(15) Schultz, N. F., Cooke, S. R. B., Piret, E. L.. Chem. En:. Progr. 5 3 , No. 5, 254 (1957). (16) White, H. .4., J . Chem. Met. Mining Soc. South Africa 43, 135 (1942-3). (17) Zeleny, R. A , , Ph.D. thesis, University of Minnesota, Minneapolis, Minn., 1957.
(8) Heney, J. L., Ph.1). thesis, Univrrsity of Minnesota, Minne-
apolis, Minn., 1951. (9) Johnson! J. F., Axrlson, J. W., Piret, E. L., Chem. Eng. Progr. 45, No. 12: 708 (1949). (10) Kern, D. Q., “Process Heat Transfer,” p. 799, McGraw-Hill, New York, 1950. (11) Martin, G.. J . Scic. Chem. Znd. (London) 45, Part 4, 160 T (1926). (12) Morey. G. W.,‘,‘Properties of Glass,” 2nd ed., p. 295, Reinhold, New York., 1954. (13) Roesler, F. C., Proc. Phys. Soc. (London) 69, 981B (1956). (14) Schellinger, A. K., Ph.D. thesis, Stanford University, San Francisco. Calif.. 1950.
RECEIVED for review February 1, 1961 A C C E P T E D August 9, 1961 Work done in partial fulfillment of Ph.D. thesis of R. A . Zeleny, University of Minnesota, Minneapolis, Minn.. 1957, and supported by a Xational Science Foundation grant.
HEAT TRANSFER IN SINGLE AND DOUBLE SHELL COOLING ROLLS A .
K
F. R
This article reports an experimental study o f heat transfer
. C H A T T E R J E E , Universitj o j Akron, Akron 4, Ohio . G R 0 S S , F. R. Gross Co., Znc., Akron 17, Ohio
p l o t t e d o v e r Re,
than the d o u b l e shell roll.
For b o t h rolls,
in single and d o u b l e shell c o o l i n g rolls which had identical
the Nusselt numbers a t l o w Re,
outside diameter and face and w a l l thickness so that Nusselt
an increase o f ReR, while a t the higher Re,
numbers of the c o o l i n g w a t e r t o the outer shell could b e
numbers generally increase with a n increase of Re.,
directly compared.
It was found that there was n o direct
generally decrease w i t h
This change in Nusselt numbers was explained b y the
relationship b e t w e e n Nusselt numbers and r o t a t i o n a l Reyn-
p r o b a b l e formation o f vortices inside the rolls.
olds number Re,
f o r the t w o types of rolls i f Re,
the Nusselt
An increase
is based o n
in turbulence o c c u r r e d in the double-shell r o l l as the centrif-
the outer diameter of the rolls and the Nusselt number o n the
ugal f o r c e o f the w a t e r rotating in the shell was a p p r o x i -
hydraulic diameter of the d o u b l e shell roll.
mately equal t o its o w n weight.
H o w e v e r , the
In the single shell roll, this
single shell r o l l h a d fienerally higher Nusselt numbers when
increase occurred a t approximately half the rotational speed.
often requires cooling of finished and semifinished protducts in a continuous operation. Some of these may be transported on conveyors, such as cured tires in the rubber industry, where heat is removed by natural convection to the surrounding air. I n other processes, as in calendering of plastics, the plastic film is cooled by passing it over watercooled rolls which usually are assembled in stacks in close proximity to the calender itself. The number of rolls needed to cool the calendered plastic sheet to the desired temperature depends to a great extent on the cooling efficiency of the rolls. ‘The more efficient the cooling roll, the fewer rolls are needed. T h e plain single shell roll has an unrestricted cavity. Cooling water passes through the roll a t relatively low velocity. This is commonly considered the least efficient cooling roll, having the widest variation of surface temperature, probably because of the low heat transfer coefficient of stagnant water in the roll ends. As the need for more uniform cooling arose in the plastics and rubber industry, the double shell roll began to replace the single shell roll in calendering operations. I n the double shell roll stagnant water is eliminated, and water velocity through the roll is increased by insertion of a closed cylinder
in the roll cavity which gives the cooling water a clearly defined annulus for passage through the roll. I n single and also double shell rolls: conventional parameters in heat transfer cannot explain the complex convective heat transfer mechanism, in which body forces together with wave and vortex effects greatly influence heat transfer and flow phenomena of the system. A full evaluation of these effects was considered beyond the scope of this study. However, the test results are indicative of the cooling efficiencies of single shell and double shell rolls. They are considered valid enough for reaching general conclusions.
