,111.J. Hrnr Mav.s Trronsfir.
Printed in Great Britain

Vol. 27. No. 7. pp. 959 970. 1984

0017-9310/84%3.00+0.00
Pergamon Press Ltd.

THE MAXIMUMANDMINIMUM

TRANSMITTED

FROM

METAL

TO BOILINGVALUES

OF THE HEATATMOSPHERICPRESSURE*

WATER

Q

UNDER

SHIRO NUKIYAMAt

J. Japan Sot. Mech. Engrs 31,367-374(1934)

Abstract-The
quantity of heat transmitted from a metal surface to boiling water increases as the temperature
difference AT is increased, but after the AT has reached a certain limit, quantity Q decreases with further
increase in AT. This turning point is the maximum value of heat transmitted. The existence of this point was
actually observed in the experiment. Under atmospheric pressure, AT corresponding to the maximum value ofheat transfer for water at 100°C falls between 204o”C, and Q is between 1080 000 and 1800 000 kcal/m2 h (i.e.
between 2000 and 3000 kg/m’ h, ifexpressed in constant evaporation
rate at 100°C); this figure is larger thanthemaximum
valueofheattransfer as waspreviously considered. Also, theminimum
value ofheat transfer was
obtained, and in the Q-AT curve for the high temperature
region, the burn-out effect is discussed.

INTRODUCTION

In the process of boiling, the water is fully agitated by
the generated
steam bubbles, and the degree of
THE IMPROVING of evaporation
rate (i.e. the quantity
agitation
first increases with increase in AT, but
evaporated
per unit time per unit area) for an
because of the lower heat-transfer rate of steam (& ofevaporator is important, because it reduces the size ofthe heat-transfer rate of water), tl is not a monotonicallythe evaporator ofa fixed capacity as well as shortens theincreasing function of AT. When the boiling is mild, thetime required for the generationof steam. If theagitation by the steam bubbling has more effect on theevaporation
rate, hence the heat-transfer
quantity Q,
heat transfer, so tl and Q both increase as the AT is
has a maximum value, the determinationof this value isincreased. Whereas, if the generation of steam becomescertainly necessary if one is to control the evaporation
too fast, most of the metal surface is covered by therate at all. This article is mainly a report of thesteam bubbles. As a result, there is no more water which
experimental determinationof the maximum value ofis in direct contact with the metal surface to be agitated.
heat transfer, although the related minimum value of
Therefore, the negative effect (lowering of m)takes placeheat transfer was also obtained experimentally.
and it becomes a matter of heat transfer between metal
As the boiling phenomenon
is so involved andsurface and steam. Thus, contrary to the conclusion ofcomplicated, the analysis for boiling heat transfer is an
the previous workers, the value ofcl at 100 or 200°C AT
almost impossible problem. Even with the powerful
is conceivably limited (in the order of 1 kcal/m* h “C).
dimensional analysis, the research to date was not very
Therefore,
in the AT-cr curve, the ordinate
firstsatisfactory ; besides, the reported work available in theincreases with increase in AT (Fig. 2) to a critical point,
literature was all experimental.
then it must decrease for further increase in AT. Since Q
Now
is the product of c(and AT, it should not decrease when tl
Q = @T),(1) first starts to decrease. Differentiating equation (1) andletting dQ = 0, one gets a/AT = -du/d (AT); thus atwhere Q is the heat transmitted from the metal surface
the point b, Q also starts to decrease (Fig. 2), and that is
per unit area per unit time to the water; c[ is the heatthe maximum value of heat transfer, Q,,,. If AT
transfercoefficient,and AT is the temperature
continues to increase, the radiation from the metal
difference between the surface and the water. Equation
surface becomes pronounced and the values of c(and Q(1) has been used for obtaining the relationship between
can go very high, so that the c(- and Q-curve should be
AT, c( and Q. Among the researchers on boiling heatconcave upward again. The relational function of a or Q
transfer are Austin Cl], and Jakob and Linke [2].
on AT is as presented in Fig. 2, where c is the point for
For the purpose of comparison, the work of previous
the minimum value of Q. Nevertheless, the bc part of theworkers is indicated by a, b, c, in Fig. 1. Austin
curve (as will be discussed later) is so unstable that it is[l] proposedthat tl asymptoticallyapproaches
hard to obtain in practice.
7000 kcal/m’ h “C (0.194 Cal/cm* s “C), and thequantity Q increases with AT without limit.
FURTHERDISCUSSION

AND a-AT* Translated from the Japanese by Dr C. J. Lee, while he wasa graduate student in the School of Chemical Engineering,
OklahomaState University, Stillwater, Oklahoma.
Dr Lee’spresent address is Heat Transfer and Process Equipment
Research
Section,Phillips
ResearchCenter, _Phillips
Petroleum Company, Bartlesville, Oklahoma,
U.S.A.
t Professor, Tohoku-Imperial
University, Japan.

