft OF.The will thickness ( b ) was measured as 16 in. Tlie heat transfer coefficient of water side (hR~)can be evaluated by the equation proposed 11y Hsu (1963). K i t h Rej-iiolds numlier a t 1.2 x lo4,the heat transfer coefficieiit of n-ater side, h,: \vas calculated to be 312 13tu, lir ft? OF.13y knon-ing h,, b, kt, aiid C- in eq 5, the mixture side resistaiice, I z , ~ ,can be evaluated. Tlie detailed procedures were presented by Farbar a i d Morley ( 1 9 5 ) . Since lieat transfer coefficients of the iiiixture side, ii,, can lie computed aiid hence the mixture Susselt iiumber can be presented as (SU)m =
hniD/ka
Results and Discussion
The mixture Susselt number calculated by the previously described procedures are plotted on log-log paper in Figures 2-4. Figures 2 and 3 present the results for equal inlet temperatures, aiid tlie results in Figure 4 were obtaiiied with different iiilet temperatures. I n these figures, mixture Xusselt numbers :ire plotted us. either Reynolds number or the "convective capacity parameter" (CCP), as indicated by the theoretical analysis presented by Tien (1960) and Farbar and Depew (1963). The slopes were obtained by least-squares fitting procedures. The slopes of mixture Susselt number us. Reynolds number for coiistaiit convective capacity parameters of 1.0, 1.54, and 1.84 were computed as 0.8, 0.62, and 0.59, respectively, and are presented in Figure 2. Kreith (1966) suggested the following equatioii for evaluation of the heat transfer coefficient for air flow passing through a duct a t uniform wall temperature (St),(Pr)
113 =
0.02(Re)-0~2(Tn1/T,)0~576
Ind. Eng. Chern. Process Des. Develop., Vol. 1 2 , No.
(6)
4, 1973 425
. 2 A
4001300
300
250-
250
200-
200
150-
150
2 Y
d
P
u’, Y
B
I 3
100
I 4
Reynolds Number
I 5 G D
I
I 7
6
I
I
8
9
J 10
I
100
I
I
I
I
2L x IO4 pa
Figure 2. Mixture Nusselt number vs. Reynolds number for various convective capacity parameters
0.35 OS40t
0
NU)^
100 1.0
1.5
2.0
2.5
4.0
3.0
0.lOj 1.0
5.0
G C
Convective Capacity Parameter
(1
-
experimental data
C C (1 +-)
0.17
0.73
GaCa
,
,
,
,
,
1.5
2.0
2.5
3.0
4.0
+a)
G C
GaC,
c o n v e c t i v e Capacity Parameter
( 1 + -)
GaC.
Figure 3. Mixture Nusselt number vs. convective capacity parameter for various Reynolds numbers with equal inlet temperatures
For the case of a n entrance region, the heat transfer coefficient from eq 6 can be modified as
he,
=
h,(l
+ D/L)
D/L
> 20
(7)
When the wall temperature was uniform and the convective capacity parameter was equal to unity the slope of 0.8 was obtained for air flow, M hich confirmed eq 6 and 7 as proposed by Kreith (1966) for the entrance region. In the case of uniform wall temperature, Farbar aiid Xorley (1957) and Danziger (1963) indicated that the slopes of mixture Nusselt number us. Reynolds number 111 the fully developed region were 0.6 and 0.66, respectively. 111the present iiivestigation of a n entrance region, the average slope was determined to be 0.61 which is in close agreement with Farbar aiid Morley (1957) and Danziger (1963). From Kreith (1966) it can be seen that heat transfer rate for an air stream a t either the entrance or the fully developed region depends on the 0 8 426 Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 4, 1973
Figure 5. Combined Nusselt number vs. convective capacity parameter
power of Reynolds number. The same relationship was obtained in this investigation. The heat transfer rate to a gassolids system varies with the 0.6 to 0.66 power of Reynolds number for both entrance and fully developed regions. Other relationships between mixture Nusselt number and convective capacity parameter were measured (Figures 3 and 4). The slopes of mixture Kusselt numbers us. convective capacity parameters for constant Reynolds numbers of 4.7, 5.6, aiid 7.3 x 104 were found to be 0.79, 0.73, and 0.72, respectively (Figure 3). For the case of inlet temperatures of particles and air at different temperatures, the mixture Kusselt number was plotted vs. the convective capacity parameter. The slopes of mixture Susselt numbers us. convective capacity parameter for constant Reynolds numbers of 4.7 and 5.6 X lo4were determined as 0.72 and 0.73, respectively (Figure 4). Comparing the results of these two situations indicates that a significant difference in the heat transfer coefficients for equal and different inlet temperatures does not exist.
