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The Mechanism of Heat Transfer in Staggered Tube Banks

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SHE HXCHAHISM OF HEAT TRANSFER IE STAGGERED
TUBE BASKS
A THasiS
PRESENTED TO THE FACOLTX OF THE GRADUATE SCHOOL
OF CORBEL!. UKIVERSITT FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
By
Cornelius Harsden Vanderwaart
September, 1940
ProQuest N um ber: 10834686
All rights reserved
INFORMATION TO ALL USERS
The q u a lity of this re p ro d u c tio n is d e p e n d e n t u p o n the q u a lity of the co p y su b m itte d .
In the unlikely e v e n t that the a u th o r did not send a c o m p le te m a n u scrip t
and there are missing p a g e s, these will be n o te d . Also, if m a te ria l had to be re m o v e d ,
a n o te will in d ic a te the d e le tio n .
uest
P roQ uest 10834686
Published by ProQuest LLC(2018). C o p y rig h t of the Dissertation is held by the A uthor.
All rights reserved.
This work is p ro te cte d a g a in s t u n a u th o rize d co p yin g under Title 17, United States C o d e
M icroform Edition © ProQuest LLC.
ProQuest LLC.
789 East Eisenhower Parkway
P.O. Box 1346
Ann Arbor, Ml 4 8 1 0 6 - 1346
AcnovLXDoasm^
the author wishes to express hie sincere appreciation
to Professor C. C* Winding* at whose suggestion this work
was undertaken, and under whose supervision It was carried
out#
His friendly advice helped the author over the many
difficulties encountered In this Investigation#
Acknowledgment Is also made of the assistance of
Mr* J* 1* Hatcher In construction of the apparatus#
BIGGBAPHY
The author was horn in Harwich, Connecticut, on
September £3, 1914, the son of Peter Thomas and Elisabeth
(M&rsden) Vaaderwaart• I® attended the public schools of
Falmerton, Pennsylvania, and was graduated from Stephen S*
Palmer high School In June, 1938#
he received the degree
of Bachelor of Science from Hamilton College in 1936*
Since that time he has been registered In the Graduate
School of Cornell University as a candidate for the degree
of Doctor of Philosophy*
During the academic years
1937-4Q he has been Assistant in Chemical Engineering*
The author is a member of Theta Delta Chi, Alpha Chi
Sigma and Phi Beta Kappa*
TABLE OP C01TEHTS
Page
Introduction *■■<»** *• *
- - « - —
—
Description of Apparatus —
* - - - —
Procedure
-------- ----- -
~ ~ ~ - —
- —
1
^—
*
g
s
Calibration of Be si stance Thermometers
~ ~ ~
*• * ~
-
Previews Woirfc - —
~ * <* ~ - -
Runs Using Steam as the Heating Medium
t a i with Stripe Heated Electrically
15
15
17
---
-- -
SO
Data and Calculations
nomenclature and Symbols
Physical Constants
~
—
—
_ —
•
20
Calibration of Resistance Thermometer®-Pitot Tube T r a v e r s e s
—
-----
Overall Coefficients
- -
Local Coefficients------ —
28
■
—
—
-
33
- —
-
58
~
Steam Heat - - - ~
Electric S e a t
—
- - —
£7
---------
Thermal Resistance ©f Tube and Steam Film
Discussion
gg
---
Assumptions
2U
- -
38
~
30
---------------
03
-------
76
Experimental Results
Single Tube
—
------ —
- -
88
Page
Experimental Results (Continued)
Tube Banks
Bow One
-
low Five
-------
Effect of Telocity
- - ~ —
Effect of Bow Humber
Effect of Row Spacing
Summary -.«*•***-«**..-■—
Bibliography
- -- - —
94
93
--------- ~
XOO
~ ------- „ « * _ * „ .
xoi
----- -*«*,.
103
~
104
---------
100
I*
m m t m m s L
toe of too m m e important types of equipment used to heat
m
oooX large volumes of gas is a bank of tubes in staggered
array*
too heating or cooling medium is circulated through
too tubes and tot gas is blown through too bank normally to
the tubes*
&uch banks of tubes art found in air conditioning
units, air dryers, boilers and economizers, and la the ton*
veetlon section of tube stills*
For toe design of such
SQUlpment it is necessary to hare information about toe heat
transfer coefficients and toe pressure drop across toe hank*
While much data of this sort has been published, there Is
little Information regarding to® individual factors at work
and toe mechanism by which the heat is transferred.
Data on
toe variation of the host transfer coefficient from row to
row. and of its dependence on gas velocity are available but
toe reasons for these variations and toe factors Involved
have not been determined*
It was toe original purpose of
this investigation to study toe variation in heat transfer
coefficient from point to point on an individual tube*
this
has been dene tor measuring toe variation in surface tempera*
tore by means of a series of metal foil resistance thermometers
affined to toe tube surface*
The effects of gas velocity,
tube position and bank dimensions on toe temperature die*
tributioa have been studied*
m m m m m
the distribution of boat flow around a cylinder in a
transverse stresst of mowing fluid has received the attention
of several Investigators*
apparently the first effort in
this direction was made by Jakemaa as quoted by Stanton** in
ISIS*
JaScaman fired a narrow strip of platinum foil longi­
tudinally ©n an ebonite rod, heating the strip electrically
and blowing air past the rod.
He found that, with a round
rod, the heat flux was greatest when the platinum strip faced
upstream and least when it faced downstream} with a square
rod She heat flux was greatest when the platinum strip faced
downstream*
01
Hay
in 1920 and Pram&nlk
so
a year later used a photo­
graphic technique by which the warmer portions of air around
a heated cylinder (a wire) appeared lighter in color than the
unheated air*
fhey found that the tone of heated air was of
nearly uniform thickness save for two horns which pointed
downstream tamgentially from the sides of the wire*
Directly
behind the wire there was a fairly large area of unheated air.
Ho calculations of local coefficients of heat transfer from
these qualitative estimations of temperature distribution
were reported*
In X98§ Bather** attacked this problem by determining
the variation in surface temperature by using ismall thermo­
couples.
He used both horizontal and vertical tubes.
Cooling
water was circulated through the tube and air at 100® C* wee
blown past the tube#
horizontal tubes#
Asymmetric re suite were obtained with
fteiher attributed this to free convection
currents set up in the water.
And, In fact, Woolfenden*7
found in 1987 that the temperature distribution of water In a
horizontal pipe was far from being symmetrical.
The heated
water by reason of its lowered density rose to the top of the
tube#
At higher velocities the temperature distribution
basest* more symmetrical*
For vertical pipes Beiher found a
maximum surface temperature at the point of incidence and a
minimum at the back of the tuba with a smooth variation
between the two#
This indicated a higher rate of heat
transfer at the front of the tube and a minimum rate at the
back of the tube#
lohriseh** in 19B9 reported the results of a long series
of indirect determinations of both overall and local heat
transfer coefficients, using an analogy between heat trans­
fer and mass transfer.
He studied single tubes and both
staggered and in-line tube banks#
For qualitative results
sheets of blotting paper were soaked in concentrated hydro­
chloric acid and fastened around the surface of the pipe.
Air containing ammonia was blown past the pipe and a picture
was taken of the resulting cloud of ammonium chloride#
For
quantitative results the hydrochloric acid was replaced with
phosphoric acid*
Analysis of the air and of the blotting
paper before and after the run provided the data necessary
for an estimation of transfer coefficients#
Estimations of
local coefficients wort made only for single tubas*
For this
work the paper was cut Into twelve longitudinal strips#
Mis
results, at variance with Reiher, show that fro® a maximum
at the front of the tube, the transfer coefficient dropped to
a minimum at or a little behind the aide of the tube and then
rose at the back of the tube to a value somewhat higher than
that at the front of the tube*
At higher velocities the rear
portion ef the tube assumed a more major portion of the trans­
fer*
In 1981 Brew and Ryan
gave preliminary results of a
long program in progress at the Massachusetts Institute of
technology on the direct' determination of the variation of
local coefficient of heat transfer*
A three-foot length of
three-inch brass pipe was cut in two longitudinally*
The
Inside of one half was divided into ninelongitudinal sections
and means were provided to collect separately the steam con­
densed in each section*
The tube was then reassembled and
mounted vertically in a wind tunnel*
Steam was admitted to
the tube and an air stream directed across the tube*
Their
results agreed in general with Lohriseh - the heat flax has
a maximum at the front of the tube and a minimum at the side*
A maximum was obtained at the back of the tube but this value
was about the same as that at the front of the tube, not
considerably above it as indicated by Lohrisch.
the authors say;
Of this
**##F©saibly the deviation fro® hohrisi^s IsMhermal
results can bo attributed to effects of heating upon the
velocity field near the sides sod rear* the full discussion
of this question will be deferred until our complete data
can he presented*.*11
x
In 19H8 Bryant, ©war, B&llid&y end Falkner reported
the direct determination of heat transfer coefficients from
an heated airfoil to moving air*
Platinum strips were
fastened to the airfoil and heated electrically to the same
temperature*
They found very intense rates of cooling at the
leading edge as compared to the rest of the surface*
This
worh was used by Harris, C&ygtll and Fairthorne* who designed
efficient wing radiators for airplanes*
By using only the
front ,twenty .percent of the wing, surface, the average co­
efficient of heat transfer was about sixty percent greater
than that of a wing radiator occupying the whole surface*
i*
Heim
in 1934 published the results of a very novel
attach on the problem*
stream of hot air*
in ice cylinder was placed in a
After a period of exposure the cylinder
was removed, a mold of the cylinder was made of pl&stloeme
and a cast made of plaster of paris.
From a study of the
amount of erosion an estimation of the heat flux at any
particular point could be made#
The method, of course, is
open to the objection that the cylinder changes In shape and
accordingly the velocity distribution is altered*
However,
the results agreed quite well with those of Lohrisch and
Drew and Ryan#
In 1935 Small
ss
made measurements of the temperature
distribution in the air stream in the vicinity of a hot tube.
■to* mated a vary considerable thickening of the boundary layer
at the sides of the tube, indicating a minimum rate of heat
transfer at the flanks of the tube# In the same year he gave
a4
results of another investigation . A steam heated cylinder
was provided with a thermopile along one element of the
cylinder which measured the temperature gradient through a
portion of the tube wall*
She tub® could be rotated to
determine the heat flux at various points on the circumference*
He confirmed his own work and that of other investigators there was a maximum rat® of heat transfer at the front of the
cylinder, a minimum at or near the sides*
The heat flux at
the back of the tube was very irregular, but the coefficient
rose to a value about equal to that prevailing®! the front
of the tube*
The irregularities were more pronounced at high
velocities*
k very considerable amount of work has been done on the
velocity and pressure distribution around single cylindrical
obstructions in a fluid stream* The results are summarised
i
by Fag® and Johansen who states
outstanding features of two-dimensional flow
behind an infinitely long obstacle of bluff cross-section are
now well known* Two thin bands of vortlcity are shed at the
after end of the obstacle and these, as they flow downstream,
separate the freely-moving stream from a low pressure region
of nearly motionless fluid at the back of the obstacle* It
some distance behind, these sheets break up with a uniform
frequency into two trails of discrete cylindrical vortices
of opposite directions of rotation to form a vortex street.*
Many investigators have measured the overall coefficients
of heat transfer and the pressure drop across tube banks*
The
nost complete study was made toy Pierson*® and Huge10*
Their
results have been analysed by Qrimison ♦ Colburn* and
McAdams
have summarised and correlated the data of
various investigators«
The variation in film coefficient from row to row has
e
sa
been studied toy Griffiths and Awtoery and Winding * They
tooth note that the heat transfer coefficient in the first
row is less than 0$ per cent of its mawimua value, that
it increases and becomes essentially constant in the third
and succeeding rows#
Seiher** observed that he could
materially increase the eonductsmee of the first row by
artificially inducing turbulence to the sir stream*
Pre­
sumably, therefore, the higher rates of heat transfer
observed in the latter portion of a tube bank are due to
the turbulence imparted to the air stream toy the preceding
rows*
The only evidence available on the velocity dis­
tribution in staggered tube banks are the smoke pictures
of lohrlseh which Indicate that after the third row the air
is in very turbulent motion*
DEscaxpma m m p a m im
The apparatus employed in the present Investigation
consisted of a specially eonstrnoted rectangular duct con­
nected to a blower toy means of reducers and a round duct
equipped with a Pilot tube*
the rectangular duet was arranged
so that tube banks of various dimensions could toe conveniently
installed*
A special measuring tube was substituted for one
of the standard tubes and means provided for moving this tube
to various locations in the bank*
The arrangement and con­
struction of the equipment is shown in Figure 1*
Air was forced through the system by an American Blower
Company number 5-El, type F, fan driven by & ten horsepower
motor*
This fan hat a rated capacity of 1200 cubic feet per
minute against a head of 30 inches of water*
The actual
delivery was controlled by an intake damper so that it was
possible to very the flow of air in pounds per hour per square
foot of minimum cross-sectional from approximately 4000 to
81,000 in any duct*
The blower discharged into a 8 5/8-inch
round duct 30 Inches long*
Concentrically located in this
duct at the blower end was a smooth conical aozssle 11 1/E
inches long*
The diameter of the discharge orifice was
5 1/8 inches*
This noazle was effective in eliminating
excessive variations in the air stream flow front*
A Pltot
tube, arranged so that both vertical and horizontal traverses
could be made was inserted 78 Inches from the blower*
The
6 5/8~lneh duct was connected to any rectangular duct by
means of a galvanised iron reducer 85 inches long*
This
extreme length provided very gradual expansion and conversion
from a round to a square duct so that the turbulence created
by the expansion was held to a minimum*
The duct itself was 8 feet long, IE inches high and
11 1/4 inches wide#
The entire structure was rigidly sup­
ported by means of a framework of 1-inch angle iron*
This
framework was composed of four longitudinal members set at
the four comers of the duct to support the 1/4-inch presswood which formed the walls, and was spaced by vertical
uprights welded to the supporting angles at the ends and the
center*
This construction gave a fixed heighth of 18 inches
for any duct that might be used*
The width of the duct was
fixed by horizontal cross-members bolted to the vertical
uprights below and above th© duct*
Plates were welded to
the vertical members and two bolts were used on the lower
cross-pieces to maintain, them at exactly right angles to one
another (see Figure 1)*
This construction insured rigidity
entirely independent of the duct walls and permitted very
close tolerances in the duct dimensions as th© steel frame­
work eliminated slight variations due to warping of the
presswood*
The tube bank itself was located near the far end of
the duct so that the last row was approximately 10 inches
from the rear of the duct*
This allowed a calming section
FIGURE I
DIAGRAM OF APPARATUS
DUCT
Blower
CROSS
Pitot
SECTION
Tube
DUCT
Tube
ELEVATIO N
Therm om eter
Bank
-lo­
in front of the actual duct that varied somewhat depending
on the actual bank being used by was approximately 5 feet in
length#
Each bank consisted of ten rows containing alternate­
ly five and four tubes arranged with a fixed distance, a,
between centers#
the five-tube rows were placed so that the
distance from the outside tubes to the walls of the duct was
1/Ha*
The four-tube rows had the same spacing between tubes,
but each tube was offset from the tubes in the preceding row
so that the center of the tub© coincided with the center of
the space between the tubes in the adjacent rows| an arrange­
ment that has been described as a st&ggered-tub© bank*
In
order to secure the same cross-sectional area in all the
rows, dummy half-tubes were placed against the walls in the
four-tube rows*
In effect, this arrangement made each row
an accurate segment of a larger bank*
The tubes themselves
were mad© from seamless, drawn 5.A.E. 1010 steel tubing,
1 1/8-inch in outside diameter, with a wall thickness of
0*065 inches*
End plates carrying 1/8-lnch pipe nipples
were soldered into the ends of each tube*
Three different tube banks were used in this investi­
gation*
The characteristic dimensions of these banks are
as followsi
TABLE X
Bank Bo*
4
5
6
a
8*25
2*25
8*25
b
*a
2*60
1.50
1*50
1*50
2*25
5*00
<*b
*•
1*752
1*50
0*75
0.75
2*0
0.75
11-
* ■«* transverse distance between tube
centere la a-row, inehes
b
r!'