ON THE Q-AT

CURVES(FIG. 2)

Some special equipment might be used to maintainthe metal surface at a constant temperature although, in
general, equilibrium temperature is attained when theheat transmitted
to the water is equal to the heat
supplied by the heat source. Let Q be the heat supplied
959

960

SHIRO NUKIYAMA- 16x IO5obAustin
Jakob

[I]
and

Llnke

[2]

-6~10~- 2x~o5AT
FIG. 1. AT vs Q curve

and the heat transmitted

to water at equilibrium

the temperature; water temperaturestate;of the metal surface at this value of Q
(point Pin Fig. 2) is then the sum of the corresponding
AT and the temperature of water. At this point, if the
supplied heat is increased by a small amount, P is
moved closer to band attains another equilibrium state.
Suppose, P reaches b now, and if we supply a little bit
more heat to increase AT, then P goes beyond b and Q
starts decreasing.
Therefore,
the excess heat (thedifference between supplied heat and the Q from Fig. 2)
accumulates in the metal material so AT is further
increased. From there, Q is becoming less and less as AT

b -___--__--__~___c)0’AT (‘c)FIG. 2.

PC)= 100°C.

continuously increases, P then moves rapidly following
the bed curve, and finally reaches the equilibrium state
at d, where it has the same value of Q as at point b(Fig. 2). In the experiment, one supplies the heat to theheat-transfer area, gradually increasing from zero, andrecords the surface temperature ; at point b, the surface
temperature
will suddenly change; from this, one
notices that the maximum point has been reached. As
will be discussed, the value of Q,,, at point b varies withdifferent curvature of heat-transfer
surfaces, but ingeneral, it is over 30 Cal/cm’ s. If we assume that
Q,,, = 30cal/cm* s and calculate LY
for the heat transfer
between the metal surface and the generated steam, wefind that the temperature at point d is in the order ofmagnitudeof the melting point of platinum. As aconsequence, for most metals, when they go beyond b,
they follow the curve bed rapidly and melt before theyreach d. The AT corresponding
to b for water is below
40°C ; accordingly the temperature of the metal surface
at point b is lower than 140°C. Ordinary metals are
solid at this temperature. As will be discussed later, theexperiments were run with metal wires of iron, nickel,
nichrome and platinum. These wires actually melt at
point b just like the fuse of low melting point (170°C)
does. Only when using an extremely thin platinum wire
for the heat-transfer
surface would the point d reallyexist, because the wire has a small diameter, hence a

Heat transmitted

from metal to boilingwatersmall value of Q,,,. Now, if we reduce the value of Q
little by little, the curve would not reverse from d to b but
it goes along de (as a result of decreasing AT), andsuddenly jumps to point e from point c, for the same
reason as for the jump from b to d. We call the region
from d to c the spheroidal state.
The purposeof this investigation
is to study
experimentallythe above-mentioned
phenomenon.
But, owing to the large value of Q,,,, we have to select asuitable type of heat-transfer surface. We were not able
to supply necessary heat for a flat surface which wasused by Austin [l] and by Jakob and Linke [2]. When
we used a thin metal plate as the transfer surface,contacting water on one side of the plate and heating
directly with a Bunsen lamp from the other side in orderto supply the heat, we could supply only a few per cent of
For various reasons, we have used thethe Q,,,.
following two methods: (a) A thin metal wire for theheating element as well as the heat-transfer surface; thewire is set in the water and supplied with the necessaryheat by running electric current through the wire. The
experiments were run with different metals of various
diameters. Subcooled water was also used in obtaining
6. The minimum value of heat transfer was obtainedwith a thin platinum wire.(b) With a special equipment
set-up, the same experiments
were repeated on two
circular flat plates of 10 and 6.48 mm diameters.

