ORNL-1370.txt

 

54

HT T

LIDELARVEVAREA
3 4456 03L0LOS 1 ORNL-1370
Physics

  
  

  

TURBULENT FORCED CONVECTION

*

HEAT TRANSFER IN CIRCULAR TUBES

   

CONTAINING MOLTEN SODIUM HYDROXIDE

   

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OAK RIDGE NATIONAL LABORATORY

OPERATED BY

CARBIDE AND CARBON CHEMICALS COMPANY

A DIVISION OF UNION CARBIDE AND CARBON CORPORATION

(=4

POST OFFICE BOX P
OAK RIDGE. TENNESSEE
 

UNCLASSIFIED
- ORNL-1570

This document consists of 42

pages. Copy R of 384 copies,
Series A.

Contract No. W-T405, eng 26

Reactor Experimental Engineering Division

TURBULENT FORCED CORVECTION HEAT TRANSFER IN CIRCULAR
TUBES CONTAINING MOLTEN SODIUM HYDROXIDE

H. W. Hoffman
Date Issued:

OAK RIDGE NATIONAL LABORATORY
Operated by
CARBIDE AND CARBON CHEMICALS COMPANY
A Division of Union Carbide and Carbon Corporation
Post Office Box P
Oak Ridge, Tennessee

MK

UNCLASSIFIED
 

 

_2- ORNL 1370

 

Physics
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ABSTRACT

An experimentel determination has been made of the heat transfer coefficients
for molten sodium hydroxide flowing in turbulent forced convection through a tube
of circular cross section and a length to diameter ratio of 200. Heat transfer
coefficients in the region of fully developed turbulent flow are reported for the
Reynolds modulus rasnge of 6000-12000 and the temperature range of 700-900°F. The
eguation, Nu/Pro'h = 0.021 Re°'8, was found to correlate the data for (L/D) values
above 100. Thermal entry lengbths are calculated for each run. Results show that
molten sodium hydroxide may be considered an ordinary fluid - i.e., any fluid other

then the liquid metals - as far as heat transfer is conecerned.
II.

III.

Iv.

TABLE OF CONTENTS

INTRODUCTION

EXPERIMENTAL WORK

A. Description of Apparatus
B. System Calibration

C. Method of Operation
RESULTS

A. Method of Calculation

B. Correlation of Heat Transfer Coefficient
C. Thermal Entrance Region
D. Analysis of Errors
NOMENCIATURE

BIBLIOGRAPHY

APPENDIX I. Sample Calculation

APPENDIX II. Physical Properties

APPERNDIX III. Solution of Conduction Equation for Tube

with Heat Generation in Wall

t:~a ~ w |
o
[1]

18
21
21
2L,
29
32
33

35

36
38
L0
 

 

INTRODUCTION

Sodium hydroxide can be used as a high temperature heat transfer medium.
This fluid freezes et 604°F and possesses temperature stability to at least
1200°F. No data on the heat transfer properties of molten sodium.hydroxide
are available in the technical literature. Therefore, an experimental in-
vestigation was underteken to determine the convective heat transfer coefficient
for this fluid in turbulent flow within tubes of circular cross section.

In designing heat transfer equipment it is necessary to know the conductance,
or coefficient of heat transfer, between a surface and the fluid flowing past
the surface so as to be able to estimate the amount of heat transferred or to
prediet the temperature differences existing within the system. This coefficient

is defined by the equation
ho A (1)

where (q/A) is the heat flux through the metal-fluid interface in Btu/hr-£t°,
tg, the temperature of the metal surface at this interface and t,, the fluid

mixed-mean tempersture. A number of investigatorsh’s’a*

have developed systems,
both of the double-tube exchanger type and the single-tube electrically hested
wall type, which enable determination of the temperature, tg. For reasons of
simplicity of assembly and more accurate determination of the heat input and the

heat transfer area, the electirically heated test section was chosen for this

experiment.

 

*Nunbers refer to references to the literature glven in section v

 

e i e bt e
6

Several factors mist be considered in designing this type of test unit

for use with molten sodium hydroxide.

1.