ODERN INDUSTRY
Present address, Thompson Products Valve Division, Thompson Ram0 Wooldridge, Inc., Cleveland 10, Ohio.
Background Heat transfer in rotating ducts and rolls has been investigated by a number of research workers. Bjorklund and Kays (7) determined experimentally the heat transfer between concentric cl-linders rotating at various speeds and speed differentials, with no axial flow of the annulus fluid. They also discussed the effect of vortex formation in the annulus on heat transfer. Brewster and Nissan (2) studied the motion of a liquid contained between two concentric cylinders with only the inner cylinder rotating. They found that a t a critical Re, the flow pattern changed from laminar type to a vortex-mixed turbulent type. VOL.
1
NO. 1
JANUARY
1962
41
Figure 1.
Section through test stand-single
Kreith and associates (3) conducted tests with various rolls. O n e type had an unrestricted cavity. another had a tubular insert, and a third one had paddles inside the roll cavity. A distinct change in Nusselt number occurred at various Re, values. Taylor (5) was the first to show hydrodynamic stability of laminar flow between concentric rotating cylinders. H e showed experimentally and analytically that, in a n incompressible homogeneous Sewtonian fluid, instability will occur at certain angular velocities of the outer and inner cylinders. Taylor found that in the fluid between the two cylinders, pairs of toroid-shaped vortices were formed. H e further showed that the spacing of these toroids along the axis of cylinders is the same for any particular equipment and rotational speed of the cylinders. Leivis ( d ) further confirmed the findings of Taylor.
Experimental All measuring devices such as meters. gages. and thermometers were calibrated before the tests. Low pressure steam to heat the outer shell of the rolls was obtained from the high pressure steam supply of the University of Akron through a pressure-reducing valve. A throttling calorimeter in the low pressure steam line was also installed to determine the quality of the steam. T h e steam pressure downstream of the pressurereducing valve was read from a gage which was installed close to the steam chamber itself. Figure 1 shows a section through the test stand itself with a single shell roll mounted inside the steam chest. T h e right side of the steam chest had a removable head through which the test rolls were inserted. Common stuffing boxes
shell roll
sealed the rotating shafts of the test rolls ivliich turned in pillow blocks resting on a structural support. .After a test roll had been installed in the steam chest, 1 .S-inch-thick 85% magnesia insulation was applied to the outside of the steam chest as shoxvn. The steam condensate left the steam chest through a buckettype trap and was then weighed. T h e condensate temperature was read from a mercury thermometer inserted in the drain line. Soncondensable gases \yere bled off repeatedly during tests to make sure that the heat transfer coefficient o n the steam side remained constant. A steam pressure gage \vas mounted on the steam chamber. Thermometers and thermocouples in the s[eani chamber determined the actual steam temperature and the surface temperature of the heated roll. T h e roll isas driven through sprockets and chain by a 5-hp. variable speed d.c. motor mounted on the supporting frame of the steam chest. Single Shell Test Roll. T h e si@ shpll roll sho\vn in Figure 1 was made from 6-inch outside diameter tubing (0.25-inch wall) 175/* inches long which was machined to a 5*j/16-inch outside diameter and jg/,,-inch inside diameter. T h e roll proper was of all-~veldedconstruction. IVater entered through the trunnion on one end and left on the other end. Heat pick-up of the cooling water through the end plates of the roll \vas kept small by sandwiching a '/,-inch asbestos insulating sheet between them and the 0.5-inch steel plates shown. T h e cooling water entered and left the roll through standard rotary unions. Double Shell Test Roll. T h e double shell roll shown in Figure 2 had the same outside dimensions and wall thickness as the single shell roll. Its inner shell was made from 4-inch standard steel pipe machined to 43/,-inch outside diameter.