EXPERIMENT

I-THE

961

(a)

Q, LXAND AT RELATIONSFOR THE SURFACEOF METALWIRESIn Fig. 3(a), D is the Pyrex glass vessel of 15 x 15 x 24 cm
for distilled water. D was set up in a sand bath andwas heated with gas or with insulated electric resistancewires in the sand to keep the water at boilingtemperature under atmospheric pressure. ab is a metal
test wire of 20 cm length ; its ends are welded to aA andbB, respectively. These silver or nickel plated copper
wires are 3 mm in diameter. A, B are connected tocopper wires of larger diameter which carry the electric
current to supply the necessary heat to ab. The current
going through the wires is about 10 A D.C.; so if aA
and bB were bare, or if a metal vessel was used for D,
the purity of water inside the vessel might have been
affected because of the electrolysis. In order to prevent
it, aA and bB are cased by glass coating. Alternating
current had been tried with the considerationthat itmight eliminate the electrolysis, but it was not suitable
due to the difficulties encountered in the measurementof temperatures,
current, voltage, etc.
The electric flow scheme is shown in Fig. 3(b). CDEF
forms the Wheatstonebridge, and the test wire ah isfixed in between CD. The wires other than for ab are
rather large in diameter so that only a few ohms fromthe resistance in ab were counted for the resistance
between section CD.R,,R,,R,,are manganin wires.
The resistance of R, and R, is many hundred ohms, sothat most of the current from the source goes to CDE,
and less than 1% of the total will go through R, and R,.

(b)FIG. 3. Equipment

for metal wire experiments.

R, and R, are put in an oil bath to avoid thetemperature variation due to the heat generation fromthe resistors. R, carries the same amount of current
which flows through ab. In Fig. 3(c), we have shown that
R, is a rheostat which was constructed with some 40
thin manganin wires stretched between a copper frame
and immersed in an oil bath. The resistance is adjusted
to the same magnitude as the resistance of the test wire
a6 during the experiment. Because of the strong current
which is flowing, the temperatureof oil during anexperiment may rise more than 20°C but since the962

SHIRT NUKIYAMA

manganin wires were used, the variation in R, can beassumednentigibleinthisexperiment.Sisa30~2ariru:;
G is a galvanometer ; N is a set of battery cells ; H is a
DC. generator; Y is a voltmeter ; and i is an ammeter.
THE EXPERIMENTS AND THE RESULTS OF THE~ETERMINA~ON

OF THE MAXIMUM

VALUE

OF Q

Same cafibration shouid be provided before thetemperature of ab can be read from the Wheatstonebridge during the experiment: immerse ub in the oilbath, and vary the oil temperature between 50 and
150°C (this temperature was measured by mercury
thermometer to &C precision), take the reading ofvariac S and plot it against oil temperature when the
weak current supplied by N is at equilibrium with thereading in G. Since the current used in this calibration isso weak that the temperature of the wire can be taken as
the temperature of the oil bath, the calibration curve
can be approximated as the reading of S vs thetemperature of the wire. When performing theexperiment, the temperature of the test wire ab istherefore obtained from the reading together with thecalibration curve.
The calibration with oil may destroy the surface ofthe met& wires, thus introducing a bad effect in themain experiment. To avoid this, we have run only one
point each for a certain kind of metal wire for suchcalibration with oil, then checked the same calibration
with water instead at the temperature from 50 to 100°C ;for temperatures above IOQ‘C, we can extrapolate theresult of the calibration.
ab is fixed in the container D [Fig. 3{a)]_and after thewater in D is heated by Bunsen flame to the required
temperature (lOOC), a current is supplied by H
[Fig. 3(b)] and by adjusting Rd. Beginning with 1 A, thecurrent is gradually increased by OS--l A, and thecorresponding I, V, S, readings are recorded. When Q isclose to the maximum value, the variac S is used inaddition to R, Fig. 3(b)] to keep G at an equilibrium
position. When Qmaxisreached, part ofthe wire ah melts
out and G will sense a violent shock. At this moment, thereadings of I, V, S, are carefully taken, and from this, AT
corresponding to the Q,,, is obtained. But, to preventthe burn-out of the metal wire, an automatic shut-off
device has been applied. During experiments, theelectrolysis occasionally introduced some error in thetemperature readings. Therefore, in order to shorten
the period of one run, the readings in the lower current
region were roughly taken. Let d be the diameter of themetal wirein~,~bethelengthin~m,thereadjngofthe
ammeter and the vohmeter be f and V,respectively, thevaiue of Q is then calculated by the following equation :The temperature difference between water and thesurface of the metal wire AT was obtained from thereading of S and the mercury thermometer ; however,there are two points which must not be overlooked :(1) If there were any difference between thetemperature of the surface of wire 7; and that of thecenter of the metal wire T,, it would introduce an error
in the value of AT. To correct it, we assume that the heatgeneration from the metal wire due to the current isuniform throughout the wire, and (To- 7;) can becalculated by the following equation (as given in any
general heat-transfer book [3]) :To- r, = wr=/41,(3)