-
* perpendicular distance between rows,
inches
d& » transverse distance between tube
1 centers la a row, tube diameters
d^ * perpendicular distance between rows,
tube diameters
d* * transverse clearance between rows.
Inches*
The method of supplying dry steam and of collecting the
ss
condensate was the same as that used by Winding * Steam
passed from a supply line through a reducing valve and into
a separator to remove entrained water*
The line between the
separator and the measuring tube consisted of a length of
1/4-inch pipe which was jacketed with 3/4-inch pipe.
By a
suitable valve arrangement steam from the high pressure side
of the reducing valve could be admitted to this annular space.
By this means the steam admitted to the measuring tub© could
be heated one or two degrees Fahrenheit above its condensa­
tion temperature at the prevailing atmospheric pressure. The
temperature of the superheated steam was measured by a
thermometer inserted directly into the steam line.
The mix­
ture of steam and condensate was discharged from the bottom
of the measuring tube into a special separator*
This
separator consisted of an inner cylinder 10 inches high and
-I3~
1 1/3 inches in diameter and an outer cylinder 10 inches high
and 3 1/4 inches in diameter#
The outlet nipple from the
measuring tube extended about 3 inches into the inner cylinder*
The condensate sms retained in this inner cylinder and the
uncoadeneed steam escaped through four 1/4-inch holes at the
top of the inner cylinder into the outer jacket and was vented
to the atmosphere through a 3/16-inch hole at the bottom*
The steam in the outer jacket maintained the condensate in the
inner cylinder at its condensation temperature and therefore
neither vaporisation nor condensation took place in the .timer
cylinder*
At the end of the run the condensate could be with­
drawn from the bottom of the inner cylinder through a valve
la a 1/6-ineh pipe line#
Both the steam supply line and the
condensate collector were heavily insulated with SB per cent
magnesia pipe covering*
To facilitate moving the measuring tube from row to row,
the bank was composed of five two-row units*
Pieces of press-
wood were cut from a steel templet and drilled to form the
top and bottom of the duct for each unit*
In width they were
exactly equal to twice the distance between row.
Accurately
spaced holes were drilled for the l/S-inch nipples of the nine
tubes constituting the two rows.
When a bank was assembled,
the front two-row unit was put In place carefully centered
and squared with the side walls and clamped with C-clamps#
The following unit was similarly positioned and clamped.
A
hole was then drilled, on each side at the joint , through the
•trips and angle Iron, and & steel bar 1 x &/$ inches in
eross-aectioa bolted over the joint*
top and bottom*
this was done for both
the third unit was than positioned and the
procedure repeated.
My this method of construction it was
a simple matter to remove any unit (and those following it),
replace it with the unit containing the measuring tube and
reassemble the bank*
the measuring tube referred to above was made from a
12g»inch- length of 1 l/2-inph cast -b&kelxte tubing, with a
wall thickness of 1/4 inches#
A brass end plate carrying
a a-inch l/©~lach brass pipe nipple was screwed and cemented
into each end*
Sixteen longitudinal strips of tin foil were
cemented to the tube with bakelit© lacquer.
Each strip was
11 B/4 inches long and l/4(io*Qi) inches wide.
0*000® inches thick, was used*
Pur© tin foil
A mechanical spacer was of
great help in properly locating the strips.
strips was approximately 0*04 inches*
laches from each end of the tube
The space between
Approximately three
alternate adjacent strips
were connected by a drop of solder (Bismuth-tin eutectic,
55£ Bl, 4SJ5 Bn, sup* 135^0*) * Strips number one and sixteen
were not so connected to each other.
In this way the strips
were connected in series in a continuous circuit*
To the
connection between adjacent strips was soldered a short length
(two inches) of Bo*SO copper wire.
To the other end of these
thin wires were soldered wires leading to the measuring
circuit*
A laminated bakelite guard ring notched to receive
-14—
the lead wires and equipped with set screws to hold each wire
firmly against the tube was slipped over each end of the tube*
By this procedure a flexible connection between the lead
wires and the strips was obtained and the electrical connections
on the tube were protected from injury by movement of the lead
wires*
Strips one and sixteen connected the strips in series
to & standard resistance of 0*1 ohms, a variable resistance
and a source of electromotive force*
the leads from the strips
were connected through rotary selector switch* and a reversing
switch to a Leeds and Sorthrup Type S, potentiometer which was
used to measure the electrical resistance of the strips*
The
potentiometer was calibrated by the standard resistance#
A diagram of the measuring tube is shown on Figure 8 and
a wiring diagram is shown on Figure 5#
FIOTtl t
DIAGMM OF IIA S u lIIO TUBE
ASSEMBLED
TU BE
S E C T IO N
GUARD
THROUGH
RING
Set
S crew s
S E C T IO N
T H R O U G H TUBE
S trips
$
O <fc (DO
L e a d s S o ldered
To S t r ip s
sT u b e
Wall
Guard
Ring
B r a s s End
P late
P o te ntia l
Leads
Brass
Pipe
\
FISURE 8
WBIHO DUOBAM
WIR ING DIAGRAM
T y p e Kq
P o te n tio m e te r
E.M.F G a
Ba.
S e lecto r
S w itch
<>► O
Q
O.I O h m
S tan da rd
S e le cto r
Swi tch
-16-
FROCEDU&B
CAXIBRATXOH OF RESISTANCE TBSRNORETERS
The major dependent variable in this investigation was
the surface temperature distribution around a tube in a
staggered tub© bank*
The independent variables were air
velocity, position of the tube in a bank and the dimensions
of the bank*
The tube surface temperature was estimated by
measuring the resistance of 1© metal foil strips ©quispaced on the circumference of on© member of the bank*
It
was first necessary to calibrate the individual strips*
This was done by placing the measuring tub© in a thermostat,
allowing it to come to constant temperature and measuring
the electrical resistance of the metal foil strips*
The thermostat was a wooden box about 24 x 20 x 12 Inches
lined with asbestos board*
It was heated by a coil of re­
sistance wire beneath a false bottom*
The temperature in the
box was controlled by a lamp bank in series with the re­
sistance wire*
A slow speed fan insured a uniform tempera­
ture within the box*
The temperature of the thermostat was
measured by three thermometers inserted through the top*
The
measuring tube, supported by two ring stands was placed in
the thermostat,the heat turned on and the fan started.
One
hour after the thermometers showed no further change in
temperature the resistance of the strips was measured*
The actual resistance measurements were made with a
Type K* potentiometer eelibrated by a standard resistance*
The standard resistance was a strip of aanganin foil approxi­
mately 12 inches long and one-half inch wide provided with
separate binging pests for current potential leads*
a nominal resistance of 0*1 ohm*
It had
Msnganin was used because
of its low temperature coefficient of resistance*
A current
of 100 milliampers was passed through the, circuit- containing
the standard realstance and. the resistance thermometers* The
standard resistance was f irst connected, to the
posts
of the potentiometer and.the slide wire adjusted to- a reading
of 0*1000*
The galvanometer was then brought to balance by
means of the battery rheostats in the potentiometer*
The
standard resistance was disconnected from the potentiometer
and each of the tin strips, in turn, was connected by
rotary selector switches to the l«JjUF« posts of the potenti­
ometer and a balance obtained by moving the slide wire* The
reading of the slide wire gave the resistance of each strip,
net in absolute ohms, but in terms of the standard resistance*
In all cases cheek readings were taken and the potentiometer
circuit was frequently checked and standardised*
This pro­
cedure was repeated for two other temperatures and calibra­
tion graphs for each strip were drawn showing temperature,
in degrees Centigrade, as a function of the strip resistance,
In ohms*
The calibration data are given on page 27.
After the three banks of this investigation had been
Studied the strips were recalibrated in the same manner*
1?
It was found that the first calibration was
bo
longer valid.
For a given temperature all strips showed a rise la resistance
of about 0*0050 ohms or about 1*5 per cent in the measured
value of resistance*
This increment represents a change in
temperature of about 3*5*0*
A careful inspection of the data indicated that whatever
had destroyed the calibration had most probably occurred la
the time between studying banks 5 and 6*
Accordingly banks 4
and ft and the runs with the single tub© were calculated on the
basis ©f the first calibration and- bank 6- on the basis of the
second calibration* '
mm mtm ami m m urns* medium
the duct and bank were assembled as already described*
Care was taken to make sure that the duct was properly
aligned* the unit containing the measuring tube was sub*
stitutad for the last two^row unit of the bank* the measuring
tube connected to the steam-supply line*aad the condensate
collector fastened In place*
The gap between strips 1 and 16
was placed onsetiy at the front of the- tube and the gap be­
tween strips S end 9 was at the back*
Thus, strips I end 6
were on the right side- of the tube and strips 16 to 9 were
on the left side of the tube#
The locations of the midpoints
of the strips in terns of <* # the angle of rotation is given
in Table II*
-
18-
t m M
<x degrees
n m
88.78
56,25
78*75
ioitse
183*76
%m a t
168*76
11
Eight fllde
Strip Ho*
toft Side
Strip So*
1
8
$
4
5
18
15
U
18
1£
6
11
7
8
18
9
The remaining portions of the duet were then assembled*
The operating procedure mas very simple*
The steam mas
termed on at toch&arvai# that a jet of star to eight inches
issued from the eondeasete collector vent.
The steam mss
allowed■to flow for mat least an hour la setter to purge the.
system of air and to heat the tube*
As described above, the
steam"Va* slightly superheated to insure dryness*
The blower
mas them turned on and the velocity adjusted by the Intake
damper*
These conditions mere- maintained until thermal
equilibrium mas established which generally required 15 to
80 minute**
The electric resistance of the 18 foil strips
mas then measured and checked.
At least twice during this
time the following data were read*
ty
temperature of inlet steam, *C«
ta
temperature of air stream, *C
FT
differential pressure on pitot tube, mm, water
-19-
&W
static pressure at pitot tub®, mm, water
above atmospherie pressure
Bar
barometric pressure, mm* Ig,
This concluded the run.
The Intake damper was adjusted
to give a new velocity and the system was allowed to reach a
new equilibrium and the above observations were repeated. At
each position runs were m&de at at least four and sometimes
six velocities*
At the conclusion of such a series of runs
the steam and blower were turned off and. the .measuring tube
moved to a new location,
Buns were made only on the center
tube* of the 5-tube rows, starting at the ninth row and work­
ing forward through the bank.
The single tub# experiments
were run with the tube five inches la front of bank 4,
Banks
were measured la the order 4, 3, 6,
In certain of the runs in Banks 4 and 6, the total
amount of heat flowing through the tube wall was estimated
from the amount of condensate collected In the condensate
collector during a measured period of time.
In similar fashion the total amount of heat flowing
through the tube wall of a bare bkkelit© tube similar to the
measuring tube was measured.
This was done in order to
determine the effect of the strips and the guard rings on
the overall coefficient of heat transfer.
BUMS WITH STRIPS HEATED ELECTRICALLY
During the course of the Investigation It became apparent
that the sietal foil strips could be
to act as electric
resistance heaters ant accordingly a second series of runs
were made with- the. single tube* bank $ and- certain rows of
bank 6*
With the tube in petitAe© the air velocity was adjusted*
A current of £*$ to &*0 amperes was passed through the
circuit containing the. standard:resistance and the. strips*
and the system was allowed to reach thermal equilibrium*
The current was supplied by three IjS-volt storage batteries
in series#
For these runs the procedure for measuring the
resistance of the tin strips was modified*
The standard
resistance was connected to the E*M.F* posts of the potentio­
meter as before* but in this case the slide wire was adjusted
to a reading of 0*8000 Instead of 0*1000*
The galvanometer
was brought to balance by the battery rheostats in the
potentiometer*
Then each of the strips, in turn, was con­
nected to the E#M*F. posts of the potentiometer and a balance
obtained by moving the slide wire*
The reading on the slide
wire was divided by B to get the resistance of the strip in
terns of the standard resistance*
The resistances were
measured at least twice and the following data were also
taken*
tft
temperature of ail* stream, *C.
ft
differential pressure on pitot tube,
mm* mater
if
static pressure at pitot.tube,
mm* water above atmospheric
pressure
I
current flowing through standard
resistance and strips, amperes
Bar
the barometric pressure, mmg* Eg*
u m
m
m
m
m
m
mmmetMtm &m mumts
A
* A r m of individual resistance thermometer,sq. ft*
&
« Transverse distance between tub© centers is a row,
inches
b
* Perpendicular distance between rows, inches
Bar
» Barometric pressure, gtmu Hg*
da
* transverse distance between tube centers is a row,
tube diameters
dfc
* Perpendicular distance between rows, tube diameters
d$
* Transverse clearance between tubes in a row, inches
0
* Effective rat© of air flow past single tube,
lbs*/hr., s%* ft*
* Bate of flow of air, lbs*/hr*, sq« ft* of minimum
free area of bank
8
* Differential heat on pitot tube, feet of air flowing
h
» hocal air film coefficient of heat transfer,
B.t.u./hr*, $q* ft*, ®F*
haT
* Average sir film coefficient of heat transfer for
whole tube, B*b#u*/hr*, sq* ft*, ®F*
h*
m Coefficient of heat transfer of steam film and
tube, B*t*u./hr., sq. ft*, *F*
1
» Electric current flowing through resistance
thermometers, amperes
sub 1 * Refers
to left side of measuring tube
-S3-
B
* Pitot tube ttftnemeter reading, mb*
Subscript
indict as manometer fluid
P
« Static ..pressure at pitot tuba srhen la rectangular
duct, mm.... Mg above atmospheric pressure
p
:«*Position n « b © ? of resistance thermometer
Ft
* Differential pressure on pitot tube at center of
$ 8/8-imeh duet, mm* H*0
$
1
'.-■* late of heat transfer, 3*t*u*/b:r*
m Thermal resistance of steam film and bakelite
tube, *F*/B*t*u*, hr*
sub r
« Befers to right side of measuring tube
S
» Pitot tube position during traverses, Inches*
Measured from top of duct for vertical traverses
and from right side for horizontal traverses*
if
« Static pressure at pitot tube in 6 5/0-**inch duct,
mm* H jjO above atmospheric pressure
t
* Temperature of resistance thermometer, *C#
ta
* Temperature of air stream, *C.
tav
* Average surface temperature of measuring tube, #C*
t§
« Condensation temperature of steam, 811#F • (99*4#C«)
ty
* Temperature of inlet steam to measuring tube, ®C.