Holes in shaft for water passage to annular space
1/8" asbestos insulation Water
/' 1/2
steel plate
Water outlet annul& space Figure 2. 42
Section through double shell roll
I&EC PROCESS DESIGN A N D DEVELOPMENT
T h e shafts of the roll extended inside the roll and had radially drilled holes to let cooling Ivater pass through the annular space formed by the inner and outer shell. The ends of the double shell roll were insulated in the same manner as the single :;hell roll. Since the outer shell of the double shell roll was removable from the inner shell. it was necessary to install O-rings between them to prevent leakage of steam to the cooling water, as shown in Figure 2. The inside temperature of the outer shell, the outside temperature of the inside shell! and the midsectional bulk temperature of the water \ v e x initially measured by thermocouples Fvhich \vere brought to the outside of the steam chest via the annular spacing and tk.e drilled passage of the shaft to the slip rings mounted on the roll shaft (see Figure 1). The speed of the roll was measured by a n electronic speed counter. T h e water leaving the test roll was collected and Iveighed. The temperature of the incoming and outgoing water and the pressure drop through the system were measured ; the latter by a differential manometer. Power input into the motor, rotational speed, water flo\v rate. and pressures were the independent variables, while the temperature rise of the cooling water was the dependent variable. lleasurements were taken after the system had reached equilibrium conditions, which took from 10 to 20 minutes. Data for single shell (Table I) and double shell rolls (Table 11) are sho\vn. Test Evaluation. In the test, the heat gained by the water per unit time equals the heat lost by the steam per unit time. The rate of heat transfer is: q =
n7cp(t,;" - t,ij
=
C'"A ( A t ) , " gmean
l o calculate h,, h, (the steam side film coefficient) has to bc known; it was calculated from the Nusselt equation: ~~
(3)
Physical properties of the liquid film were evaluated at the arithmetic average of the vapor and the wall temperature. I t was considered possible that the steam side film coefficient, /is, calculated from the above Nusselt equation may not be fully valid in the case of high steam velocit!- and turbulent condensate flow rate. Further calculations were made to find the percentage of error in the calculated values of h, by 4 = n7C, (two-
fwL)
=
h,d (t,,, -
(4)
tjj
It was found that for the entire range of the tests: the variation of h , between the two methods was between 1 and 5Tc. The steam side film coefficient h, calculated from the Susselt equation was 2170 B.t.u. per hour-square foot F.. jvhich is in general agreement with values obtained by other observers. This value was used to calculate h,. Any errors in the calculation of h,, the Lvater side coefficient. are small because h, is much larger and, therefore, the least influential of all coefficients involved. The accuracy of the thermocouple readings of the inside wall of the outer shell. ivas checked \\-ith Equation 1 and the relationship : Heat gained by water = heat conducted through the outer shell of the roll
(1 j
where c', is based on a specific surface of the roll. In this case, the outer roll surface LT0 was selected as the reference area. T h e average heat transrer coefficient is:
The hydraulic diameter ( D h )of the double shell roll is that of the annulus through which this \\ ater flows or Dh = 2d. Susselt numbers for both rolls based on the hxdraulic diameter
1
Dh
of the double shell roll. Nu
=
h
D h
-"K-, are assembled in Tables
I and 11. They were plotted over the rotational Reynolds
Table 1.