Corrosion. The extreme corrosiveness of molten sodium hydroxide
drastically restricts the materials available for constructing the
system. At the time the problem was begun, static corrosion test32
indicated that only three construction materlials would be acceptable
for a system containing sodium hydroxide. These were pure silver,
graphite and A-nickel. Of these silver appeared to be the best
material. However, silver is structurally weak and at high tempera-
tures is unable to support its own weight. To be effective corrosion-
wise the silver must be oxygen free and thus the cost of a silver-
lined system becomes prohibitive. Graphite would require heavy,
awkward structural sections to give sufficient strength. Hence,
nickel remeins as the only feasible construction material. While
weeker than most construction metals it still possesses reasonable
strength at.high temperatures and is commercially available in most
of the required forms.

Electrical Conductivity. While the electrical conductivity of molten
sodium hydroxide is not high as compared to the liquid metals, 1t is
still sufficlently large to necessitate that the system be designed to
minimize.the heat generation in the test fluid. From this aspect
nieckel was also satisfactory since its electrical conductivity was

such as to allow 95% of the heat generation to occur in the tube well

for a reasonably sized experimental system.
3. Pumps. Due to the unavailability of pumps for handling molten
sodium hydroxide another method of causing fluid flow through
the system must be devised. This was aecomplished by pushing
the fluid through the system under the pressure of an inert gas,

argon .

4. Melting Point. The high melting point of sodium hydroxide (604°F)

increases the difficulty of system design.

II. EXPERIMENTAL WORK
A. Description of Apparastus

The experimental system designed to measure the heat transfer
coefficient is illustrated schematically in Figure 1. It consisted of
a sump tank, a test section with associated power supply and temperature
and power indieating de;iees, a tank resting on a scale for measuring the
fluid flow rate and a gas system for moving the fluid through the test
section. Figures 2, 3, and 4 present several views of the apparatus.

The sump and weigh tanks were electrically heated by strip heaters,
and the lines connecting the test section to the tanks were traced with
Calrod heaters. The entire system was well-lagged and was maintained at
a temperature of 650°F. Preliminary tests indicated that even when the
weigh tank was rigidly connected to the rest of the system the scale
readings were consistent and accurate. This was checked by visually
observing the scale action while introducing weighed amounts of water into
the tank and while placing weighed lead bricks on the scale. It was possible
to reed the weight of fluid entering or leaving the weigh tank to within

1/2 pound.
UNCLASSIFIED
DWG. 16324
THERMOCOUPLES

VY \/

©®

 

00000000000000Q
(0060000 0005000)

|
l
|
| l  POWER SUPPLY
|
|
|

 

 

 

l— ————————— GAS SUPPLY b—m—— — — — — —I

 

 

 

Test Section: Nickel Tube-3/16"0.D. X 0.035"
Wall Thickness X 24" Long.
22 Thermocouples welded to

outside tube wall.

Fig. l. Schematic Representation of System for Measuring Heat Transfer
Coefficients of Molten Sodium Hydroxide.
 

UNCLASSIFIED
Y-12 PHOTD 65227

T

 

 

TL AR d!

 

 

ekl

FIGURE 2. VIEW OF PANEL BOARD
 

S S T e IS UNCUASSIFIED
P - E s Rl v - 17 PHOTO 65225
: , f = ' f a5 3 ] ;

..fi

i}

 

FIGURE 3. GENERAL VIEW OF EXPERIMENTAL SYSTEM

— Ok —
LN (Ia.a Hli‘n
Y. 12 PHOTO 63226

 

. POWER LEADS .
Tir’- VOLTAGE TAPS:;> !

| Wfi

= 1."--‘, e

MIXING POT R . TEST SECTION
9 TuBE WALL e e

“THERMOCOUPLES S

-
!
- g
¥ - . i s -
- - e
i .,.H T

FIGURE 4 TEST UNIT

 
 

12

In the design of an electrically heated test section, the size of
the tubing used is dictated by severai factors; namely, allowable pressure
drop through the test seetion, desired length to diameter ratio, avail-
ability of the proper size tubing, the temperature drop through the tube
wall as related to the temperature difference between the inside tube
surface and the fluid mixed-mean, the physical size of the system as
related to the fluid inventory, the minimization of heat generation in
the test fluid and the total power available. On the basis of these
considerations a test section was designed of nickel tubing, 3/16" 0.D.

X 0.035" wall thickness, 24 inches long. With this test section & Plow
at a Reynolds modulus of 10h could be obtained with a pressure drop of
35 psi. The heat generated in the tube wall accounted for 95% of the
total heat generation.