0
* Overall coefficient of heat transfer, B.t.u./hr.
St* ft*
*F*
u
* Point velocity of air stream, ft*/sec*
V
« Average linear velocity of air through 8 5/8-*inch
duet, ft#/[email protected]*
-
W
J%.
24-
* Weight of steam condensed in 45 minutes, grams
** Electrical resistance of resistance thermometers,
ohms
Bun 451 * A run number applied to Bun 1 in Bow j| of
Duct £, stea& heat
tun ASA * A run number applied to run 4
Duct 1, fle.et^ie hiSS
Bow jg, of
-85-
(
PBXBICM, COSSTAM'S
Area of 0 5/8-inch pipe
*
0*2265 ft
Minimum free area of bank » o .3125 ft*
Total surface area of measuring tube « 0*393 ft*
Area of resistance thermometers
Strip Ho*
length (in*)
Area in*
Area ft
X
8*98
Ba$
*0X5$
2
9.06
8*86
*0187
$
9*08
8*26
*0157
4
8*90
8*88
*0154
5
8*08
8*18
.0148
@
6*88
8*88
.0187
7
9*80
8*80
.0160
8
9*18
8*89
.0159
9
9*10
8*89
*0159
10
9*14
8*88
•0158
XX
9*80
8*38
.0101
in
9*38
8*34
*0168
IB
9*80
8*30
•0160
14
9*06
6*86
*0187
Xi
9.04
8*16
.0137
16
8*68
8.80
.015$
-
26-
MBmpfiom
The following assumptions were mads for both the 9steam
heat*1 and the Electric heat® runs* a discussion of their
validity, as well as a general discussion of accuracy and
probable errors will be Included later:
1#
fh© local coefficients of heat transfer are sym­
metrical with respect to the longitudinal vertical center
plane of the bank*
$U
The strips and guard rings and the surface condition
of the measuring tube have no effect on the coefficients of
heat transfer*
o* , There is no appreciable variation in temperature
along the resistance thermometer *
4*
An average coefficient for the whole tube can be
obtained by determining the arithmetrie&l average of the
local coefficients of heat transfer*
$,
The circumferential flow of heat in the tube wall
is negligible*
8*
The transfer of heat by radiation is negligible*
In addition, the following assumptions were made for
the "steam heat® runs:
K 1*
The sum of the thermal resistances of the steam film
inside the tub© and of the tube wall is constant and indepen­
dent of temperature variations*
£«
The steam condense® at a temperature of 211*F*
(99.4*C.)>
The following assumptions were made for the "electric
heat® runss
1*
The standard resistance has a resistance of exact­
ly 0*1000 ohms#
t*
Only the actual area of the strips between contacts
Is available for heat transfer#.
-87 a-
cM,iMAfios
of beeisxauce
rammmmm
Single fufee
*C*
hanks 4, 6
25*3
.60*0
Starip Mo»
Ohms
1
*5215
8
12
hank 0
MmSL _Jflal.
81*0
Ohms
Ohm
Ohm®
Ohms
Ohms
*37
m
*3015
*3218
♦5610
♦4040
♦siis
*3785
*5878
*3200
•3590
♦4020
1
*8885
*3375
♦3510
*2681
,3240
•3830
' 4
•8907
*3507
*3653
•2983
•3330
♦3752
5
♦3040
*3555
*3098
•3022
•5392
•3300
8
•8000
•3403
•3635
•8968
*5330
*3730
7
•8078
*3473
*5815
#2858
•3320
♦5720
8
•SOSO
*3563
.3705
*5090
♦3475
•5090
f
•3145
*3677
•3818
♦3190
•3562
♦4010
10
.3130
#5665
*3805
*3135
♦5520
•3940
11
•3848
*3003
*5955
*5875
♦3675
.4118
18
•3108
#3740
*5688
♦5175
♦3365
•3990
IS
*8677
*3378
*3510
♦8870
•5220
•3605
14
*3118
*5740
♦5885
•5810
•3002
♦4032
IS
tSSS?
#3038
*4090
♦5340
•3745
•4195
16
*3305
♦3070
*4135
•5583
*5795
•4250
-26PXTOT 10 BE T U V m & W
VERTICAL TRAVERSES IH 6 5/ 8 -ISCH PrPS
Bar 760
1
0.17
0,65
0.95
1*4©
8*21
4*8©
1*00
8*81
5.93
©*st
3.28
0*1?
©*8i
0*96
1*46
2* SI
1.11
8*§©
6*01
5.95
6.29
3*83
5*93
6.29
3*25
Bar 733
E
fH*0
U
§0*6
157*0
100*6
§0*0
185*0
109*3
63*0
181*0
111*0
201*0
68*5
115*8
75*0
280*0
119.1
75*5
881*3
119.5
©6*5 = 204*0
104*8
110.6
©4*3
169*4
©0*8
107.1
177*8
§3*0
155.7
.100.X
average 10©*©
E3B.G
70*0
122.3
.
Bar 738
i- §3*5
§5*0
103*0
81*5
40*5
119*2
87.7
42*0
89.2
m*e
44*5
131*0
91.9
145.6
49*5
96*9
49.5
143*6
96*9
' 44.5
91.9
131*0
41*3
122*1
86*8
88.5
83*5
113.2
70.4
§3*5 .. §8*3
average 89*0
153.0
99*4
38.0
Bar 733
0.17
0*33
8*93
1.4©
2*81
4*2©
5*80
5*51
t& §3.5
*a 34*5
42*8
31*6
34.8
59*0
©7.8
©7.8
60.5
56.0
80.18
44*25
average $9. 6
24*0
70*8
14*3
17.5
18.5
28*0
83*0
23*0
20.5
19*0
17*0
18*0
52.5
57*7
59*3
©1.6
66*1
131*0
91*9
88*4
150.0
157.4
100*9
166.1
103*6
181*0
108*1
188*4
108*3
166*1
103*6
99*3
154*5
96.9
143*6
123*0
89*7
average 10C>*1
©4*5
189.7
110*6
Bar 733
34
73*8
23.0
©8.8
29*3
74*8
86*9
30*3
89*8
78*0
35.0
97*2
79.1
§7*0
83*9
100.0
56.5
107*5
83*2
§3.5
08.8
79.7
76.0
89*0
30*5
28*3
85*9
73.5
24.0
©7.8
70.8
average 76. §
36.2
§9*0
114*0
Bar 733
©7*5
12*0
86.8
M
44*5
51*0
55*5
56*6
©1*5
62.0
80# 5
52*5
48*3
42*5
33*4
66.1
M
%«0
7.8
8*3
9*0
10*0
11*0
11*0
10.0
9*0
@*0
7.5
62.4
©0*1
ta §3.5
tft §8.0
22.3
37.9
25.25
40.3
96.7
41*5
#*7
29*7
45.9
82*7
45.9
82.7
48.7
29.7
41.5
86*7
59.1
83*75
57.9
22*3
average 41,►7
47.9
§5*65
fioftxxma f M T O B s u
*U 36*5
Bar 742
8
0.17
0.5S
0.94
1.45
8.19
4.88
4.97
5.48
5.90
6.85
8.81
%*0
192*0
3X7.0
336.0
544.5
347.5
m % *5
206*5
193*3
177.2
136.2
average 1X5.6
566*0
36.3
Bar 742
0.17
0*98
0.94
1.45
8.19
4.88
4.97
5*46
9.90
6.85
8.81
188.2
140.0
148.8
157.0
168*0
147.8
137.0
188*1
119.3
91.3
average 93.2
134*6
52.5
Bar 742
0.17
0.58
0.94
1.45
2.19
4*22
4.3?
5.46
$.30
6.25
3*21
61.7
70.5
77.9
00.0
@3.3
78.0
@4.7
58.8
53.3
42.6
average 65*6
79.4
87*0
il.o
84.0
30.3
87*5
£3.5
<4.3
22.0
20.0
19.0
14*3
®M*0
1X1.3
118*3
123*3
185.5
186*3
119.0
115*4
111.7
106.9
93.8
@4,0
60.5
@5.0
@0,0
88.S
64,5
60,5
66.0
5S*i
40,3
183*3
t* 37*5
41*3
47*5
50.5
53*3
33*0
56*0
46.5
4045
40*3
31.0
Bar 748
u
1
65.5
74.0
80.5
53.5
54*3
76.0
70*5
86.0
60.5
46.5
5/a-iaCH FIFE
88.8
95.0
98.0
100.9
ioa*s
97.4
94.0
90*9
87.7
70*7
99.9
37.0
@3*1
@7*4
70.8
78.1
73.5
60,1
64.5
01.5
@0,0
51.6
71.5
*u 37.0
H
u
153.0
173.0
191*0
300.0
801.5
169.6
173.0
164,7
134,5
119*1
avai•age 105*3
193,3
68.5
118.5
Bar 748
37.3
H
89. 8
100.1
110*5
114.9
116*3
104.6
07*2
@9.8
S3* 9
@4.8
average 78*9
113.4
36.3
50.3
34.0
37.5
59,0
39.3
53.3
33.0
50.3
83.5
22.0
Bar 742
76,0
80*3
84*5
@6,1
86*6
82*1
79,1
76.0
73.5
64.6
85*5
t* 57.0
32,4
36.8
39.75
42.7
44,2
36.3
33*9
50.9
23.0
23.6
average 47.2
41.2
14,0
11.0
12.5
13*5
14*5
15*0
12.5
11.5
10.5
9,5
8.0
101*2
107*8
111.0
113,6
114.0
110,5
107,8
103,1
99.8
07.6
45,7
48.7
50*6
52.5
53.3
48.7
46.7
44.6
42.5
39.0
51.5
-250TRAVEBBES IH RECTAHGUUR DUCT
20 INCHES UPSTREAM PROM SINGUS TUBE
horizobtax.
749
34
4
Bar
t©
P
BP
ft
?
22
85
115
Bar
te
P
73©
35
2
B
»H*0
H
u
Bb 90
1
4*09
4*43
4*9®
3*57
5.90
0*00
5*7S
11*35
12.8
14* B
16. S
17*1
17*4
10.0
13*3
13*6
ia *o
0*40
27.0
28.7
30*2
32.2
33*2
33.4
32.6
31.2
29*6
27.8
23*2
1*92
2.16
2*41
2*73
2*23
2* 90
2*70
2.43
2.17
1 .9 3
1.32
t
5
4
5
0
7
3
9
10
U
4*70
4*15
9*90
1
2
$
4
§
6
7
a
i
10
n
n
749
35*5
0
Bar
ta
P*
*33
*40
*40
*43
*43
*43
*43
•40
*34
*30
*34
bp
V
pt
BP
V
H
5*65
0*86
7*10
8*05
8*04
8*55
7*93
7.82
6.40
5*69
3*32
6
4
20
7.87
8.68
8.99
9*20
9.50
9*50
8.99
0.68
7.99
7.51
0*71
*901
1*105
1*059
1*311
1*400
1*400
1*252
1*105
*99
*375
.700
TOHTICAL
la
Bar
ir
.
n
BP
75®
758
34
6
a
0*95
1
2
5
4
5
6
»H*0
2.37
3.68
4*35
4*80
5.1 8
5.48
5.6 4
V
H
6 . 04
10.70
18.65
14.02
15.00
10*00
16.45
80
88
118.5
u
81.1
26.8
28.5
80.0
31.0
32.0
32.4
41
1©
80
u
13.02
20*2
21.4
82.8
83*6
23*4
82*6
81.0
80.2
19*1
13*8
-21-
VBRTICAL (Cont.)
lg#0
5*51
8.34
5*08
4#50
3»9^
8*48
6
7
B
0
10
IX
11.95
H
16*10
15*58
14*88
13*15
10*45
7*07
u
31.6
30.7
29.0
2.89
21.8
TMVmSV AT G&sm OF BOW 6 OF
Bat 741
If m
Bar 741
7EBTICAX,
P
35*8
*4*5'
8
^ c c i 4-h *o
*08
.8
32
41
43
45
45
43
46
43
45
43
43
45
45
48
1*0
2.0
3.0
4.0
5*0
e.o
7.0
8.8
9*0
10,0
11*0
11.3
11*95
m
10
7 115*5
ta
P
H
*CC1«-H*G
u
35.0 59*4
70.4 67.8
77.3 71*0
77*5 71.0
77.8 71.0
77.8 71*0
79*0 71.8
77.3 71*0
77.8 71.0
77*3 71.0
77*8 71*0
77.3 71.0
77*8 71*0
78.1 68.0
63.0 66.3
34.7
•*•{)•2
9.0
12*0
18.3
12.3
13*0
15.0
13.0
15.0
13*0
13.0
18*0
12*0
12.0
10.0
18.0
BMS
PT
B
P
7
H
6
87
7
63*6
u
15*55 51.0
36*5
21*6 37.2
37*8
81.6
22*4 38.8
82*4 38*2
22*4 38*2
28*4 38.2
88.4 38.3
38.2
22*4
80*75
30*75
80*75
80.73
20.75
36*5
36.3
36.5
56*3
17*29 55.5
38
BATE OF AIK FhOW
SJXttJI Cj&CUMTIQB
Bun 411
Observed data
Bar
»
746
t&
*
m
PT *
bp
64
«
m
The total prosaura at the pitot tuba
* 74B 4 'jf^g
*
^
The density of air at standard
conditions is
V
0*0608 lbs*/cu.ft#
(Perry1*)
The density of air at the pitot tub© is
0,0808 * %ffg* * STZ +'IS
“
°*009® lb«,/ea, ft.