where Wis the quantity of heat generated by the metal
wire per unit time per unit volume of the wire, r is theradius and J. is the thermal conductivity of this metat
wire. Since the heat transmitted from the surface of aunit length of wire to the water is 2nrQ which must be
equal to the heat generated from the corresponding
surface, rrr’ W, then, from equation (3):T, - T, = QrJ%.

(4)

This(T, - pis within 1°C for platinum and nickel wire,a.nd is less than 2-3°C for nichrome wire. If we would
make more precise correction, we should also consider
the variation of the electric resistance due to thetemperature difference of the surface and the interior of
the metal wire; i.e. the surface of the wire may csrry
more current because of its lower temperature and its
lower resistance. With this consideration, (T, - T)
could be obtained by solving a simply formulatedBessel function. When it is done, the value of (r, - T,) isactually Lessthan the one obtained from equation (4)+and is within $C. fn the present experiments, we cannever neglect the correction made with equation (4),because of the imperfect reproducibilityof theexperimental results and of item (2) to be discussed,
Although the correction can be easily done, it may not
positively assure the improvement of the final result.
This will be better expiained in item (2).
(2) The surface temperature of the metal wire is by nomeans uniform. This is due to the non-uniform, local
generation of steam from the surface. When thevaporization is mild, the bubbles are seen first from thesurface where there are scratches or impurities on thesurface, then gradually the same bubbling is observed
from other locations of the surface after a few seconds.
Once the vaporjzation gets vigorous, most of thesurface is covered with steam bubbles, but still there issome part of the surface which is in direct contact withwater instead of with steam bubbles. Therefore, thesurface temperature will never be everywhere the same,and the surface temperature we recorded during theexperiment is therefore only an average value. The
degree of non-uniformity of this surface temperature is
not yet certain; however, it may be in the order ofmagnitude of A7’,if we consider the temperature for thesurface where it is in direct contact with the water to be
100%. But, actuatly the temperature of this part ofsurface is higher than the boiling point of theHeat transmitted from metal to boiling water

surrounding
water, and therefore
the degree oftemperature non-uniformityof the metal surface is lessthan AT [4]. In view of all these considerations,the few
degree centigrade non-uniformity
in temperature is notvery surprising. Inaccurate measurements
may also
introduce this amount of error.
The experiments
were run with platinum, nickel,
nichrome, iron and fuse wires. The results with iron andfuse wire were similar to those with others, except that
their surfaces
were more seriously
affected byelectrolysis. Thus, we have omitted the data for iron andfuse. The experimental
results
were not quite
reproducible, therefore, the average value from several
runs of the same size and same kind of metal has beentaken. The dimension ofmetals and the number of runs
is summarized in Table 1.

Table 1

DiameterdL
Length(mm)(mm)

No. of
runs

0.14
0.14
0.40
0.535
0.575

200
200
200
200
200

8
10
20
I
9

Metal
Platinum wire
Nickel wire
Nickel wire
Nichrome wire
Nichrome wire

963

Tables 2 and 3 are lists of some data for illustration.
Table 2 is for Run No. 6 with nickel wire of d = 0.14 mm
and Table 3 is for Run No. 3 with nichrome wire of
d = 0.575 mm. The experimental data and the calculated
Q and o!are listed in these tables. The numbers in the lastlines of Tables 2 and 3 are the values for the moment
when the metal wires burned out, but in the columns for
LY, the maximum
values appear
in bold type
before the last line in Tables 2 and 3. Figures 49 are theplots ofQ vs T(the temperature of the metal wires) fromthe experimental
data for various metal wires. The
curves have been drawn in such a way that a straightline is connected
betweenevery two adjacentexperimental
points. The temperature
for water has
been assumed at 100°C for all cases, and the last point inevery graph represents the point when the metal wire
burned out. The results as shown are rather scatteredamong each individual
set of data ; however,arepresentative
curve is drawn in Fig. 10 for each metal
wire. Figure 11 is the c(vs T curve, where a is calculated
from experimental data. The a-curves for metal wire of
d = 0.14 mm were omitted, because of inconsistent
results.