Roll Sfeed, R.P.M. 895
Test Data and Evaluation of Single Shell Roll
lthter Flow,
G.P.M. 1.45 5.34 9.92 12 30 14 40 14 5 12.5 9165 5.26 3.54 3.52 9.04 12.44 14.80 4.98 3.48 6.26 10.24 12.40 14.40 14.4 12 44 9 72 7 36 4 38
water
Temp., Steam F. Chrst Out Temp.,'F. iYua ReRh X 7 0 - 5 177.5 248 149.4 31.1 87.5 247 134.0 18.55 70.5 247 146.0 15.90 62 5 248 124.0 14 48 58.5 248 135.0 14 10 53 0 252 81 5 8 70 56 o 249 87 9 9. no . 62:Q 246 10615 9.40 82.0 246 107.8 10.80 101.0 246 116.0 12.35 101.5 249 109.0 7.10 69.0 256 5.70 92.5 59.5 92 5 251 5.25 55.0 247 5.03 102.0 80.0 6.13 91.5 250 98.0 251 100.0 2.42 75.0 246 103.0 1.835 62.5 238 107.0 1.86 58.0 230 117.0 1.79 55.0 1.74 226 125 .O 54 241 98 5 0 56 5 245 . i o 1 5 n _ 61 5 242 ioi 5 o 68 5 242 95 9 0 83 252 83 8 0
In 48.5 48.5 43.5 42 0 40 5 575 40 5 40 5 40.5 41.5 42.5 324 43.5 43.5 42.0 40.5 42.0 112 43 43 42 41 40 0 40 40 40 5 41 5 42 0 a Based on DI,. Based on Do.
Table II. Test Data and Evaluation of Double Shell Roll M'ater Temp., steam Roll Water Speed, Flow, "F Chest R.P.M. G.P.M. In Out Temp., " F . 4Vua ReRb X 10-6 928 2.18 50 144 251 136 0 27 5 6 . 6 2 48 80 251 109 0 18 3 9 . 8 5 44 5 66 251 96 5 16 1 1 1 . 6 4 42 5 61 251 106 0 15 35 1 2 . 9 0 41 5 59 251 106 0 15 I 591 13.55 41.5 57 252 98.5 9.36 11.64 4 1 . 5 58 253 86.5 9.45 8.83 42.0 61.5 254 75.0 9.84 5.60 42.5 72.0 254 77.2 10.55 3.08 44.5 103.0 254 89.7 12.75 1.17 4 5 . 0 177.0 253 104.0 10.15 297 3.26 46.5 85.0 255 52.6 6.0 7.02 45.5 66.0 234 61.6 5.24 9.92 44.0 61.0 254 73.3 4.95 12.16 42.5 58.0 253 79.2 4.78 14.76 41.5 56.0 252 90.9 4.92 122 14.70 4 1 . 0 56.0 252 106.0 1.88 12.20 41.5 57.5 252 87 A 1 96 1 0 . 3 6 41 5 60 o 254 85 o i 91 7.60 42 0 65 n 254 84 2 2 22 4.36 42 5 76 0 254 62 7 2 16 0 4.34 43.5 79.5 251 72.4 0 7.66 43.5 72.5 251 114 0 10.44 43.0 64.0 251 105.5 0 12.76 42.0 60.0 250 112.5 0 14.3 41.5 58.0 251 118.7 0 Based on Dh. b Based on Do. -
VOL. 1
NO. 1
-
JANUARY
1962
43
I: 3. Nu vs. Rea for single shell roll
Figure
number Re, =
D,=W ~
Figure 4.
Nu vs. ReR for double shell roll
in Figure 3 for the single shell roll and
in Figure 4 for the double shell roll. The decision to base the Nusselt numbers on one hydraulic diameter was made to simplify the presentation of the test results. The hydraulic diameter of the double shell roll was selected. The rotational Reynolds number was selected as likely to give meaningful results in evaluation of other rolls. However, this relationship has not been proved a t this time. Heat losses through the trunnions of the roll \vere neglected, since they ivere found to be less than 3% of the total heat transferred. This heat loss is small because the end plates of the roll are insulated. In addition, the roll shafts have a thick wall and only a small area exposed to the steam.