Since gas pressure was used to move the molten sodium hydroxide
through the test seetion, the system.wfis capable only of intermittent
operation with the fluid Fflowing first from the sump to the weigh tank
and then from the weigh to the sump tank. A total of 220 pounds of sodium
hydroxide was put into the system.

The power was supplied to the test section by a transformer capable
of delivering a maximum of 360 amperes at 7.5 volts. This was introduced
to the test section through small rectangular copper flanges silver-soldered
to the tube at the inlet and outlet of the test seetion. The current to
the test section was measured with a multi-range ammeter. The accuracy of
this meter is claimed as 3/4%.

The temperature of the outer surface of the test section was measured
at 20 points along the tube and at the power flanges at the inlet and outlet

of the test section. The couples were of 36 gage chromel and alumel wire
 

15
and were welded to the tube surface by a single-pulse resistance welder.
They were then wrapped around the tube for about one-quarter of a turn
in order to minimize conduction losses along the thermocouple leads. At
the two ends of the test section thermocouples were encased in pieces of
two-hole ceramie insulator, inserted in small holes in the power flanges
and arc-welded to the tube wall. All couples were then connected to a
Leeds and Northrup portable precision potentiometer through selector
switches. A commofi cold Junction was used. This consisted of an ice-water
mixture in a one pint Dewar flask which was Jacketed by a can filled with
thermal insulation.

Temperatures for control purposes were measured by thermocouples of
28 gage iron and constantan wires located along the tubing and in thermo-
wells in the tanks. The temperatures were indicated on a precision
temperature indicator.

The voltage was measured at the 10 locations along the test section
indicated in Figure 5. Two of these voltage taps were loceted on the power
flanges to the test section. The voltage taps were of 28 gage bare copper
wire, arc-welded to the tube. These were then ecoated with #7 Sauereisen
cement to reduce oxidation of the copper at the operating temperature of
the system. The volltage was measured by a multiple-range Ballantine
electronic voltmeter, for which an accuracy of 2% is claimed.

The mixed-mean temperature of the fluid entering and leaving the
test section was obtained by inserting mixing pots in the test line. These
were located one inch from the inlet and outlet of the test section. The
mixing pot was & two inch length of standard one inch nickel pipe capped
at both ends. A perforated nickel disc was located at the ecenter. The

inlet and outlet were tangentially positioned at the top and bottom.
Volts

UNCLASSIFIED

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

DWG. 16325
_”
AT
o
5 /
4
'
>
3 /
2 /
s
/,
| 7
//
//
O
0 2 4 6 8 i0 12 14 16 18 20 22
Distance from Entrance of Test Section, inches

Fig. 5. Voltage Impressed on Test Section as a Function of Tube Length.
 

15
Thermowells were placed immediately behind the inlet and before the
outlet. A mixing pot is shown in Figure 4. It is believed that with
the whirling flow caused by the tangential inlet and the mixing caused
by the diffuser dise, & good mixed-mean temperature was obtained. An
aixalysis of the error due to conduction losses by the thermowell at an
average fluid temperature of 950°F shows the correction to the observed

thermoeouple reading to be negligibly smell. The mixing pots were

- wrapped with a double layer of monel-sheathed nichrome heating wire.

The current ‘through these heaters was adjusted to maintain a temperature

of approximately 650°F in the mixing pot so as to prevent freezing of

the sodium hydroxide and reduce heat loss from the fluid.

The entire test unit - test section plus mixing pots - was Jacketed

by a metal container filled ?i'l;h thermal insulation.

System Calibration

 

1. Heat Loss
In order to obtain an estimate of the heat loss from the

system, current was passed through the tube wall without fluid
flow through the test section. At equilibrium, the power input
for a given average tube wall temperature with no fluid flow was
taken to be the system heat loss for the same average tube wall
temperature with fluid flow. The outside tube wall temperature
is shown in Figure 6 as a function of the distance along the test
section for various power levels. Figure 7 shows the system heat
loss as a function of At, where At ris the average outside tube wall
temperature, by gyve, minus the temperature of the system environment,
te. The average outside tube wall temperature was cbtained by

graphical integration of the curves of Figure 6.
1200

10O

1000

900

800

ELECTRICAL HEAT
INPUT, Btu/hr:

o — 33}
A— 310
0— 269
v— 214
¢— |98

Outside Wall Temperature, °F
fl
o

600

500

400
0 2 4 6 8 10 12 14 16
Distance from Entrance of Test Section, inches

 

UNCLASSIFIED
DWG. 16326

 

18 20 22 24

Fig. 6. Axial Profiles of Outside Tube Wall Temperature for Varying Heat Input with no Fiuid

Flow.
UNCLASSIFIED

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

DwG. 16327
350
3
300 /(
A
250 7 o
£
.
3200
lva)
- S’ L
150 /
100 ///
50 /,l
//
O« /
0 100 200 300 400 500 %OO 700 800 900 1000
(fw ave "fe ’ °F
, .