The differential head on the pitot in feet head of
f l a w flowing i*
* lk x foefs
“
847 ft*
The average linear velocity through the 6 6/8-inch pipe
as read from the graph on Figure 4 is 115*0 ft./sec.
the weight rate of flow of air through the minimum free
area of the bank is
%m x m
*
115*0 x 0.0695 X 3600 X
f
SO,800 lbs./hr*, sq* ft*
nomat 4
PIfOT TOBK CAXJBBATXOll (fUAPH
fop P ito t tube a t center of 6 5/8~ineh pip©
A
Average velocity from horizontal traverso
0
Average velocity from vertical traverse
Solid graph is averaged graph
150
140
130
120
AVER AG E
VELOCITY
F T ./S E C .
NO
IOO
90
80
70
60
50
40
30
20
O
20
4 0
60
FEET
80
IOO 120
HEAD,
140
FLU ID
160 180 2 0 0 2 2 0 2 4 0
F L O W IN G
FIGUBE S
GAU8MCX0H G M B H
Conversion of average linear velocity in
Bound Pipe to effective veioelty past single
tube
L B S / H R . , SQ. F T.
7000
6000
5000
FOR
3000
2000
VELOCITY
SINGLE
TUBE
4000
OOO
O
50
AVER AG E
60
70
80
V E L O C IT Y IN ROUND
F T /S E C
90
IOO
DUC I
IIO
I2C
-88-
8ingle Tub©
The average linear ©r rate of flow through the @ 3/8inch pipe was estimated la the same way a© Indicated above.
The effective velocity past the tube was then read from the
graph on figure 5,
m m m t besistahce of w m
Am m n m
wiim
Method X
Bun Mo*
*av *6
451
458
458
454
455
451
4m
455
454
458
411
418
415
414
45*8
48*6
47*9
50*5
58*9
46*1
47*3
48*6
51.0
58*9
48,0
49.2
50.8
55*8
tav *F
118*5
116,0
118*3
195*0
188*8
115*1
117.3
119,6
124.0
189*8
1X8*5
180*7
183*3
131*6
bs*»t&v# °f
97*5
93*0
98*7
88.0
78*7
95,9
83.7
91,4
87.0
61.3
98.5
90.5
87*7
79.4
W
%
98,7
93.1
83.Q
@2*4
66.7
97*8
94*5
@9*3
63,7
76*1
92.0
92*0
$9*0
77*6
882
266
233
256
191
278
870
830
240
819
262
262
254
222
I
*346
•358
.366
*574
*881
,845
*847
*337
.564
.375
<3tK1
•Q&0
*544
*544
*359
Sample computation
Bun Mo* 451
Bun Ho, 451 » Duct 4, Mow 5, Bun 1 with tube in this
position*
t&v *C * average surface temperature of the tube, the
arithmetic average of the temperature indicated by the 16
resistance thermometers degree Centigrade (for data see
page 44)*
*F, tav *G converted to degrees Fahrenheit
(45*2 X 9/5) + 82 * 11$*$
v #* ** the temperature gradient through the steam
Film and tube wail* degrees Fahrenheit,
£11-113#5 * 87*5
w
n the weight of steam condensate collected during
43 minutes, grams
4
* heat transferred, B.t.u./fer#
98*7 rn 4/3 X 3§5 x 97© *£
1
•
882
* thermal resistance of steam film and tub®, re-**
ciproeal 3*t.u#/hr., *F
97.5/282
*
0,346
Method 11
Bun Bo#
631
Bit
633
@34
t . T *c
t s- t av
ta *©
t* ~ ta *C
0
a
41.8
44# 6
48.6
$4*3
58*1
$4*8
$0*6
44*9
33*0
$5.7
06*4
©5*7
64.6
62.5
5.68
$.35
4.92
4.30
•598
•596
,405
•405
$4*8
$6.9
©ample Computation
Bun @31
tun to# 831 »
Boot 6, Bow S, Bun 1 with tube in this
position#
tav *C » Average surface temperature of the tube, the
arithmetic average of the temperatures indicated by the 16
resistance thermometers, degrees Centigrade * 41,$*C#
-35-
(For data see page
%
~ \v
59 )*
* the temperature gradient through the
steam film and tube wall, degree* Centigrade
99.4-41,5 » 58.1
ta * air stream temperature degree* Centigrade
tg - tj *C » overall temperature gradient
99.4
0
*
- 55.0 « 08,4 degree* Centigrade
Overall coefficient of heat transfer « 5.68 B.t,u,/hr,
•F, ft*, determined from data in neat section
bale*! page
H
«
36 ,
Tnernal resistance of steam film and tube,
reciprocal
P I
B.t.u./hr., *F
@6,4
jg m m I m
.393
SS
0 .39JSi
the arithmetic value of B of 14 determination* by
Method 1 and 4 determinations by Method IX 1* .0*808 reciprocal
B,t.u./hr., •?.
Thl» gives * value of
B*t.u,/hr*, *F, ft* outside surface area.
used for *11 *steam heat* runs.
» 0.1448 reciprocal
This value was
Overall Coefficient#
Measuring Tube
Bun Mo,
ft
MW
Bar
655
656
657
SO
55
%M
10
7
5
742
742
742
555 .
56
27.8
Sgu
f
20,600
14,680
7,560
80.0
04*2
76*7
0
5*67
5.58
4*90
Bare B & k*U te Tube
Bun I:Q«
058
659
6510
6511
FT
m
Bar
*a
aaaac
79
88
10
8
7
5
789
759
759
789
84*0
85.8
86,5
80*0
20,500
10,900
10,700
0,000
m
10
1
92,4
84,9
76.4
69*5
0
5,66
5.56
5*11
4*54
Sample Computation
Bun no. 655
Bun Ho* 655 ® Buot 6, Bow 5, Run 5 with tube In this
position*
ft m differential pressure on pltot tube at center
of 6 5/6-inch pipe, tm *ia0
SF m static pressure at pltot tube, mm *1*0
above atmospheric pressure
Bar » Barometric pressure, mm Mg
®ta* m ^«lfht rate of flow of air
Xbs./hr./ft*
minimum cross section of duct*
For method of computation see page
W
m
The weight of steam condensate collected during
45 minutes*
0
«
32 «
Overall coefficient of heat transfer
B*t.u*/hr*,ft®, *F,
-37-
* 88 * I *
* 9TO*2 * 3
?*
For these seven runs 0 was plotted as a function of
Qgiax*
points for both the measuring tube and the bare
balselite tube fall on the same curve (±$i) . For the
computation of the thermal resistance of the steam film
and tube by Method IX in the previous section above,
values of 0 were read from this graph, on Figure 6,
LOCAL HEAT TRANSFER COEFFICIENTS
STEAM HEAT
SAMPLE CALC0LAT10M
Run 401
f
p * 1
» see above, page
33
* A r «* measured resistance of strip, 013805; ohms
tj* * temperature of strip read from calibration graph of
Strip, 4®*8®C*
*^1 * measured resistance of strip, .3686 ohms
tx
* temperature of strip, read from calibration graph of
strip, 46*7
t
* arithmetic average of tT and tx
(46*8 * 46.7)/ « 46»8*C#
h
«
air film coefficient of heat transfer
B*t.u./hr., sq.ft., *F.
hw
* ■- .X
.1M #
t-li
28*4=ISjtS
46.8 - 32
a 24.8
haY « average air film coefficient of heat transfer,
B*t*tu/hr*# sq.ft.,
The arithmetic average of
the 8 local coefficients » 17.8
h/hav * The ratio of local to average air film coefficient
84.6/17.8 « 1.488
-39
LOCAL HEAT TRANSFER CQEFFICISHTS
STEAM HEAT
M m 401
6
T.
Bar
82
742
*
JH*.
V
1
2
&
4
5
6
7
8
.8808
.8492
#8178
.3262
.5438
*8882
.8808
.8886
46.8
48.8
49.8
54.1
86.7
54. 5
52.3
51*9
.
PT as
'
BP
t
n *
.8698
.3012
*3000
.mm
•3483
•3475
S2
t
%
46*8
40*7
47#1
47*0
49*3
48*0
54*0
33. S
85*5
50.1
54*6
54.6
38*4
38*4
50*7
51.8
average
h
Vfcgv
84*8
22.8
19.6
14*3
12.4
13.7
15.9
17.2
17.5
1*405
1*285
1.120
*816
.709
.782
•209
.984
G
&ua 40f
Pi
6P
2a
88#5
Bar 740
♦3532
.3520
•8808
*3332
•8480
•8800
•8888
•3418
48*9
80.6
88.0
56.4
60*0
57.7
54.7
84.1
•8785
#8698
*8£p
.8250
.8648
.3690
.3818
*8806
48.6
49*3
51.1
56*1
88*7
57.5
54.9
83.1
40*8
49.6
81.6
36.8
59.3
87*0
84*8
58.0
average
M m 408
t1
''
i&
Bar
PT
IP
88
742
i
A *
%
jfi
1
2
3
4
3
6
7
6
.8580
.5888
•3222
•3418
*3510
*3425
•5363
•3440
50.1
®ut
33*4
58.£
02*3
00 #8
86.0
86.0
*8740
.8712
.5500
*8270
.3678
.8728
*3843
.3880
H
42*0
50.5
52.6
57*7
61.1
60.0
87*0
34.9
5880
60
80
%
f
X
X
s
4
s
§
7
8
7830
h
h/h&v
'22*9
21*4
18.E
13.8
10.6
12.0
14.5
15.8
10.1
1*42
1*327
1*129
.319
.070
.744
.899
.980
9
40.6
IS
4900
t
h
b /b if
49.8
51.7
83.0
58.0
61.7
60.8
86.9
5S.S
average
80.4
17.7
16.0
11.2
9.10
9.96
12.8
13.5
14.0
1.486
1.28
1.140
.799
.649
.710
.877
.962
^*40**
0
Bun 404
84
748
PT
BP
t
ti
t
p
53.9
66.0
.8798
.8766
53,5
54*3
84£6 &
©8*1
©6*7
#B*0
©5*2
80*5
3420
17
9
&
53*?
55. B
5 ? .l
82 .3
8?.3
©?*©
63*2
©1*2
average
16*1
14*4
13.2
9.05
6*7©
8.8Q
0*80
9*85
^3©
1*518
1.350
1.841
.851
.630
•640
♦810
.926
0
Bu& 405
fa
Bar
P
*ftr
1
$
3
4
§
6
7
8
.3863
*3660
*3336
#55116
*3645
*3590
*3535
Eiaa 4X1
P
A r
1
8
$
,8485
.8468
.8188
4
5
©
7
8
*6585
•m o
•684?
*5880
35*5
74$
t
^1
6 8 .7
6 9 .8
6 8 .9
8 7 ,7
7 8 .9
7 8 .6
7 0 .6
68*9
' orA*t JK
*eo©&
*3040
*3650
*3365
.3325
.5900
.3722
*3700
5 0 .5
3 9 .4
©1*9
©7.8
72.2
7 3 .3
70*3
67*7
45.3
46*8
40*5
4 0 .6
58*0
31*1
47.5
46*7
30*5
39*4
62*4
©7.5
72*6
7.3*4
70*4
66*3
average
Pf
BP
32
746
%r
©
4
n
$P
A i
.3675
6S©®0
*5465
*5180
*$586
•568$
•5458
*8428
H
4 5 .1
4 8 .9
45 .5
4 6 .8
50 .9
68.9
8 0 .1
4 7 .1
04
40
»
45.8
46.7
4 6 .0
47*4
5 1 .9
88 .0
4 8 .8
46.9
average
h
12.30
11*60
9*90
6.90
5.00
4*75
5*73
0.35
7.84
fc/&aV
1.670
1.400
1*861
•660
.638
•606
•754
.855
OfflUC 60,800
h
26.6
87*8
86*4
$3*4
16*3
16*4
90 .0
84*4
88*9
h/fe*y
1*841
1*165
1*150
1*080
*719
.714
*906
1*008
-4l«*
t
n
m
< W
X M »
740
P
r
X
*
X*!
4©a
46*3
>*4
$
xaa?
x.