The experimental results of both cases, therefore, were combined to obtain a general correlation. If the combined data of mixture Susselt number are divided by Reynolds number of the 0.61 polTer [(Su),,,’(Re)0,61], and plotted 2’s. convective capacity parameters (CCP), i t provides a 0.73 poxer correlation as illustrated iii Figure 5 . The intercept value a t a convective capacity parameter value of 1 was 0.17 t’o provide the follon.ing dimensionless correlation
+
(Nu)m = 0.17(Re)@,61[1 (G,C,/G,C,)
10.73
(8)
Ctiliziiig all experimental data, a standard error of estimate of +2.7% was established for eq 8. Equation 8 is valid for convective capacity parameters greater than one and within the entrance region for R uniform wall temperature system. These results reveal that heat transfer occurs differently in the entrance region of a tube than in the fully developed region. Farbar and Morley (19%) indicated that the mixture Susselt number did not change in the fully developed regioii when the loading ratio is less than one. Tien and Quan (1962) and Jepson aiid Smith (1963) attributed the decrease or lack of cliange in Susselt a t loading ratio less than one to a reduced scale of turbulence in the gas stream wheii solid particles are added. The results of the present investigatioii in t’heentrance region illustrate that ally addition of solid particles increases the heat transfer coefficieiit from wall to the mixture. This iiicrease ma>-be due to tlie additioii of particles at the eiitraiice causing more turbulence. -\fter the addition of particles, eam must ,xcelerate particles to t’he constant velocity as well as distribute particles within air stream according to a momentum balance. This rearrangement of air stream may continue from the particle entrance location to where the fully developed flow is attained aiid coiisequently increases the scale of turbulence in the entrance region. The heat transfer rate ~ o u l dbe . increased also. Farliar aiid Depen- (1963) and Jepson and Smith (1963) iiir-estigated the effect of particle size on the heat transfer coefficient. Hoth iiivei.tigatora indicated the same relationship in t h a t nri increase iii particle diameter reduced the heat transfer rate. The maximum diameters were determiiied as 200 and 500 p for glass beads and sands, respectively. Farbar arid Ilelien (1963) also illustrated a reduced effect of heat transfer rate with uiiiform sized particles greater than 30 p and ail approximately equal effect for 30-p glass particles. Kilkinsoii and S o r m a n (1967) presented heat transfer data obtained iii a vertical heated tube on suspensions of glass beads and graphite in air. -1plot of (Su),,’(Re)0.8 us. T,’T,,, revealed a negative cube root depeiideiice. Conclusions
(1) Iii a gas-solids rnixture system, the mixture Susselt iiumber varies with the 0.6-0.66 power of Reynolds number for either entrance or fully developed regions. ( 2 ) There is no significant difference in the mixture heat transfer coefficient between equal and different inlet temperatures of air and particle:, iii gas-solids system. (3) The mixture SusF.elt number for an entrance region to a tube \vas correlated ( d ~ 2 . 7 7 ~as) ( X u ) , = 0.1’i(Re)@,61[1 (G,C, G,C,) This empirical equation is valid for the convective capacity Iiarnmeter values greater than unity for the case of uiiiform n-all temperature.