INTERPRETATION OF RESULTS

As has been previously
mentioned,
different
positions on the surface of a metal wire may have

Table 2. Experimental results for Run No. 6, nickel wire of d = 0.14 mm

Q

a

a

A

V

W

cal

(Cal/cm’ s)

AT(Cal/cm’ s “C)(kcal/m* h “C)

1.2
4
8
10
15
20
25
30
34
35
38
39.4

0.25
0.8
1.6
2.0
3.1
4.1
5.2
6.1
7.0
7.3
7.9
8.2

0.3
3.2
12.8
20
46.5
82.0
130
183
238
255.5
300
323

0.0715
0.763
3.05
4.76
11.07
19.52
30.96
43.51
56.68
60.85
71.5
76.9

0.0284
0.303
1.214
1.896
4.41
7.775
12.33
17.35
22.51
24.23
28.46
30.6

0.8
4.1
9.3
10.5
12.5
14.3
17.0
19.3
23.5
26.5
30.0
32.5

0.03550.0645
0.130
0.181
0.353
0.544
0.126
0.913
0.965
0.915
0.949
0.942

1277
2320
4680
6500
12700
19 56026 10032 90034600
32 90034200
33 900

Table 3. Experimental results for Run No. 3, nichrome wire of d = 0.551 mm

Q

a

A

V

W

cal

(Cal/cm’ s)

AT(Cal/cm’ s “C)(kcal/n? h “C)

1
5
10
15
20
22
24
25
26
26.7

0.8
4.2
8.25
12.8
11.0
18.7
20.5
21.4
22.3
23.0

0.8
21.0
82.5
192
340
411.4
492
535
580
614

0.191
5.0
19.6
45.7
81.0
98
117
127.4
138
146

0.0527
1.385
5.44
12.66
22.42
27.15
32.43
35.29
38.22
40.48

3
8
13.5
18.8
25.7
31.0
35.5
38.0
44.0
46.5

0.0176
0.173
0.403
0.674
0.873
0.876
0.914
0.928
0.869
0.860

634
6230
15500
24 30031400
31600
32 900
33400
31300
31000

SHIRO NUKIYAMA

30
;
p 20
5
G

“E

IO

0I
90

Temperature af metal wire, r(t)FIG. 4. Platinum

wire, d = 0.14 mm; water temperature= 100°C

Temperature of metal wire,

FIG. 5.Nickelwire,d

T

100

110

Temperature(“C)= 0.14mm;watertemperatureloo= 100°C.

110

130

I0

wire, T (“C)

FIG. 7. Nickel wire, d = 0.40 mm (Nos. 1l-20); watertemperature = 100°C.

different ab curves (Fig. 2), because the temperature
varies from position
to positionon the surface;
however, when any of these points reaches b, the wireburns out. Experimentally,sometimes the wire burnedout before it reached point b. Suppose on the average,
the wire will burn out at b, ; then the differences betweenb and b, will depend on the diameter of the wire-thesmaller the diameter of the wire the smaller will be thedifference, so the value Q,,, and the correspondingAT
are smaller for wire of smaller diameter. In Fig. 10 theburn-out point observed ford = 0.14 mm is at the point
where the Q-curve begins to show a change of slope,though the burn-out points as experimentally detected
lie below the Q,,, the CCcalculated in most cases isbeyond the maximum point in the curves (Fig. 11). The
result varies somewhat
with the material
used.
However,
if we take into accountthe possible
experimental
error involved, we conclude that theresult may be independent of the material used.

120

Temperature of metal wire, T (“C)
FIG. 6. Nickel wire, d =120of metal

0.40 mm (Nos. l-10); water temperature = 100°C.

Heat transmitted from metal to boiling water120
of metaL wire, T (“C)

I IO

loo

90

Temperoture

130

965

140

FIG. 8. Nichrome wire, d = 0.535 mm ; water temperature = 100°C.