X«i
65 4
7
3
51*7
48.8
mm
47.8
0
f *.8&1
Bar 74#
f
-O. #'
-^x
X
8
*
4
5
#
7
-.6
49*2
41
8# ' '
ft
SP
3708
m m
$490
6X68
8678
607#
$608
$4#8
t
*1
47*1
47a
47*8
40*1
68*0
56.6
5$*$
48*7
47*1
47.6
47*9
49.6
66*0
6#*$
82.8
49*5
average
mm
*r
50.0
52.0
59.8
55.9
61*6
61*9
55*9
53.6
-“-I
•876©
*8720
.5540
.3202
*$#8$
.3745
,3502
•$506
h/hgv
h
X.808
X
1.X90
1.042
.7X8
•660
.661
1*049
$6*8
$8* 4
01.8
10.1
18.1
18,1
15.8
10 *2
16.8
Owury
PS
8P
52
74#
14,650
8*740
IS
IS
%X
t
30.7
51.0
31.8
58.5
58.0
81.5
50.8
54*6
90.a
51.6
51.6
58.8
50.8
81,7
57.8
54.0
avenge
h
17*9
17.0
X6.6
14.5
9.66
8.7#
11.1
14.3
15.7
h/h|t
1.802
1*289
1*210
1,05#
.719
.680
,809
1.041
~4E~
0:max
Pf
SP
40
_a
f
4
5
6
7
48*0
44*$
48*1
48*1
48*8
48*8
48*0
47*7
6
8
a
a
a
6
a
a
45
46
47
;«
$ m 482
n
8P
*1
44*4
45*0
46*8
47*8
47*8
47.8
49*1'
88*9
eg
88
t
44*5
45*6
46.6
47*4
48*0
47*8
48*9
49*0
average
58*1
45*5
88*7
86*4
34*4
89.e
SO.8
SO. 8
a?.7
&WMX
h
44*6
41*0
88*0
83*1
31.0
31*6
28.2
28.0
84.4
18,100
&/&av
1*80
1*19
1.102
•961
•900
.919
*820
.814
**48—
Em 4 m
fa
Bar
p
1
f
3
4
3
3
7
3
m
**
*3485
*i**'
♦M«0
<&SOO
♦MM
♦MS*
4* jfr-
45*5
47*5
43*8
49*1
*S86B:
*:0EWf^f'm
*r
.3070
Pf
if
$6*$
50*0
43*5
53*1
50*3
^ 1
*0373
*w5w
*8430
*5153
*5550
*5530
*8430
.8470
h
t
45*1
43*1
47.3
43*5
49.5
43*4
45.2
43*3
47.3
43*3
43*3
43*4
50*4
50*4
50*8
§0*«
f&
Bar
*8503
*5508
*5133
*5553
.5593
•p
-ira™aw
*5533
*5515
*5405
m
47*9
4 3 .5
80*5
81*7
58*0
83*5
53*9
55*1
*5693
*5878
*8513
*5133
*5060
*8320
.5490
*3803
48.7
47. i
49*4
00*9
53*5
83*8
53*5
83*3
Itm 48$
ffl
Bar
1
3
3
4
5
6
7
3
*8532
*5882
*5213
*3870
*8440
.8370
* in »
*5443
avaraga
Gmax
h
53.3
80.4
01*7
83.0
35*3
35*0
33*3
33.3
33*3
14,500
h/h
w ®aa
1*84
1*33
1*10
*990
«*j
#wft
*338*790
.730
10,050
M m 454
1
3
5
4
5
0
7
3
43
t$
m
if
1#
40*3
43*0
49*3
51*3
53*3
$2.4
Bi*l
03*3
averaga
Ft
if
B7
741
48*9
51*5
58*0
54*8
38*8
03*3
56.2
00*1
n
*3722
*370$
•3550
*5230
.3610
.5370
*8040
•8540
48*4
$0*0
51*3
55*6
56.3
50*0
00*0
30*0
07
10
48*0
50*8
53.4
54*1
00*0
55.9
00 *4
55.3
avaraga
87*2
50.4
23.8
23*4
20*4
§1*2
19*9
$0*3
24*9
9ipay
30*4
84*4
21*3
13*4
15*5
15*9
15*4
13*1
19*7
1*40
1*22
1.063
•040
*320
*550
•500
*318
3,300
1*84
1.230
1*074
*030
*785
*305
.750
*318
~44~
80; 550
n
f»
it
44.0
44*4
4
4
i
7
3
81
39
46.5
#3473
46.7
46.3
E m 433
3463
3
7
43*4
48*3
46.7
44.4
45.5
46.8
43.3
47*6
46*6
€iver&ge
ft
if
740
46*7
m* |
48*3
46.4
44.4
46*3
46.0
46a
47*4
46*4
43*3
44*7
43*7
47.6
47.7
47*3
43*9
47*9
60
36
46*4
44*3
43.3
47*0
47.3
47*4
46*5
40,1
average
39*0
47#0
43*7
37*3
©4*4
m a
31*0
63.0
40*1
1.470
1.170
1*933
.989
.399
.783
*381
Gratax 17,730
38*3
48*0
37.4
63.0
89.9
61.6
88*8
89.4
35.6
1.470
1.809
1.050
.986
•940
.399
.791
.885
-45
Bun 455
t*
8**
41
50
55
745
S>
^
1
n
44*5
5
4
45*7
40*5
1
5
4
(m
U
%
h
44*4
45.7
46 #8
40* i
45*5
45*5
50 .1
45*0
44*5
45*6
46*6
48.0
48*5
46*5
48*0
40 .4
average
46*6
07*5
55*6
68*1
66*1
.ft*
84*7
85 .6
U,*40
!•*
l* i
l.<
•<
*554
I'
i a n 10,500
ft
m
1
5
5
4
5
4
7
46 .5
46*0
45*1
50 .6
68*7
58.0
66.7
S lil
.6005
*5675
.6616
*5150
.6660
.5600
.6495
•6455
46.5
47.8
40.8
61.1
58.5
51.5
68 .1
68.8
46*4
48*0
40*0
6 0 .0
5 8 .6
58.8
08.0
0 8 .4
average
ft
8f>
45.5
50.1
51.8
55.9
66 .1
56.0
56 .4
55.1
01
it
11
10
48.0
50.5
51.7
50.6
56.8
05.8
66*1
56*4
average
50*1
58.4
86.6
84*4
80.8
81.0
80.5
81 .0
86*0
1
1
1
615
*31431 i |* P r
60.6
87.7
24 .8
20.4
17.5
17.0
16.6
17.0
81.6
1.540
1.870
1*110
.955
.794
•760
•760
*604
H
t
h
h/h*v
8S.7
«*»*
56.6
53.8
38,3
38,8
68,6
30.8
58.8
53.0
53.3
53.0
88.3
68.8
68.3
61.1
average
m s
1*63
1.51
u s
u s
uim
- ft ■ m
HP 40
m s
m s
s®*a
40.9
40*9
41*1
48*4
41*1
m s
m s
ST.i
50*9
40*6
43*1
42.5
42.6
43*9
43.6
n a
18*6
00
03
37*?
33*3
40*0
41*7
43*6
43.0
43.4
43*0
average
*048
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•708
.788
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00 *4
50 *0
80*1
40*4
41*0
40*6
41.9
41*3
average
FT
EP
n.s
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m
m
m
m
s
s
s
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33*3
04*0
41*3
1*46
1*31 1*000
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35*0
40.3
36*4
34*3
31*3
83*3
33*6
80*8
37.1
1*403
1*810
1*084
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m
n
m
m
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40*0
41*5
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43*i
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44*5
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average
50*5
41*1
55*6
31.0
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69*6
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83.8
41.0
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42,9
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46*6
48,4
51*1
55.3
54.0
54.1
52.4
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44*5
46*6
40.6
50.5
55,4
53*6
53.9
52.6
average
50*4
£5*1
£2*0
16*5
14.9
14.5
14# 4
15.7
19,4
1,566
1*291
1.152
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30,9
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33,3
56*5
38*1
40*9
41*1
42*7
41*5
40*4
41*0
m* 7
42.2
41*0
average
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05*8
58*4
45* 4
59*3
30*8
36,0
58*6
34,6
48*9
h/h*T
1*488
1*88
1*038
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17,800
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4 8 .9
4 1 .8
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.8070
.8488
.3489
.8878
.3370
57*8
59*8
40,4
48*0
48*4
48*5
44*1
48*7
m
m
57*7
89*4
40*4
41.0
48*5
48*5
45*8
48*7
average
58*3
43*1
40*0
33*8
38*0
33*0
88*4
31*4
87*7
1*500
1*198
1*000
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88*5
89*9
41*1
45*0
45*5
43.6
45*5
43*9
48
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88*4
40,0
41*8
48*0
45*7
45*5
44*6
43*9
average
33*5
43*8
37*7
58*3
89*3
30*4
87*0
88*8
39*3
1*51
1*88
1*089
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41*0
44*0
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40*9
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average
1*10
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2
3
4
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40*0
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61*1
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43*0
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40*7
47*0
40*1
49.9
64*6
64*6
60*6
40# 4
10
00
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40*9
47*4
46*0
49*0
06*3
64*6
61*1
60*4
average
08.4
09*6
85.0
21*0
17*8
17*6
16*9
16*0
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1.275
1*10
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87.8
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85.0
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1.19
1.15
1.08
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58.7
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60.7
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12*1
10.6
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16*0
17*1
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54.4
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56.0
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60*8
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.5653
.8656
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,•2486
.2655
*8643
,5605
.5362
49*0
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81.4
82*8
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60*8
88*3
84*2
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FT 13
55.9
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88.1
33.1
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88.4
81.8
64.3
63*8
60.0
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57*8
58.7
59.8
81.0
87.4
70*6
87.0
64*2
average
18*6
18*8
18*1
14.9
9*60
6.90
10*2
12.3
18.3
1.#
1.36
1.21
1.12
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15.0
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11*1
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40*9
54*4
55*0
89*3
87*4
86*6
85*0
1*46
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1.04
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45*7
47*6
43*4
49*0
50*0
50.7
86*3
average
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46*8
49*8
50*9
67*1
5553
46.7
43*8
5 1 .3
88.7
54*6
86*8
55*4
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40.7
43.3
51*1
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84*7
54.9
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m
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48,0
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52.6
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86.4
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19.6
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84.4
1.45
1,86
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84*8
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48,7
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50-1
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88*1
45-6
46-4
47,8
56*6
54*0
46*4
51*1
49*6
50*4
49*4
86*0
50*6
88*8
68*1
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1.49
1.86
1.05
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*670
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43*0
43*3
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47*1
48*3
50.4
51*9
§3*8
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19*4
26*4
34*3
39*0
34*4
31*4
18.8
16.5
17*8
15*3
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1*09
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52*7
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60*0
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86*4
81*6
13*1
18.7
13*6
13*3
13.8
11*5
16*8
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1.88
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43,8
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47,0
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49,5
49,6
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48,6
35,6
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82,7
83,6
30,8
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45,6
47,6
48,0
30,7
50,3
52.1
53-0
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38,8
28.5
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57*1
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56*4
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56*5
51.7
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47*8
40*4
43*6
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25.9
21*0
18*1
16*8
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16*4
15*8
19*5
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1*09
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65.8
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56.6
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39*7
40.0
41*1
46*6
41*6
45*6
41*9
38*8
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42*0
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6*77
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14*9
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41*4
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47.8
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37*6
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49.6
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41*7
38*4
39.3
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43,0
48,0
44,1
48,4
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78*1
80.1
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44,6
39,0
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43,0
50,2
1,553
1,52
1.190
,690
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48*5
43*0
45,7
47*0
40*4
47,7
45*1
34
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40*8
48*0
42.8
45*1
46*8
46,3
47,0
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57*8
47,8
43,1
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87,8
88,6
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1*30
1.172
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45,7
46,4
40*6
31,9
51*0
51*9
49.3
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43.8
45,8
46*8
48*8
31*4
51.3
08,0
50.1
average
42.7
36,2
32*4
85,1
20.1
20.2
19.1
2l,0
27.2
1,570
1.530
1,190
,920
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48.S
48*8
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88*4
87*0
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66*8
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.8488
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.8778
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*8888
.8888
*8690
*8790
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.8648
48*0
50*6
61*6
55*5
59*3
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50*1
55*0
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48*0
60*1
61*3
64*4
88*8
58.6
68*4
15*9
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102 871
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1
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9
4
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8
7
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*5440
*5455
*5110
.5237
*5250
*5150
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52*5
709
00*0
58*7
59*6
41*0
42*9
42*8
45*6
42*4
.5620
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*8118
*8462
•8560
.3428
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80*5
58*6
59*6
41*0
42*8
42*0
43*8
41*2
80*5
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83*6
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41*6
42*3
42*2
48*6
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8
4
3
6
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48*7
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46*9
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•3622
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*3160
*3520
*3613
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40.9
41.5
42*7
43*2
46*9
43*9
47.8
44.6
31
66
40*3
41*5
42.7
45*0
46.9
46*3
37*4
45.4
average
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20*9
23.2
17*8
16*4
13*1
15*2
15.9
19*1
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1*555
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69.0
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44.6
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59.1
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43.6
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45.8
48.4
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XfOCAtf COEFFICCTTS OF HEAT XfUBAFEft
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Run 40A
I
8»ax
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tr
p * 1
* measured current flawing through strips, 8*74asps.
**
above, page
52
* measured reelstance of strip, *3508 ohms
<*temperature of strip read from calibration graph of
strip, 47*0#C*
hr
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s
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the arithmetic average
*
18#0
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*
85.8/18.0
v
1.40
-64-
LOCAL COEFFTCIE8TS OF BEAT TMNSFEB
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50.9
58.4
58.1
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88*7
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15*1
14.3
13*4
16.4
18*2
average
85*3
21*4
18.1
15*6
14.0
15*8
16*7
17*3
18*0
1*40
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49.6
80.8
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55.6
59*6
59.3
56.2
55*7
23.6
21.8
18.9
13.8
12.7
13.5
14.7
16.6
average
23.8
20.5
17.6
13.7
12.4
13.4
15.0
16.2
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64.8
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16.4
15.9
11.6
10.8
11.8
12.4
18,8
average
1.48
1.26
1.06
.625
.748
.605
.900
.976
35
786
41
16
20.2
17.6
15.0
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10.7
11.6
12.6
15.3
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1.48
1.86
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6
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68*3
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average
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20*5
18*2
16.8
13*1
12*1
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16*8
1*36
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58.8
60,0
61* 3
71.1
74,7
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64*3
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15.6
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10.1
8*05
7*56
8.36
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14, 5
13.1
11.6
10.6
8*57
7*60
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1,59
1.26
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44*9
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46.5
48.7
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24.0
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31.5
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59*8
52.0
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1.80
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22.4
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17.9
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13*9
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47*9
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98*0
53*3
35*6
53.7
91.4
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18.4
17.1
15.9
19*7
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average
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17.0
16.8
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58*8
68*0
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48*5
45*9
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58*4
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51*6
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87*0
85*0
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50.6
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80*0
85*4
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ASP CAtCUMTlOIS
sxiccmxoi
STEAM HEAT
As outlined previously (page 26) certain inherent
assumptions were necessary la the computations of experimental
results*
Errors in measurement of variable magnitude were
also unavoidably present.
The importance and effect of these
errors and assumptions are discussed below.
When heat flows by steady conduction through a series
of resistances, th© overall resistance is equal to the » m
of the individual resistances and the overall temperature
gradient is equal to the sum of the Individual temperature
gradients*
Furthermore, the individual resistances bear to
each other and to th® total resistance th© same ratio as the
corresponding temperature gradients*
Coefficients, however,
are inversely related to the temperature gradients.
The
calculation® for the 9steam heat*1 runs are based on this
fact*
In these experiments the flow of heat was through three
individual resistances - a steam film, a tube wall and an
air film outside the tube#
The air film resistance was
calculated from measured values of the temperature gradient
through th© air film, the temperature gradient through the
bake11to tub© and steam film and an experimentally measured
value ©f the resistance of the tube and steam film.
The
resistance of the tube and steam film was calculated from the
average surface temperature
ing*
the total amount of heat flow­
For runs made under the extremes to be met In this
Investigation, the determined values gave an average of
0*$$$* 0*01$ reciprocal B*t.u./hr,,*F. for th® total thermal
resistance of the tube and steam film*
The average deviation
was 4*4 per cent of the average value*
The thermal resistance
may also be expressed as 0*1442 reciprocal B.t*u./hr«,*F.,
s%*ft# which is a value based on the total outside surface of
the tube*
This value was used in all of the calculations*
The temperatures as read by the resistance thermometers
are probably not in error by more than £D»5*€*
At high
rates of heat transfer, the temperature gradient through the
air film is decreased, in some cases, to 5*C.
Under these
conditions, the temperature error will eauae an error of
ten per cent in the air film coefficient*
Accordingly a
precision of better than ten per cent Is not claimed for
these calculations*
In calculating local coefficients, the surface tempera­
ture indicated by corresponding thermometers on the right
and left sides of the tube have been averaged and the local
coefficient calculated from this average temperature*
Air
flow conditions should b® symmetrical with respect to a
vertical center plane as should be any temperature distribu­
tion in the tube*
This was found, generally, to be the case.