Fig. 7 Heat Loss from Test Section
18

2. Thermocouple Calibrafion

 

Bead thermocouples of 36 gage chromel and alumel wire were
calibrated at the melting points of lead and zine. OSamples of
the wire used for the tube wall thermocouples were calibrated
in a tube furnace. The results of these calibrations are in-
dicated in Figure 8. A maximum correction of 5°F at 900°F was
observed.

3. Effect of Tube Current on Thermocouples

 

The possible effect of the current flowing through the tube
wall on the readings of the thermocouples attached to the wall was
considered. Therefore, with no flow through the tube, the system
was allowed to reach equilibrium and the reading of one wall thermo-
couple recorded. The power to the tube was then turned off and
readings of this thermocouple taken every 15 seconds. These power-
off readings were then extrapolated back to zero time. As is seen
from Figure 9, the current in the tube wall has no effect on the

readings of the thermocouples.

Method of Operation

 

Prior to operation, the entire system - sump and weigh tanks and the
test unit - was heated to an average temperature of 650°F. During a
sequence of runs this temperature would drift up to about 750°F due to the
heat put into the fluid by the test section. The desired flow rate was
obtained by proper adjustment of the gas pressures at the sump and weigh
tanks. Runs lasted from 20 to 40 minutes depending on the fluid flow
rate. Tt was found that during this period the system reached approximate

equilibrium. This is indicated in Figure 10 which gives the readings
 

2

O

0

1., millivolts

Test Thermocouple Reading,

5

o

o

@

~1G- UNCLASSIKIRD
DWG. 16328

 

 

 

 

 

 

 

 

*c = tfr

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

O— BEAD THERMOCOUPLES

 

CALIBRATED AT MELTING
POINTS OF Pb & Zn

 

 

 

x— TUBE WALL THERMOCOUPLES
CALIBRATED IN TUBE FURNACE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4 6 8 10 12 14 16
True Reading, t,, millivolts

Fig. 8. Calibration of Thermocouples

18
UNCLASSIFIED
DWG. 16329

 

 

 

 

 

 

 

 

 

@® —-THERMOCOUPLE READING WITH CURRENT ON,

 

SYSTEM AT THERMAL EQUILIBRIUM,

 

o
O

O —THERMOCOUPLE READING WITH CURRENT OFF.

 

 

 

 

o
O

 

g, mitlivolts

»
o

 

 

 

»
o

 

-0z~

 

Themocouple Readin
N
i

o
O

 

 

2.5

 

2.0

 

 

 

 

 

 

 

 

 

 

 

30

45 60 . 75 90 105 120 135
Time, Seconds

Fig.9. Effect of Current on Tube Wall Temperatures

150
 

21

from a given thermoecouple as a function of time during an experimental
run. The tube wall thermocouples were read every 3 to 5 minutes during
a run. Data were obtalned with the fluid flowing from the weigh to the
sump tank, as well as from the sump to the weigh tank.

The sodium hydroxide charged to the system had an original assay of
98.5% NaOH, 0.31% NapCO3 and the rest water. The water was removed during

the melting cyele by maintaining the systeém under vacuun.

ITI. RESULTS
 A. Method of Caleulation
The coefficlent of heat transfer at any point, x, along the test
section is known as the local coefficient of heat transfer and is defined

| by the equation
(tS = EE x .

For values of x large enough to be beyond the thermal entrance region,

hx =

hx reaches a limiting value, h, the coefficient of heat transfer for the
region in which turbulent flow has been fully established both thermally
and hydrodynamieally.

In order to determine the local coefficient of heat transfer, it is
necessary to obtain from the experimental data the heat flux, the tempera-
ture of the inside wall of the tube and the fluid mixed-mean temperature
at each point along the tube.