Figure 12 is the result of the experiments with nickel
wire of d = 0.19 mm and with water temperature at 70,
80, and 9O”C,respectively. Q,,, is rather great when thetemperature of water is low. The experiments withwater at these temperatures were more difficult tocontrol, and there might have been introduced an error
ofabout 10”Cin the value ofAT. Figure 13 presents thevalues for x as obtained from Fig. 12.
THE EXPERIMENTS AND THE RESULTS
DETERMINATION

OF THE MINIMUM
OF

OF THE
VALUE

Q

The equipment is the same as the previous one;however, in order to lower the temperature at d (Fig. 2),
the platinum wire of 0.14 mm diameter was used1

because it has a smaller value of Q,,, and is more
durable at higher temperature. When the state moves
from b to d in Fig. 2, the electric resistance of theplatinum wire R increases rapidly due to the rise of thetemperature. When the resistance R, in the circuit
CDER,H (Fig. 3) is greater than R, the current I is not
lowered much by the increase of R ; hence, the quantityof heat 12R is very much increased. In this case, point dof Fig. 2 is at a position higher than point b and at atemperature so high that even the platinum wire ismelted. However, if we reduce the value of R,, thedifference between the Q at d and the Q at b is lessened.
For this reason, we have used a smaller value of R, inorder to prevent the burn-out of the platinum wire.
(Recall that we have used large values of R, in thedetermination of Q,,,. The change to smaller R, is toobtain a more adjustable range of the current.) Even so,
the point tends to jump from lower position to a higher
position as shown by the arrow in Fig. 14.
Experimentally,
the minimum value of Q wasdetermined by reducing the current from the hightemperature regime beyond the point b. In the vicinityof the minimum value of Q, the platinum wire turns
from shining color to red or dark-red spot, and when itu

110

Temperature

120

I30

of metal

wire,

FIG. 9. Nichrome wire, d = 0.575

140

I

T PC)

mm; water temperature= 100°C.

passes the point Qmin,the temperature rapidly decreases
and the gaivanometer fluctuates, the brightness of thewire disappears completely and the wire returns to theinitial state. Experiments were run with 12 platinum
wires and the results are shown in Fig. 14.The resistancevs temperature curves for platinum wire at higher
temperature were extrapolated from the data obtained
for the calibration with oil at temperatures below
200°C. The resistance vs temperature curve for aplatinum wire changes every time after the wire is used
once. The reason for this may be due to the annealing

966

SHIRO NUKIKAMA

I 600 COO
Nichrom
d= 0.53!

TX)

FIG. 10. Average value of Q for various

metal

effect or the expansion of the platinum wire under
tension during the strongly heating process, or may be
due to the effect of electrolysis. It is not yet completely
explored. We presume that all these have caused somelOC.of error in AT, especially at higher temperatures.
During the tempering process, the metal is changed
from high temperature along the Q vs AT curve. Whenit reaches Qmin, it instantaneously
passes Q,,,, andliberates a large amount of steam. The wire finallybecomes black. The Q vs AT curves can be used todetermine the temperaturechange of the material.
Therefore, if we study the case of water in motion or use
other liquids instead of water to obtain the similar Q vs
AT curves for each case so as to investigate
themechanism of tempering of metals, we may be able toget some very interesting results.

wires; water temperature = 100°C.

EXPERIMENTWITH A FLAT PLATEAS HEATING ELEMENT

A horizontal flat plate with the water boiling on the
top surface was used. The Q vs ATcurve must vary withthe size of the flat surface used. Facing the difficulties ofbeing not able to supply sufficient heat to the large flat
surface, we had to limit ourselves to two circularsurfaces of small diameter, 10 and 6.58 mm, in order toobtain the Q,,, for the flat plate. Figure 15 is theapparatus set-up : A is a copper solid cylinder with asmaller neck in B, where ab is the heat-transfer surface.
C is a cap made of ebonite or of porcelain in the insideand carbonized corks in the outside parts. They wereused as the heat insulators. But, if one uses the porcelain
and carbonized corks, care must be taken to avoid

T (“C)

FIG. 11. Averagevalue of c( for various

metal wires; water temperature= 100°C.

967

Heat transmitted from metal to boiling water

Wire temperature
FIG. 12. Q curve

T (“C)

for water temperature below 100°C.

absorbing water. The resistance wire D was wound on
the electrically insulated surface of A and the wholesystem was insulated with asbestos. The heat generated
in D is transmitted to the good conductor A and then to
the surface ab by means of B. In this way, we have beenable to supply the necessary heat to the surface ab.
There might be some heat loss through C, but it is verysmall comparedto the magnitudeof the heattransmitted
to the water through ab, because theconductivity of C is only &of the conductivity of B.
This fact was experimentallytested by attaching

Wire tempemture T PC)

below 100°C ; platinum
wire, d = 0.19 mm.