Especially was this true of the front portion of the tube.
The temperatures of corresponding points on opposite side
-78-
generally differed by lees than G.S*C*
On the back side of
the tube the agreement was not as good.
Differences up to
1.5*C. were noted, especially with Bank 5.
This method of
averaging ironed out and minimised the effects of such dif­
ferences.
During the heating incidental to the calibration of the
resistance thermometers, blisters were developed under the
strips.
Presumably these blisters were caused by vaporisation
of the solvent in the lacquer used to fasten the strips to
the tube.
It was feared that these blisters together with
the strips themselves and the guard rings would seriously
alter the air film coefficient by altering the surface con­
ditions.
To check this, overall coefficients from steam to
air were determined with the tube in Bow 5 of Bank 6 and com­
pared with the overall coefficients obtained with & bare,
Smooth bakelite tube in the same position,
this comparison is given on figure 8.
k graph showing
The graph indicates
that the coefficients obtained with the tube with the
resistance thermometers are about
the bare bskellte tube.
higher than those of
It was assumed, therefore, that the
surface conditions of the measuring tube was of negligible
effect.
The guard rings and the electrical contacts between
strips were purposely placed at some distance from the ends
i
of the tube*
effect*
This was don© to minimise any wall or end
Such effect could corse from either an unsyametrical
fioghe
e
EFFECT OF SURFACE CONDITIONS ON HEAT TRANSFER
o Meeauring Tube
A
Bare Bakelit® Tube
7
6
B.TU/HR.,SQ.FT.
5
4
3
2
I
O
O
4000
8000
Gm ax -
12000
16000
L B S . / HR., SQ. F T.
20000
-
79-
vertical flow front or from entrance and exit effects on the
steam side*
A fluid stream moving in viscous or stream-line
flow has a parabolic flow front#
The flow front for turbu­
lent flow is considerably flattened and becomes flatter the
more turbulent is the flow*
parabaloid.
hut even so it is distinctly
If the vertical flow front in the duct were
appreciably curved the vertical variation in velocity must
result in a vertical variation in surface temperature of the
tube, especially of the front portion*
several pitot tube traverses were made*
For this reason
A vertical flow
front in the approach section of the duct and flow fronts
taken at the center of Bow 6 of Bank 6 are given on Figure 7*
The latter show that the flow front In the bank Is extremely
flat, the velocity only one-half Inch from the walls being
95 per cent of the maximum or mid-point velocity.
This con­
dition Is probably reached by the third row of the bank*
The vertical flow front In th© approach to the bank Is dis­
tinctly parabalaid, but even here the velocity 1 1/8 inches
from the wall Is 95 per cent of the maximum or mid-point
velocity*
While this variation must affect the temperature
of the front part of the tube, the average temperature of
th® front strips closely correspond to the average velocity
of the air stream.
only*
This is of interest for the front rows
The Horiaoat&i flow fronts shown on Figure 8 were
taken in the approach section of the duct and Indicate that
the velocity is uniform for the portion of the air stream
jrxatntB 7
TOTXCAh FLOW ffBOVfft
Oraph 1
Center of How 8, Bank 8, T * 115*5 ft*/sec*
Qraph S
Center of How 8, Bank 8, V * 85.8 ft*/sec*
Cr&ph S
Approach section of Duct
7
Twenty-five inches upstream from
How 1
Bsafe 4,
V * UB*5 ft./sec*
80
70
POINT
V E L O C IT Y -
FT./SEC.
60
50
40
v
30
20
D IS T A N C E F R O M
T O P - INCHES
pmtm a
m m m m i h flow m o m $
£5 inches upstream from Bank 4
Graph X
V » 115 ft./sec*
Graph 2
V *
00 ft./sec.
Graph 5
T *
BO ft./sec.
38
36
34
32
30
28
26
<24
Q- 12
R
2
3
4
DI STANCE F RO M
5
6
R' GHT w
7
a l l
-
9
8
'LC-r S
intercepted fey the measuring tube.
As an excess of steam was
always passed through the tube, no entrance or exit effects
would fee expected.
The calculation of an average or total air film coeffielent of a whole tufee presented some difficulty*
average could fee composed la'at least two ways*
Such an
An average
tube surface temperature could fee computed and a coefficient
calculated from this temperature#
Alternatively, the local
coeffieieats:eoull fee averaged to give am:average coefficient
for the "tube*- In general, averages computed fey these two
methods are not the Same} the former feeing about seven per
eent lower than the latter*
There 1$ no clear and obvious
reason why one of these methods should fee preferred to the
other*
It was finally decided to use the average of the eo-
efficients*
An average so calculated Is explicitly the
average ©f the local coefficients and Is a true mean value*
The coefficient calculated from the average surface tempera­
ture is patently a fictitious value.
It would fee more proper
to calculate an average or "effective0 surface temperature
frfeh the average coefficient than to calculate the average
coefficient from an averaged surface temperature.
It is
recognised that many of the air film coefficients that appear
in the literature are calculated from an average tube surface
temperature*
In these calculations the circumferential flow of heat
in the tube wall has been considered to be negligible.
This
'•'SX-*
fact can be demonstrated by calculation*
in E m 481, for
esaumple, the *eff#etlve* tube surface temperature Is 45*0*€*
The variation in terfaee temperature in the quadrant between
the front and side of the tube i» 4«**d»
From this And the
distensions of the tmb# veil It wee calculated that the clr~
eumferentl&i flew ©f heat was hut ©#1B per cent of the radial
flow of ■heat • - Obviously it- Is .only'a very minor ■fester#
In a l l calculations ©1X*F (ii*40C#) was taken as the
eondensing steam temperature#
Since the steam supply line
was bled to the atmosphere from ,the water separator, the
condensation in the tube must have taken place at essentially
atmospheric pressure* -the barometer varied between 781 and
746 mm Mgjthe corresponding range In condensation temperature
of water is £09#© to 811.5*F.
An error of less than one per
cent is thus Introduced! it Is negligible in comparison with
the error in estimating the temperature gradient through the
air film#
because of the low surface temperature the amount of
heat, transferred from the tube to the surrounding unheated
tubes by .radiation was small.
The amount of heat lost by
radiation:was greatest for runs at low velocities and. for
the single tube rune where the low rates of heat transfer
resulted in higher tube surface temperatures#
Thus, for
Bun 401 the average tube surface temperature was §Q*C# and
the unheated tubes were at a temperature of S8*C. (the air
Stream temperature)#
Assuming&n emmisslvlty for bright tin
of 0.045 (recommended fey Perry1*) the amount of heat trans­
ferred by radiation was 0.055 B.t.n./hr,,s$.ft.,*F. or less
than half of one per cent of the total heat transferred by
conduction and convention.
For this reason none of the
experimental results hare been corrected for radiation*
While the experlMental wort of this investigation was
in progress, overall coefficients of heat transfer from steam
to air<■for individual tabes in these and other banks were
being measured ■fey J* I. hatcher®.
the tubes used in his work
were drawn from S.i.B. 1010 steel with an outside diameter
of 1*5 (10.01) inches and a wall thickness of 0*068 inches.
Steam was supplied to the tube and condensate collected as
described on page
11 •
It was immediately noted that for
the same position in the same bank, the average air film
eeeffielent as determined in the present work by both steam
heat and electric heat were about ihrity per cent higher than
the overall coefficients determined by hatcher,
the overall
thermal resistance is the sum of three individual resistances}
the resistance of the air film, the resistant e of the metal
tube wall and the resistance of the steam film inside the
tube,
ffee resistance of the metal tube
is small and constant.
If a value of 1000 is assumed for the steam film conductance,
the sum of the resistances of the steam film and tube wall is
but S.fe per cent of the smallest overall coefficient.
It
had therefore, been expected that the overall coefficients
obtained by Mr* Matcher would closely agree with the average
-83-
air film coefficient* of the present investigation.
An in­
quiry was made into possible causes of the discrepancy.
the effect of the surface condition of the b&kelite
measuring tube was determined by measuring the overall coef­
ficient for a smooth bare bakelite tube*
As discussed above
(page 78) the surface condition was without appreciable
effect*
Similarly overall coefficients were determined with
a steel tube carrying sixteen tin strips and compared with
the overall coefficients obtained with a plain steel tube#
the agreement was excellent.
The flow front ©f the air
stream also has shown to be without effect (page 79).
A high value for the thermal resistance of the steam
film inside the tube would easily account for the lack of
agreement between the directly measured air film coefficients
and the overall coefficients.
To estimate the steam film
coefficient a steel measuring tube, similar to the b&kelite
measuring tube used In this work, was constructed.
A steel
tube which had been used by Hatcher was given several coats
of b&kelite lacquer and four longitudinal tin foil strips
were cemented in place*
The tube was calibrated by the
procedure given ©m page IS • Buns were made with the
tube in Bow 9 of Bank 8*
tained!
The following results were ob­
—34—
BANK
8
tOW 9
• * *•06
$*$©
Bun number
4«ax';..
1
14500
0
25*5
t*v
25.3
*w
fcaw
...
;,.«W
25.9
&* ® g.00
4b » 1.72
2 ■'
10300
5750
4
5780
8
10800
6
14300
18*9
14.0
18.8
20*4
24.6
95*0
94.3
98,5
92*8
187
.808
200
199
240
20*7
15.0
16.8
88.7
27.4
this coefficient for the siea© film of approximately two
hundred 8*t*u,/Sf*ft., hr., *F, la much lower than wae expect­
ed*
A search of the available literature revealed no reported
values for the heat transfer coefficients for steam condensing
%%
inside short vertical pipes* Jakob and Irk
studied the
condensation of steam at 101*C, inside a vertical tube 0*409
meters long and 4© millimeters in internal diameter*
Their
data are presented as heat flux (K*eai*/s$*flu# hr.) as a
function of the tube wall temperature (#C.).
Thus for a
tube wail temperature of 03*C* and a steam velocity of 10
meters per second the heat flux is 50000 Kcal./e<&#8i*,hr, or
210 B«i.u«/sq*ft.,hr *,®F. , a value with which the present
data are in excellent agreement.
It appears, therefore, that
the thermal resistance of the steam film is ten to fifteen
per cent of the overall thermal resistance and that a third
to a half of the lack Of agreement between the average air
-85-
film coefficients and the overall coefficients is due to this
cause alone*
A discussion Of the method of determining the the average
air film eoefficieht from the local coefficients has been
given above (page 80 ) *
If the overall coefficients of
Hatcher were corrected for steam film conductance'and compared
withaverage' air‘fit® coefficients of this work calculated from
im average tube temperature, it appears that the two sets of
results would be brought into satisfactory ($5$) agreement*
WM&tX&BBM
the air film coefficients in the ^electric heat*1 runs
were computed from the measured power dissipated by each
strip and the measured temperature gradient through the air
film*
the power was computed fro® measurements of the current
flowing through the strips and the resistances of the strips*
fhb'cwrremi was measured with a precision ©f 0*25 per cent
and the resistances With a precision of ©.SO per cent.
The
major source of error, as in the *steam heat* runs was in
estimating the temperature gradient through the air film.
An error of ©*$#C. in measuring a temperature gradient of 6*C.
introduces an error of tea per cent in the film coefficient*
The »electrie heat* m s
are subject to many of the
limitations of the •steam heat* rums as discussed above*
There are, however, other end special assumptions*
It was
assumed that the standard resistance had a resistance of
-66-
eractly 0.1000 ohms.
The absolute resistance is not known,
but the nbc&nal value is 0#09© ohms*
Accordingly, a con­
sistent error of about two per cent is introduced into all
Calculations*
This error is masked by the error in air film
temperature gradient#
It was further assumed that only the actual strip area
IS available for'heat'transfer and the'coefficients are
based on this area#
This assumption follows from the reason­
ing that the electrical energy is supplied only to the actual
Strip area and it is this area which dissipates the heat
whether iireetly through the air film or indirectly by way
of the Adjacent portions of the tube surface which are not
severed by the resistance thermometers#
iocat coefficients at corresponding points on the right
and left Side of the tube were averaged to get a more
representative variation of coefficient with position*
Tube
average air film coefficients were, as with *steam heat* runs,
the arithmetical average of the local coefficients*
M M 6 0 R E C T T OF THE HATE OF FLOW OF AIR
The rate of flow of air through the bank was estimated
from an observation of the differential pressure of a pi tot
tube set at the center of the 6 5/8-ineh pipe*
tial pressure was measured by a water manometer*
The differen­
At each of
six velocities 10—point horisontal and vertical traverses were
made*
For both horizontal and vertical traverses a graph was
-07calculated and plotted showing the average velocity as a
function of the mid-point differential pressure*
These two
curves were averaged and the resultant curve used to estimate
the rate of flow of air through the bank*
used for all banks*
(See Figure 4)*
The same curve was
k redetermination of
this curve at the conclusion of the experimental work reveal­
ed differences of less than one per cent with the original
graph*
The data and computations are given on page 28 *
For the experiments in which the measuring tub® was an
Isolated single tube and not a member of a tube bank the
effective velocity past the tube was estimated in the follow­
ing ways
k series of horizontal and vertical pitot tube
traverses were made at & point 15 inches upstream from the
single tube#
Inspection of these flow fronts showed that
the average velocity for the full height of the duct and
for a middle portion 5 1/8 inches wide (equivalent to the
tube diameter plus one inch on e$ch side) was about 85 per
cent of the Maximum or mid-point velocity*
This effective
velocity was plotted as a function of the average velocity
In the 8 8/8-Inch pipe and this graph (Figure 5) was used
to estimate the effective velocity past the single tube*
In the nomenclature the single tube is considered a member
of Row 0 of Bank 4*
xxpiBuanm
s ik g l e
msolts
mm
Graphs showing the variation of local coefficient ere
given
heat*
Flgw # a for Steen heat and on Figure 1© for electric
The two sets ©C curves agree extremely well.
They show
that the local heat transfer coefficient fro® a maximum, at the
front of the tube fall# to a minimum slightly behind the side
of the tube ami them rimes to smother maximum at the bach of
the tube*
At low velocities (0 * SOm ) the minimum is found
at a point 120* front the front of the tube#
This point moves
forward with increasing velocities until at 0 « 7250 the
minimum is at a point 100* from the front of the tube.
At
low velocities only a small portion of the heat is being
transferred at the bach of the tube*
With increasing
velocities, the bach of the tube assumes an increasingly
Important part of the heat transfer*
These same phenomena have been observed by other inas
restlgators. Lohriach
found that at law values of the
Reynolds iwd w r tha front of the tube was more important
than tha back.