+
(4) Heat transfer rate as expressed by the mixture Nusselt number increases with loading ratio in the entrance region, as compared to the decrease in rate betn-een loading ratios of 0 and 1 for the fully developed region. Nomenclature
thickness of tube wall, ft specific heat of air, BtuJb O F C, specific heat of particle, Utullb O F D1, D z = small and large tube diameter, ft D = tube diameter D, = (D1 D 2 ) ,2, equivalent diameter, ft G, = mass flow rate of air, lb/’hr ft2 G, = mass flow rate of particle, lbihr ft2 ha = heat transfer coefficient of air alone, Btu/hr it2 O F he, = heat transfer coefficient of air a t the entrance region, Dtu,’hr ft2 O F h,,, = mixture heat transfer coefficient, B t u / h r f t 2 O F /I,+. = n-ater side heat transfer coefficieiit, Dtu,,lir f t 2 O F kt = thermal coiiductivity of tube wallqDt,uihr ft O F (Su),,, = mixture Kusselt number (Su), = water side Susselt number L = tube length, ft (I+) = Capalka.Prandtl number Reynolds number (Re) = GaDl’pLa: (Re),,, = water side Reynolds number (St), = Stanton number for air alone T,,, = mixture temperature, O F T,,,i = mixture inlet temperature, O F T,,,. = mixture outlet temperature. OF T , = n = l J , . . , l 2 , temperature with respect to the thermocouple locations as indicated in Figure 1, O F T , = wall (or water) temperature, O F = overall heat transfer coefficient, Btu,,lir i t 2 O F
b
=
C,
= =
+
GREEKLETTER pa
=
dynamic viscosity of air, lb,’ft see
literature Cited
Danaiger, \T. J., Ind. Eng. Chcm., Process Des. Develop., 2 , 269 ( 1963). Farbar, L., JIorley, 31. J., Ind. Eng. Chon., 47, 1143 (1957). Farbar, I,., Ilepea, C. A.j Ind. Eng. Chem., Fiindani., 2, 130 flq6:3>
Ilafi;C.’W., Hedrick, T. I., “lhying of JIilk and 1Iilk Products,” The AYI Publishing Co., Westport, Conn., 1966. Havashi. H.. Heldman. I). 11.. Hedrick. T. I.. dlzch. Bar. E x p . Sta., &art. Bull., SO,’93 (1967). Heldman, D. R., Rang, P. Y., Chen, A. C., J . Food Sei., 36, 311 11971 \ - - . - ,).
Hsii, S. T., “Engineering Heat Transfer,” Van Sostrand, Princeton, N. J., 1963. Jepson, C;. A , , Smith, W., Trans. Inst. Chcin. Engr., 31, 207
il963). Kreith, F., “Principles of Heat Transfer,” International Textbook Co.. S r r g n t o --, n . PR.. --.,1966. - - ~. Sadek, S.E., Ind. Eng. Chem., Process Des. Devcl., 11, 133 (1972). Tien, C. I,., Trans. BSJIE, J . Heat Transjer, 83C, 183 (1960). Tien. C. I,.. &an. V..ASJIE PaDer No. 62-HT-1,; (1962). Cited b< Soo, “Fiuid ’Dinamics of ?;Idti-Phase Systems.” Blaisdell Pithlishinz Co.. Toronto. 1967. Wang, P. I?,,Ph.U. The& Department of Agricultural Engineering, IIichigan State L-niveraity, 1970. Wilkinson, G. T Sorman, J. I{,, Trans. Inst. Chem. Eng., 45, -.I
~
~
~
T.314 (1967).
RECEIVED for revien- June 28, 1972 ACCEPTEDApril 27, 1973
This investigation was supported by the Agricultural Research Service, US Department of Agriculture, under Grant KO. 12-14100-9114 (1973), administered by the Eastern Utilization Research and Development Ilivision, Philadelphia, Pa. 19118. JIichigan Agricultural Experiment Station Journal Article No. 6019.
Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 4, 1973
427