FIG. 13. a curve for water temperaturethermocouples(copperPconstantan)
to two positionsof B, and to a point in the water close to the surface ab.
The axial temperature distribution as shown in Fig. 16
is a straight line. Thus, the radial heat loss from ab tothe water was calculated from TI and T2 (Figs. 15
and 16) and the thermal conductivityof copper.
The thermal conductivityof copper was taken as
320 kcal/m h “C = 0.89 Cal/cm s “C.
The copper element AB can hold 10 cal of heat, sothat we have to reduce the frequency of the current
variation. But, it was found that the frequency of
current variation did not affect the experimental resultsvery much. The temperatureof ab was found by
extrapolating
the line between xi and x2 (see Fig. 16).
The heating current, I, was recorded in addition to Tl
and T,. When Q reaches the maximum value, T, and T2change very rapidly, and with our measuring devices,
we could only record Tl and I. T2 is then obtained fromTl, I and Fig. 16. With the Tl and T2 we can calculate theAT. The results arevalue of Q,,, and the corresponding
shown in Fig. 1, where for a smaller heating surface, wehave a larger value of Q at a certain AT reading, suchis also greater for smaller heating surface. To
that Q,.,go a step further, we have designed a device to study theeffect of the flow pattern on the Q,.,. The 10 mm
circular surface, with a hollow, ebonite cylinder of thesame diameter as the copper surface (top of Fig. 1) wasused to control the flow ofwater adjacent to the copper
surface. Notice that there is an adjustable thin plate
which divides the ebonite cylinder into two parts. The
experiments were repeated with various S, which is the
distance between the dividing plate N and the surface
ab. When inserting the dividing plate N, the steam
bubbles arise along the sides of N and the circulationof water is laminar even with vigorous
boiling.
Experiment for each value of S was repeated 4-5 times
and the average results are presented in Fig. 1. Lifting
the distance S 1 mm each time speeds up the flow ofwater, so that Q has a greater value at a certain AT, andso Qmx is also greater. But, when S becomes infinity, i.e.
without the dividing plate N, the flow becomes very
turbulent and the Q,,, becomes small again. Figure 17
is the a-curve as calculated from the above results,
which is similar to Fig. 11 for the case of metal wires.

CONCLUSIONSAND SOME AUXILIARYOBSERVATIONSIN THE EXPERIMENTS

There exists a maximum value of Q for the Q vs AT
curve, which is independent on thematerial ofthe metal
heating surface. The values of Q,,, are rather greatcompared to the value of AT, which are about 2&4O”C
as has been determined experimentally.
The Q,,, isabout 30-50 Cal/cm* s for all dimensions of different
heating surfaces, except for the tiny metal wire,
provided
there is no disturbanceto the naturalconvectionof the water. This value for Q,,X is far
greater than the value which was conventionallyaccepted. In ordinary evaporators, the value for Q is less

SHIRO NUKIYAMA

968- 14x IO5
- I2 x IO5- IOx I05
-a

x 105

=
ri
yo

-6: I I05

0

x I05

x I05

I

I

I

I

I

I

200

400

600

800

1000

I200

Temperatureof metal

wire,

T PC)

FIG. 14. The determination of Q,, for the platinum

than 3 Cal/cm’ s even at the position where it is closest
to the furnace. Therefore, under normal conditions, theheating surface will never reach the spheroidal state,
except possibly when there is scaling on the surface ofthe evaporator. The problem of scale and the cases for
local pressure difference will be treated in the later
study.
In the experimentswith metal wires some sparks
along the surface of the wire were observed. As has been
mentioned previously, when Q is small, the bubbling ismild [ 11, but when AT is about 12”C, no matter if thewire of d = 0.14 mm.

temperature of water is 100°C or lower, the generationof steam bubbles becomes suddenly violent, so that all
the heating surfaces are covered, and Q abruptly
increases at this temperature in the Q vs AT curve.
What is the temperature of water in contact with thesurface, when AT is 20 or 3o”C? Granting that there
should not be a sudden change on the interface of solidand liquid, we conclude that the water is being
superheated. Partridge and White [S] has experimentally studied the mechanism of steam generation fromthe dry spot, mn on a surface (Fig. 18). The temperature

FIG. 16. Axial temperature
FIG. 15. Apparatus

for the flat plate experiment.