With increasing values of tha Reynolds
number the baek of the tuba iapreved uore rapidly than did
tha front and eventually baeaaa aupariar. .mall,*4
who
worked with higher velocities than wore used in the present
investigation, found that as tha Reynolds matter ineraased
frha BE,600 to 84,000 the point at which the mlnlaum is
-89-
found moved forward from 90* to 80*#
Apparently the impingement of the air stream on the
front of the tube reduces the film thickness to a minimum
and high rates of heat transfer result*
The film thickness
builds up as the air passes around the tube and causes a
drop in the rate of heat transfer *
The film thickness in­
creases to such an extent that eddies are formed and shed
from the hack side of the cylinder*
These eddies produce a
turbulent condition which tends to decrease the film thick­
ness*
The direction of rotation of the eddies is such that
the air in contact with the rear portions of the tube is
moving in a direction opposed to the main air stream*
This
gives rise to a region near the sides of the tube where the
air Is relatively stagnant*
It is at this point where the
minimum rates of heat transfer are found*
The eddies are
shed more rapidly with increasing velocities and become in­
creasingly effective in reducing the film thickness and
increasing the rates of heat transfer*
At high velocities
this action Is more effective than the impingement of the
air stream on the front of the tube*
At low velocities the
eddies are shed slowly and the rates of heat transfer at the
back of the cylinder are only slightly better than at the
sides*
As the velocity increases the eddies become bigger
in sise and the point at which they are shed moves forward
on the cylinder*
heat transfer*
Accompanying it is the minimum rate of
rxatms a
FAHIATIOU OF LOCAL All FILM COBFFIC11HT OF
hbat m m & w m
Single Tube
S team
Bmt
SIN G LE T U B E
STEAM H E A T
32
30
28
26
24
22
20
18
16
14
12
IO
8
1940
6
4
2
O
20
40
60
80
IOO 1 2 0 14 0
DEGREES
160
180
FXGMI m
VABUIIOI Of LOCAL Alt FILM COEFFICIMf OF
heat
m m E
Singl© T^abe
lleetrle Heat
36
SINGLE
34
TUBE
ELECTRIC
HEAT
32
30
28
26
24
B T.U./HR., S Q .F T ,
L. 2 2
20
G=
7250
G=
6000
G=
4940
jc
G3620
G2400
OC
DEGREES
The variation of local coefficient of heat transfer for
several investigators are compared on Figure 11#
The
published data are for a value of Beynolds number of 38,600,
& value which was not attained with the present equipment*
The results agree in general characteristics:
the local co­
efficient has maxima at the front end back of the cylinder
and minima at the sides*
The curves exhibit some dis­
crepancy at the back portion of the cylinder#
The work of
bohriseh** Indicates that the rear portion of the cylinder
is more effective in heat transfer than the frontj the work
as
s
of both Small
and Drew and Byan indicated that the two
portions are about equal in effectiveness, while the present
data indicate that the rear portion is inferior*
Drew and
Byan suggested that their deviation from IiOhrisch’s data
i
*
was due to the effect of heating on the velocity field near
the sides and rear of the pipe*
Both the present data and
lohrisch's indicate that the rear portion of the pipe im­
proves with increasing velocities more rapidly than the
front*
In part at least, therefore, the low results of the
present data for the back side of the pipe are due to the
lower velocities which were used*
The trend of the data
does not indicate that the back of the tube would equal the
front of the tube in effectiveness if the velocity were
increased to such a point that the conditions would be com­
parable to those of the other investigators.
Fsge4, by pitot tube explorations, measured the total
FiamiK 11
VMIATIOH OF LOCAL All FILM COEFFICIIMT OF
HEAT TAAKSrai
Slxtfle Tube
Comparison of Results of Different Worker*
8
Drew end Ryan
Tube Diameter » 5*10 inches
Air Telocity * S4 ft./sec*
Reynolde Ho* * 39*60©
Lohrleeh**
Tube Diameter * 1*97 inches
Reynold* So# « 59.*600
Staull**
Tube Diameter « 4*90 Inches
Air Telocity « 81*4 ft./sec.
Reynolds Ho. * 59*600
Author
Tube Diameter » 1*50 Inches
Sir Telocity * 85*7 ft./sec.
Reynolds Ho. » 16*900
320
—L
SMALL
/
R e -39600
300
280
LOHRISCH Re = 3 9 6 0 0
260
240
2 20
200
180
DREW&RYAN
Re
39600
60
AUTHOR Re = 1 6 2 0 0
140
20
OO
80
60
40
20
oc
DEGREES
91
head of an air stream in the vicinity of a single cylinder
under iso-thermal condition**
Mis graphs showing the vari­
ation of total head around.the circumference of the tube
have the same fora as the graphs of the present data showing
the variation of local coefficient of head transfer.
The
total head IS at a maximum at the front and back of the
cylinder and at a minimum at the sides*
At low velocities
the recovery of pressure at the hack of the tube is slight,
but improves greatly with increasing velocities,
m
showed,
further, that the air film is lamellar at the front of the
tube, that the film thickness increases going around the
cylinder and that, finally, at the sides of the tube, the
leynelds mseber (based on the film thickness) has increased
to sueh an extent that the flow becomes turbulent and eddies
are formed# .These eddies grew in sis# and are finally shed#
Me identified the point of minimum head as the point where
the eddies originate and shewed that this point end the
point at which the eddies are shed moved downstream with
Increasing velocities.
The mechanism of heat transfer given
above agrees with these points except for the effect of
velocity on the point of minimum heat transfer*
The dif­
ference may be due to the effect of heating on the viscosity
field around the tube.
When the air comes in contact with
the cylinder and Is heated, the viscosity is lowered, and
the Reynolds number (based on film thickness) increases more
rapidly*
Consequently the eddies should be formed sooner
and the vortex sheets are shed earlier*
Correlation of the location of the various curves is
boat given by dorr els.tioa of the average coefficient*
Such
a correlation in terms of the Husseli number as a function of
the Reynolds number Is given on Figure 12*
The data fall in a rather wide band, the upper edge of
which is defined by the present data*
It will be noticed
that the data of Individual investigators is self-consistent}
the spread is between the different sets of data.
This sug­
gests that some variable was not taken into account by the
correlation*
Such a variable may be the amount of turbulence
in the air stream.
The Reynolds number is a criterion of
turbulence la a fluid, stream under steady conditions*
Turbu­
lence may be artificially imparted to the air stream by the
use of baffles or otherwise altering the conditions of flow*
Beiher showed that this additional turbulence will increase
rates of heat transfer.
It Is possible, therefore, that the
differences between the various sets of data are due to
different degrees of turbulence in the air stream.
At
present we have no method of measuring this extra trubulence.
Brawn on this graph Is the correlation curve recommended
by McAdams14.
The only data which lie below this curve are
the extensive results of Hughes.
In light of the data which
has been published since McAdams’ correlation, It appears
reasonable to draw the curve somewhat higher above Reynold1s
numbers of SQQ0*
graph*
Such a revision has been indicated on the
-93-
CJnder present methods of correlation, the present date
agree satisfactorily with that of other investigators*
nouni is
HSAT MUNSTER FROM SINGLE CaiiSDBS
0
Author
a
Gibson1*
v
Griffiths and Asbery6
A
Hughes18
@
P&ltz and Stair31*
♦
Helher1*
X
Small**
7
Vornehm
la
i
Graph X
Correlation of Present Pets
Graph 8
Correlation recommended by McAdams4*
Graph &
lerised Correlation
yagwnN
nggsnN
-94-
rmm bases
row
BUB
The variation of tha leeal eoeffieiemt in the first row
of & tub* bank is Quite similar to that of a single tube.
The oeeffioieat has maxim* at the front and back of the tube
and a minimum slightly behind the side*
The general share
of the curve is unaffected by velocity.
With increasing
velocities the point of minimum shifts slightly toward the
front of the tube and the difference between the maxima and
minimum Increases*
With increasing velocities the ratio of
local coefficient to average coefficient tends to drop for
the front portion of the tube and tends to rise for the
bach portion of the tube.
This is in line with the observa­
tions of Lohrisch1* for single tubes indicating that the back
of the tube showed a greater improvement with velocity than
the front portion.
The difference between the maximum at
the front and the minimum at the side is not as great for
the first row as for an isolated cylinder and the drop in
coefficient from the front to the side is not as rapid.
As
the air stream enters the restricted space between the tubes
in the row its velocity is greatly increased.
This increase
in velocity does not allow the air film to build up to the
thickness found at the sides of an isolated cylinder.
For
tubes in the first row of a bank the rear of the tube is
more effective in heat transfer than in the case of an
Isolated cylinder.
The increased velocity and the reversals
-95-
In direction of the air stream caused by the second roe of the
bank increase the turbulence and the higher rates of heat
transfer result#
nevertheless, it is still at the front
portion of the tube where most of the heat is transferred#
the direct impingement of the air stream is more effective
in reducing the film thickness#
Graphs showing the variation
in local coefficient for How 1 of Bank 6 are gives on Figure
IS#
For the first row of the bank there were no essential
differences between the three banks studied and hence graphs
for only one bank are presented here#
m u s s is
v A H i m o i of mcAt*
MAT
axr
n m
c o m i c m m of
T M m F M
Bmk 8
Bow I
Heat
a « 8.85
dft * 1*5
b * 3*00
db « 1.5
d8 * 0.75
36
BANK 6
ROW I
34
32
30
u max
20500
28
26
22
O
a
120 140
DEGREES
160
180
-96-
80i n v i
The distribution of the local coefficient does not change
aftw
the third so* has been reached.
(Figure M ) •
typical
of this distribution as© the graphs for to* $ of the three
banka studied whieh aregivemea Figaros 14 to 17*
At lo* velocities the graphs for the different banks
reseabif saoh other end bear s resemblance to the curves for
a single tube*
Ihe coefficient has maxima at the front and
back and a minimuia at the side of the tube*
the back of the
tube, however, is m % as effective when the tube is in a
bank as when the tube is isolated*
With close spacing be­
tween rows (Bank S) the coefficient at the back of the tube
has the same value as at the side of the tube*
As the die*
tancebetween rows increase*, so does the effectiveness of
the back side of the tube*
At high velocities these curves resemble each other for
the front portion of the tube and exhibit considerable
difference at the rear portion of the tube*
In all
cases
the local coefficient has & maximum at the front and drops
off rapidly to a low value at the side of the tube,
kith
close spacing between rows, the coefficient continues to
fail
and
reaches a minimum at the back of the tube*
As the
spacing between rows increases the back portion of the tube
greatly increases in effectiveness and s characteristic
irregularity appears*
From the minimum at the side of the
tube (100* from the front) the coefficient reaches a maximum
-97
at aboat 1£Q* t w m the front*
At 150* it again go as through
a minimum, the valueof which la leas than that of the
mlnlmum&t tha side.ef the tube#
At the extreme back another
is reached, the value of whieh la about equal to the
Velue:for the whole tube*
These irregularities
here pronounced at high velocitiesj at low velocities
llsappear completely,
it is'only m
the:graphs show, further, that
the front third of the tube that the local
coefficient has a value higher than the average coefficient*
It is, therefore, this front third of the tube that is
for most of the heat transfer*
These same
are all found in hows $, 5, 7, 9*
The shapes of these graphs suggest a mechanism by whieh
the heat la transferred in a tube bank,
A tube in the latter
portion of a tube bank Is considerably more efficient in
heat transfer than either a single tube or a tube in the
first roe,
Hot only is the average coefficient higher, but
the local coefficient is greater at all points.
The great­
est improvement in heat transfer Is at the front of the
tube*
The transverse distance between tubes in a row acts
like in orifice of a noasle,
The air stream emerges from
this nosale at a high velocity and impinges on the front of
the tube in the following row#
This direct Impingement
effectively wipes away the air film and very intense rates
of heat transfer result*
As with isolated cylinders, the
film thickness increases going around the tube and causes a
■98-
drop In the rate ©f heat transfer.
The minimum found at the
aid© Is still considerably greater than that found at the
eeme point on a single tube or a tube la the first row*
When the air stream reaches the after side of the tube a
vortex sheet starts to term and the rate of heat transfer
Increase#*
Wo sooner has the heat transfer coefficient begun
to improve than the air stream starts to enter the restricted
diagonal space between the tube and the following row*
Here,
as at the side of the tube, the sir film builds up and the
rate of heat transfer again starts to fall and a minimum is
reached at the point of minimum clearance*
la the slot
distance widens the air stream in the vicinity of the rear
of the tube becomes turbulent and the heat transfer coefficient
Increases until the back of the tube is reached*
If the spacing between rows is too small (Bank 5) It
appears that the back of the tub© is effectively blanketed
and turbulence is not developed*
The low rates of heat
transfer Indicate that there is a relatively stagnant region
where the sir film Is not swept away by swirls and eddies.
At low velocities a small ©mount of turbulence is
developed at the rear of the tube*
This turbulence, by re­
ducing the film thickness, slightly increases the rat© of
heat transfer*
The amount of turbulence increases with
velocity and at high velocities the >ack of the tube assumes
a greater share of the heat transfer#
These graphs also suggest why lower rates of heat trans­
fer are found in in-line banks than in staggered banks.
In
staggered tube banks most of the heat is transferred to the
front of the tube where the impingement of the air stream
has reduced the air film to a minimum thickness*
Placing
the tubes In line eliminates this impingement and the cause
of high rates of heat transfer is removed*
The close agreement between the two quite independent
methods of 11steam heat11 and Belectric heat11 are shown by
the two sets of graphs for Bow § of Bank 5 and also in the
graphs of tube average air film coefficients which follow *
PiatHSUS 14
Y m i m 01 of eocal m
m m
film coefficient of
m s e m
Bank 4
Bow
§
Ste&a Heat
a * 2«£B
da * 1.50
b * £.80
dfe * l,7»8
de » 0*76
72
BANK 4
ROW
68
5
64
60
56
52
SQ. FT.