Results a n d Discussion For both rolls, Nu =
h Dh
was plotted over Re, =
D2W.
y
I n each test series, roll speed was kept constant while the cooling water flow varied from approximately 1 to 3 gallons per minute to 14 gallons per minute. Figures 3 and 4 show that there is no direct relationship between Nu and Re,. Both rolls have, however, the following in common: At the lowest rotational speed of the rolls, Nu increases with a n increase of Re,. while at high rotational speeds Nu decreases with a n increase in Re,. Since for each test series roll speed was constant and viscosity of the fluid was also considered in the calculations,
one must reason that the cooling water flow increased or decreased vortex formation and Xu, as explained by Taylor and Lewis. I t may be reasoned from Figure 3 for the single shell roll that a t a low rotational speed of 112 r.p.m., turbulence decreased with an increase in Re, while a t higher speeds of 575 and 895 r.p.m. turbulence increased significantly. At a medium speed of 324 r.p.m. turbulence first decreased, then increased. This region of Nu change was between a n ReR of 5 to 7 x 10-5. A similar flow pattern must also occur in the double shell roll shown in Figure 4. However, the change in flow occurred a t a higher rotational speed of 591 r.p.m. and at a higher Re,, namely 9 to 10.5 X 10-5. It is interesting that a t 650 r.p.m. the centrifugal force acting on the water, if it were rotating in the annulus at the same rotational speed as the roll itself, equals the Xveight of the water itself. At the top of the roll where the centrifugal force is in the opposite direction of the gravitational force. the water is therefore in a weightless state while a t the bottom of the roll. the water would be twice its normal Iveight because centrifugal force and gravitational force act in the same direction. This phenomenon apparently has an effect on the flow pattern of the water in the double shell roll. Kreith and associates ( 3 ) found a change of Susselt number occurring a t somewhat lower rotational Reynolds number.
112 RPH
4
+&L l
y o - R P M
30-R 2 4PM RPM
100
f
575RPY
5
10
COOLING W A T E R ,
Figure 5. roll
V 44
15
GPM
Nu vs. cooling water flow rate for single shell
8 9 5 r.p.m. 1 1 2 r.p.m.
A
+
5 7 5 r.p.m. 0 r.p.m.
3 2 4 r.p.m.
I&EC PROCESS DESIGN A N D DEVELOPMENT
Figure 6. roll
V
Nu vs, cooling water flow rate for double shell
9 2 8 r.p.m. 1 2 2 r.p.m.
A
+
5 9 1 r.p.m 0 r.p.m,
2 9 7 r.p.rn.
An interesting question is: How do the local Nu numbers change along the circumference and across the face of the rolls? An answer to this question cannot be given a t this time. since the elaborate instrumentation required for a meaningful test was not available. It must be understood that the Xu numbers of this report are averaged numbers, lumping all local coefficients together. The Nusselt numbers are also based on the hydraulic diameter of the double shell roll. The Xusselt number was also plotted over cooling water flow for both single and double shell rolls in Figures 5 and 6 . These curves are less meaningful than those in which Nu was plotted over ReR. However, they are more conventional since the heat transfer coejficient hw is plotted over cooling water flOW.
T h e results of this r:tudy contradict the commonly accepted opinion that the double shell roll has better heat removal capacity than the single shell roll. The cooling trains of the early calenders in the rubber industry had single shell rolls. By touch of hand, one could often detect warm roll end:; while the middle of the roll was fairly cool. \\Then the rubber industry branched out in the plastics field, the speed of the calendering operations increased and double shell rolls replaced the conventional single shell rolls. It is not clear if the preference for the double shell roll is due to more uniform cooling, elimination of warm roll ends, or possibly also to be1:ter average heat removal, which might occur in rolls dimensionally different from those tested.
c,
Dt Du D,
= = = = =
heat transfer area, sq. ft. heat capacity, B.t.u./lb. O F. inside diameter of cooling roll, ft. outside diameter of cooling roll, ft. log mean diameter of pipe, ft. = D, Dt
-
In
D -' D,
Dh
= hydraulic diameter of double shell roll = 2d
d g
= =
P
(At),og, n L B n = log mean temperature difference, O F. t , , = temperature of saturated vapor. F. tu. = temperature of wall surface, O F. t, = average wall temperature, inside and outside, F. tl. = mean temperature of inlet and outlet cooling water, O
t,, tui two
cr, Lf'
x !