distribution
experiment.

for the flat plate

Heat transmitted969

from metal to boiling water-_-----------_-__---_--_--_--_---------------------_----_____-__---_--------__-__-----_--------__-_---------------------------------___--------__--_----------____~-:~~I~~___

FIG. 18

0

I

I

I

10

20

30

I

40”

AT PC1
FIG. 17. AT vs a curve; water temperature= 100°C.

at this spot on the metal surface is much higher thanthat of water; therefore, we should say that the AT isactually the average of the temperature of a few higher
temperature spots and most of the 100°C parts.
Of course, superheating
is required
before thepressure can overcome the surface tension of water togenerate steam bubbles in the water. The present
author has been attempting for years to measure thedegree of superheating, but has unfortunately failed. In
1932, Jakob and Fritz [4] first succeeded in themeasurement and they confirmed that it is superheatedsomewhere
near the heating
surface.
But, thismeasurement was at the position about 1 mm from thesurface, and only 1°C superheating
was reported. It

remains as an area for someone to measure the degree ofsuperheating at a location closer to the surface.
In the present experiments, the temperature of water
should be able to keep at 100°C with heating on theoutside of the water container and with the inside
heating element. But, as Q becomes large, the watertemperaturesometimes dropped 0.220.5”C; and theexperiment was forced to pause (to find the possible
cause of discrepancy). The author thinks that it might
be due to the steam bubbles which encourage thevaporization and subcooling of the adjacent water andthere is a heat flow from the bulk water to the water
adjacent
to the steam
bubbles;
therefore,
thetemperature of the bulk water dropped.

REFERENCES
1. L. Austin, Z. VW. Dt. Inq. 46(2), 1890 (1902).
2. M. Jakob and W. Linke, Fors. 3,75580(1933). (Also refer toabstract No. 82, J. Me&. Sot. (1933).)
3. K. Oga, Introduction to Heat Transfer and its Application,
p. 139.
4. M. Jakob and W. Fritz, Fors. 441 (1931).
5. E. P. Partridge and A. H. White, Ind. Engng Chem. 21,834(1929).

LES VALEURSMAXIMALEET MINIMALE
DE FLUX THERMIQUEQ TRANSMISMETAL A L’EAU BOUILLANTE
SOUS PRESSION ATMOSPHERIQUE

DU

RbsumC Le flux de chaleur transmis d’une surface metallique a I’eau bouillante croit quand la difference detemperature
AT croit, mais apres que AT ait atteinl une certaine limite, le flux Q diminue si AT continued’augmenter.
Ce point de changement est la valeur maximale du flux transmis. L’existence de ce point a irte
observte dans les experiences. Sous la pression atmosphirique,le AT correspondantd la valeur maximale detransfert pour l’eau a 100 C est a 2G40 C, et Q est entre 2000 et 3000 kg/m* h. Ce rtsultat est superieur a lavaleur maximale anterieurement
consideree. Aussi la valeur minimale du transfert thermique a et& obtenue etsur la courbe Q-AT pour la region des fortes temperatures,on discute l’effet de brtilage.

MAXIMALE

UND MINIMALE VON METALL AN SIEDENDESWP;RME BE1 ATMOSPHARENDRUCKWASSER UBERTRAGENE

ZusammenfassungDie von einer Metalloberflache
an siedendes Wasser t’ibertragene Warme nimmt mit
steigender Temperaturdifferenz
zu. Nachdem jedoch AT eine bestimmte Grenze erreicht hat, fallt derWarmestrom
mit weiterhin zunehmendem
AT ab. Dieser Wendepunkt gibt die maximal iibertragene WCrmean. Es wurdeim Experiment beobachtet,daB
dieser Punkt tatslchlich existiert. Beimmaximalen
Wlrmestrom
fur Wasser bei 1OOC liegt AT zwischen 20 und 40°C und Q erreicht Werte zwischen 1080 000 und 1800 000
kcal/m’h (d. h. 2000 bis 3000 kg/m2h, wenn man es durch eine konstante Verdampfungsgeschwindigkeit
bei
100°C ausdriickt). Dieser Wert ist gr(iBer als das Maximum der iibertragenen
Warme, von dem man friiher
ausging. Weiter wurde das Minimum der tibertragenen
Warme ermittelt, und der Burnout-Effekt
anhand der
Q-AT-Kurve
fiir den Hochtemperaturbereich
diskutiert.

970

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