44
B.T. U./HR.,
48
36
40
"max
20550
32
3m a x
7 780 -
28
^max
14540"
vmax
10300
20
cx
DEGREES
FXGQES 15
Y M I O T G H OF XiOClL AXE FILM- COEFFICIENT OF
HEAT TRANSFER
Bank 5
low
5
Steam Heat
a * £*H5
d&
b * 2 M
lb * 1*50
la * 0*75
* X*SO
72
BANK
5
ROW
5
68
64
60
56
52
48
44
40
36
32
28
24
20
max
20700
16
max
2190
G m ax
7560
^max
4300
12
8
4
O
20
4 0
60
80
lOO 120 1 4 0
oc DEGREES
160
180
FIGURE 16
VARIATION OF LOCAL AIR FILS COEFFICIENT OF
HEAT TRANSFER
Bank S
Row
5
Electric Heat
a * 2.25
da =» 1.90
9 * S.S5
db * 1.50
ds a 0.75
72
68
BANK
i ROW
64
60
56
5 2
^
48
B.T.U./HR.,
SQ. F T
v
36
28
24
umax
20600
20
Jmax
12500
o( D E G R E E S
FIGURE 17
i mxmm
of local air fils cossricmT of
BEAT X&Uftra
Ban* 6
How
5
Steam Heat
a » 2.H5
dft w l.&o
b * B.OG
db * £*00
ds * 0.75
76
72
BANK
6
RO W
5
68
64
60
56
54
u max
20700
48
44
40
36
max
3220
32
28
24
20
16
12
8
4
20
40
60
80
o(
IOO 120 140
DEGREES
160
180
Effect of Telocity
Correlation of heat transfer data is generally presented
as a relationship between the Busselt and Beyaolds numbers
with the Eusselt number expressed as a power function of the
Reynolds number*
For a given tube diameter and a constant
film temperature these equations reduce to one which defines
the heat transfer coefficient as a power function of the
velocity} the power which relates coefficient and velocity
is the same as the power relating the Husselt and Reynolds
numbers#
the dependence of the average air film coefficient
of heat transfer on air velocity is given for the odd-numbered
bows of Bank 6 on Figures 16 and 19*
approximately linear.
the relationship is
These same date are presented on
logarithmic paper on Figure 90.
The slope of the graphs
indicate that the heat transfer coefficient varies as the
0*56 power of the velocity#
Similar graphs indicate a value
of 0*50 for Bank 4 and of 0.57 for Bank 5#
These values are
so
in excellent agreement with the results of Huge
on banks
with the same spacing but with smaller diameter tubes#
He
found that the Busselt number varied as the 0.56 power of
the Reynolds number#
Other reported values in the literature
are 0.88 by both Konrad1'* and Griffiths and Awbery* and 0.89
by Beiher**.
(baaed
to
In correlation
lleAdaaa14 recommend* 0.69
Beiber) end Colburn* recommend* 0.60.
FIGURE 16
EFFECT OF m O C I K OF AVERAGE AIR FILE COBFPICIEST OF HEAT TRANSFER
Bask 6
Ron® 1, 3, 5
0
Steam Beat
□ Electric Heat
28
BANK
6
24
ou:
h av/
BTU./HR., S Q. F T ,
RO W
40 00
80 0 0•
12 0 0 0
16000
L
* B S / H R . . 5Q. FT.
^max
BANK
20000
6
48
F
36
RO W 5
ROW 3
32
28
24
av
BX.U./HR.,
40
SQ.FT,
44
JC 20
4000
12000
16000
8 0 0 0i
L
B
5
.
/
H
R
SQ
FT.
max
20000
fiuvm m
EFFECT OF VEEOCITY OM AVtBAQE AXE T i m
C0IFFICIE1T OF HEAT TRAEBFKft
Ban* 6
Hows 7,
0
Steam Heat
9
a
Electric Heat
BANK
6
48
h av
B . T . U / HR., SQ. F I
u:
o
40
ROW
7
36
32
28
24
20
O
4000
8000
12000
Gm ax
L B S ./H R ,
16000
SQ. FT.
20000
BANK 6
c*v
B.T.U./HR.,SQ. FT.'F
48
44
40
ROW 9
36
28
24
20
4000
8000
Gmax
6000
12000
LBS. / HR SQ. FT.
20000
FX0U8I
m
XFfSCT OF TO&OCXYZ OH A7EBAGE AXE FILM
COlFFXCXElf OF H A T XBAH0FE&
Bank 6
0
Bow 1
a
Bow 3
v
Bow 5
a
Eow 7
0
Bow 9
90
80
BANK
6
B.T. U./
HR., SQ. F T.
o1 7 0
*N
60
50
40
30
>
to
4 000
6000
Gm ax
IO O O O
20000
L B S . / H R ., SQ. F T
101-
Bffeet of Bov Humber
The effect of row number on the distribution of the
local coefficient of heat transfer is indiested on Figures
Sl~28»
Her© are given, for the maximum velocities attainable,
the distribution of the local coefficient of heat transfer
for the single tube and five rows of each bank*
The graphs
are plotted to the same scale but have been displaced to
permit comparison*
The graphs show that a decided change in
the mechanism of heat transfer occurs between Bows 1 and 8*
As discussed above, the distribution for the first row of
the bank resembles that for the single tube*
The first two
rows of the bank serve to establish the flow conditions and
the mechanism of heat transfer that are characteristic for
each bank*
The variation of average air film coefficient with row
number is indicated by the graphs on Figures £4, 25, 26*
note* above W inding**, and Griffith* and le b e ry
As
observed
that low rates of heat transfer are found in the first row
of a staggered tube bank*
The rate of heat transfer Increases
In the secondrow and becomes constant in
ceeding rows*
the third andsuc­
This also was the casefor Bank 5 of the
present investigation but the maximum and constant rates fo r
Banks 4 and 6
reached*
were not attained until the f i f t h row was
In line with the previous investigators, the heat
transfer coefficient for the first row is about 60 per cent
of the value finally reached*
These data are interpreted as
indicating that three to five rows of tubes are required to
establish the characteristic flow condition of the bank*
These conditions of impingement of the air stream and the
high degree of turbulence are responsible for the high rates
of heat transfer in the latter portion of the bank.
ftmm
IFFBCT OF BOW 10MBIE
bx
0®
IISTBIBOTIOU
OF LOCAL COIFFICIKHT OF HEAT TBAK8FEH
SIHOLE TUBE
0 » 7,280
lank 4
Bow 1, OtIwfitaCl
MF
W s» 20,000
Bow 8, ®jaax * 00,400
Bow 5,
SB 20,550
low 7, Omax
as 00,700
low t, Oaax
«
00,700
BANK 4
ROW 7
ROWS _
B.TU /H R
oLu
SQ. F T ,
ROW 9 _
RO W 3 -
O
20
60
80
oc
IO O 120
DEGREES
140
160 180
FIOUBE 82
EFFECT OF BOW 80IK8SZI 08 DimiBUTXOB
OF EQCAB COEFFICIENT Of HlAT THA&’EFEB
EXHOLE TOHE
0 » 7,230
Mmk
5
ts.
20*700
3, Omax
m
20,800
low 0, 0&ax
m
20*700
low 7, 03B&X m
20*650
m
20,900
mam i,
Mm
«W*J*
low 9, % m x
BANK 5
ROW 9
b_
a
in
cr
x
ROW 7 —
\
D
ROW 5
CD
ROW 3 “
ROW I
SING LE
TU B E
O
80
CX
IOO 120 1 4 0
DEGREES
160
IBO
notro m
EFFECT OF
BOW BOBBER OM
DISTKIBOTON
Of LOCAL COEFFICIENT OF HEAT TRAE5FEB
iXHOLE % m %
0 * 7,E50
Bank 6
Bow X,
»
80,500
tow B, % a x
«
BOt TOO
Bow 8, 0®ax
*
SO, 700
Bow 7,
m
BO,400
tow 9, ®ma*
M
SO,500
BANK 6
ROW 9
SQ. FT.,
°F
ROW7
B .TU /H R .
ROW 5 ~
ROW 3
ROW
SINGLE '
TUBE
O
20
40
60
80
1 0 0 120
(X D E G R E E S
140
16 0 180
FIGURE £4
EFFECT OF ROW RUMBER OR AVERAGE AIR FILM
COEFFICIENT OF HEAT TRANSFER
Bank 4
A ■* 8*85
fig * X*&
b * S.80
db • 1,788
4, • 0,75
BANK A
40
umax
2QOOC
38
36
34
3m a x
5000
32
Li_-
'u
30
bs
28
yH/ni'8
26
^max
lOOOO
24
22
ROW
NUMBER
FIGQBJS 26
EFFECT OF SOW SUsSEER OH AVERAGE AIK
nm
COEFFICIENT OF HEAT S K A H S m
Bank 5
a * 2.25
da - 1.5
b * g.25
db « 1.5
d, • 0.76
BANK 5
38
36
34
°max
32
20000
30
28
^ max
I50 00
. U./HR.,
SQ. FT.
. 26
24
22
^max
IOOOO
20
ROW N U M B E R
5
6
7
4
8
9
IO
FIGURE 26
EFFECT OF ROW 1GMB11 OI» AVERAGE AIR FILM
COEFFICIENT OF HEAT t&AfldFBft
Rank 6
a m a#R5
dn 88 1*5
b * 3»00
db * S»O0
0*75
DU
BANK 6
°nnax
48
20000
46
44
4 2
40
vm a x
15000
. U . / H R . , S Q .F T .
38
30
f- ° m a x
: io o o o
24
22
20
14
ROW
NUMBER
j
-103Effect of Row Spacing
To illustrate the effect of row spacing graphs showing
the variation of average coefficient with velocity for two
rows of the three hanks studied are given on Figure B5*
For
the first row of the hank the distance between rows has
little effect on the coefficient*
This Is expected as the
variation of local coefficient for all three banks resemble
not only each other hut also that of the single tube*
The
characteristics of flow condition for which the distance be­
tween rows is responsible have not been established*
By the
time the fifth row has been reached and the flow conditions
established the curves indicate that an Increase in distance
between rows causes an increase in coefficient*
This is at
%9
Pierson**
data
variance with the data of other observers*
show the reverse as does the work of Hatcher*®
Both of
these observers show that a small drop of about five per cent
accompanies this Increase in row spacing*
The cause of this
variance of the present data has not been discovered*
The effects of bank dimensions, air velocity and row
position on the overall coefficient of heat transfer in
staggered tube banks and the relationship between heat trans­
fer and pressure drop are the subjects of a current program
of investigation carried out in this laboratory by J* E*
Hatcher*9
Be studied the three banks used in this investi­
gation and five others*
A more complete discussion of the
variable may be found In his thesis entitled
and Pressure Drop in Staggered Tube Banks*"
"Heat Transfer
riows m
EFFECT OF SOB 8FACXSQ OB ATEEAGE AIR FILM
oosmczssT of
seat t m m f m
.Bows I and $
0
Bank 4
A
Bank 5
v
Bank ©
ROW
24
ha v
B .T.U /H R .,
SQ., F T ,
L_
o
O
4000
8000
Gmax
ROW
12000
16000 2 0 0 0 0
L B S . / H R , SQ. F T .
5
48
av
B.TU/HR.,
SQ. F T-, °F
44
40
36
32
28
24
JZ
20
4000
8000
m ax
12000
16000 2 0000
L B S / H R , SO F T
104-
Summary
A study has base mad# of the surfaee temperature dis­
tribution around a tube in a staggered tube bank*
The follow­
ing conclusions are drawn*
1*
The Street impingement of the air stream on the front
of the tube redoes* the air m »
thickness to a minimum and
Internee.-rate*:.of heat transfer are found at the front of the
tube*
2*
The air film thickness increases from the front to
the side and the rate of heat transfer drops sharply#
$#
A minimum rate of heat transfer is associated with
both the transverse and diagonal minimum distances between
tubes*
4#
With sufficient spacing between rows turbulence in
the airstream is developed on the after
side of the tube
and the rate of heat transfer increases*
5*
With close spacing between rows the back side of the
tube lis effectively blanketed and extremely low rates of heat
transfer at the rear portion of the tubes result.
6*
On only the front third of the tube is the rate of
heat transfer above the tube average.
T*
Three to five rows of tube
are necessary to
establish the characteristic flow conditions responsible for
the high rates of heat transfer in staggered tube banks.
rates of heat transfer are found in the first row.
Low
-105-
8#
The average coefficient of heat transfer increases
with the 0*58 power of the velocity*
9*
The distribution of local coefficient of heat
transfer for the first row closely resembles that of on
isolated cylinder.
18*
On an isolated cylinder the heat transfer is a
t
maximum at the front and back of the tube and a minimum at
the sides of the cylinder*
-106-
BIBLXOGRAPHY
I*
8ryant# Gwer, Halliday and f&ltoer, Tech. liept. Aero.
K#*» Com. (Or. Brit*), jg£, X O m (1928).
8.
Colburn, Trans* Am. Inst* Che®. Eagrs., jjg, 197 (1986).
8.
Brew and 8y*&# Trans. A®. Inst. Che®. Eagre., £6, 118
(1931)*
4.
Fage, Phil. Meg., (7), 2# ^5$ (1929).
5.
F&ge and Johansen, Tech* Kept. Aero. Bee. Com®. (Or*
Brit.), S h 114 (1927).
§.
Griffiths and Awbery, Proe. Inst. Mech* Engrs., j2frf
879 (1933).
7*
Grimison, Trans, A®. £oe* Mech. Engrs## £4, 583 (1937).
8.
Harris, Caygill and Fairthorne, Tech, Kept. Aero* Bee.
Cops# (Gr# Brit.), J4, 1298 (1930).
8.
Hatcher, Thesis In Chemical Engineering, Cornell
University, 1940.
10.
Huge, Tran®. Am* Hoc. Mech* Engrs*, ££, 563 (1937).
11*
Jakob m i Irk, Forsehuags&rbeiten, 31Q (1828).
12.
Hein, Archiv f&r Warmewirtsh&ft, June 1934*
18.
hohrisch, farsefaungsarbeiten, JSgg, 3. (1929).
14*
McAdams, ®Heat Transmission®, p. 226 et seq., Hew York,
McGraw-Hill Book Co., 1935.
15.
McAdams, Trans. Am. lust* Ingrs., £&* * (1940).
18.
Konrad, Ind. Eng. Che®., 24, 505 (1952).
-107-
17#
Perry, ^Chemical Engineers1 Handbook1*, p. 559, Me® fork,
MeOraw-Hlll Book Co*, 1954*
18*
Perry, "Chemical Engineers* Handbook**, p* 882, Mew fork,
McGraw-Hill Book Co*, 1354*
19*
Pierson, Trans* Am. Ho g . Hech. Engrs*, J|g, 573 (1937).
20,
Pra®anik, Proc. Ind. Assn. Colt. Bet*, £, 115 (19£1).
El.
Ray, Proc* Ind. Assn. Colt* Act*, §, 95 (1320).
82.
Reiher, Forsehungsarbeiten, #63* 20 (1925)*
25.
Small, Phil* Mag., (7), M s
24*
Small, Phil. Mag., (7), M s SSI (1955).
25*
Stanton, Tech. Kept. Adv. Com. Aero. (Or. Brit,), p. 45
SI (1935)*
(1912-13).
86,
Winding, Ind. Eng. Che®.,
942 (1938).
S7.
Woolfenden, Thesis In Chemical Engineering, Massachusetts
Institute of Technology, 1927.
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