F.
steam-side wall temperature, F. water-side wall temperature, ' F. temperature of incoming water, O F. temperature of outgoing water, O F. average over-all heat transfer coefficient based on outer area of shell. B.t.u./hr. sq. ft. ' F. = mass water flow rate, Ib. moles hr. = shell thickness, ft. = dynamic viscosity of water, Ib. moles/hr. ft. = kinematic viscosity, sq. ft. /sec. = density of water, lb. moles/cu. ft. = angular velocity = 2zV/60 set.-' = = = = =
t,,
J
v P w
Nomenclature
,4
Re,
latent heat of condensation, B.t.u., lb. mole convective steam-side heat transfer coefficient, B. t.u./ hr. sq. ft. F. convective water-side heat transfer coefficient, B. t.u./ hr. sq. ft. F. thermal conductivity of water, B.t.u./ hr. ft. ' F. mean thermal conductivity of pipe materi:l based on average wall temperature, B.t.u.1hr. ft. F. face of roll on \vhich heat transfer calculations are based, ft. Susselt number, h,DhjK heat transfer rate, B.t.u. hr radius of inner tube, in. outside radius of outer pipe, ft. inside radius of outer pipe, ft. Dozw = rotational Reynolds number, __
literature Cited
(1) Bjorklund, I. S., Kays, LV. M., Trans.'4m. Soc. .Mech. Engrs., 81,175 (1959). (2) Brewster, D. B., Nssan, A. H., Chem. En?. Sci. 7, 215-21 (1 OiAI \-'--I'
(3) Kuo, C. Y., Lida, H. T., Taylor, J. H., Kreith. F., Trans. Am. Soc. Mech. Engrs. 81, 139 (1960). (4) Leiris, LV. J., Proc. Roy. Soc. (London) A117, 388 (1923). (5) Taylor. G. I., Phd. Trans.Roy. Soc. (London) A223,289 (1922).
annular space between two rotating surfaces, in gravitational force ft./hr.*
RECEIVED for review March 9, 1961 ACCEPTED October 23, 1961
MEASUREMENTS OF GASEOUS DIFFUSION THROUGH POROUS MATERIALS J O H N BEEK Shell Development Co., Emeryaille, Calif. W h e n an experitnerit is carried out in which t w o opposite surfaces o f a porous plug are bathed in different mixtures of a pair of gases, the fluxes of both gases must b e measured in o r d e r t o calculate an effective binary diffusion coefficient from the experimental results.
The situation in which Knud-
sen diffusion is significant is excluded from consideration. It is also pointed out that it is n o t necessary t o maintain an accurate balance o f pressure on the t w o sides of the plug, since the quantity that is derived from the experimental measurements is the product o f density and diffusivity, which is substantially indepen'dent tal conditions.
of pressure under the experimen-
N
1941,
W I C K E AND KALLENBACH
(5) measured the steady
I flow of COZ through a layer of porous material, the two surfaces of which were bathed in different mixtures of COz and nitrogen, and calculated the effective diffusion coefficient through the layer from the measurements. Since that time, Hoogschagen (2) and Weisz ( 4 ) have measured diffusion through porous materials by essentially the same method. Scott and Cox ( 3 ) have recently used measurements of diffusion through porous plugs as a convenient means for studying the temperature dependence of diffusion coefficients. This note discusses the calculation of binary diffusion coefficients from such measurements, giving attention only to ordinary diffusion in the gaseous phase-that is, excluding cases in which surface diffusion or Knudsen diffusion is important. VOL. 1
NO. 1
JANUARY
1962
45