The inside tube wall temperature is calculated from the measured

outside tube wall temperature by the equation

2
where the subscripts w and s indicate the outside and inside tube walls,

. 2_p 2
ty-ts = 2#;1.(EW2 In Ty/Ts - Ta 75 ) (3)

respectively, and r is the tube radius; ky; is the thermal conduetivity of

the nickel tube.
UNCLASSIFIED

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

DWG. 16330
20 33
___-ii—-——J""

Qo
Z '
'E //
o -
c
ol9
o
Q
o
Q
a
=3
Q
O
O
e
Py
£
}.._

18

17

4 6 8 10 12 i4 16 18 20 22

Time, minutes

Fig. 10. Variation with Time of Thermocouple 10 During Run 12 Showing
Approach to Equilibrium.

 
 

25
This equation takes intc account the effect of the heat generation
in the tube wall on the temperature drop through the wall. The
derivation of this equation is given irn Appendix III. The source term,

W, is given by

 

w= & 3" I (4)

vhere E and I are the voltage and current at the test section, ¢ is
the conversion factor, 3.413 Btu/hr-watt, and V is the volume of metal
in ‘the tube wall of the test section.

It is assumed that the heat generation is uniform in the tube wall.
This is borne out by Figure 5 which shows the voltage impressed on the
test section as a function of distance along the tube for a typical
run. With uniform heat generation, the fluid mixed-mean temperature
as a function of the distance down the tube is given by a straight line
drawn between tp j and *m,o, the fluid mixed-mean inlet and outlet
temperatures, respeetively. Actually, dve to heat losses in the wvicinity
of the power flanges, not all of the heat generated is transferred into
the test fluid. This results in & slightly lower slope for the mixed-
mean temperature curve in the immediate vieinity of the power flanges
and a correspondingly slight raising of the slope tkrough the central
portion. However, since the heat loss through the power flanges was
found to be low, less thar 2% of the total heat input, the error intro-
duced by assuming a straight line between ty ; and ty o is small.

The total heat generation in the tube wall is determined from the
measured voltage drop across the test section and 4the current passing
through the tube wall. Part of the total heat goes to external loss

and the rest intc heating the fluid in the test seection. The external
 

24

heat loss can be obtained from Figure 7 for the average outside
tube wall temperature for the given set of experimental data. The
heat transferred into the fluid in passing through the test section
is given by the equation

ap = W ep(tm,0 - tm,1) (5)
where w is the fluid flow rete in 1bs/hr, and tp,o and tm,i the
fluid mixed-mean outlet ana inlet temperatures, respectively. The
heat transfer area is taken as the inside surface area of the test
section between the two power flanges. The heat flux was based on the
heat gained by the fluid as given by equation (5). This was checked
by the electrical power input corrected for the measured external heat
loss. A maximum deviation between these two of 9% was observed. The
heat balance for each run is shown in Table T.

A sample calculation for the determination of the loeal coefficient
of heat transfer is presented in Appendix I. Figure 11 shows a typical
tempereture profile for the inside tube wall.

The physieal properties of sodium hydroxide necessary to these
calculations are presented graphically in Appendix II. The physiecal

properties were evaluated at the average fluid mixed-mean temperature.

Correlation of the Heat Transfer Coefficient

By c¢onsidering the dimensionless differential equations describing
heat transfer and fluid flow, a2 mumber of dimensionless moduli arise
which characterize forced convection heat transfer in similar systems.
These dimensionless parameters (Nusselt, Reynolds and Prandtl moduli)
are functionally-related by the equation

Nu= & {(Re, Pr) (6)
UNCLASSIFIED

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

DWG. 16331
950
900 ot ™,
TUBE INNER WALL I,
‘Q-; —7 o™
=2
©
g -~
| "}
— /
FLUID MIXED-MEAN
850}~
(
800
0 2 4 6 8 10 12 14 16 I8 20 22 24
Distance from Entrance of Test Section, inches
Fig. Il. Typical Temperature Profiles Along Axis of Electrically Heated Test Section.

_ga_
 

26
Reynoldslz, Prandtlll, von KérménG, Boelter, Martinelli and
Jonassenl and others have determined the analytical form of the
function, ¢ , for turbulent flow by comparing heat and momentum
transfer within the fluid for several ideal systems approximating
real systems.

For convenience, equation 6 is usually written in the empirical

form _
Nu = a Rel PrP (n

where the constants a, n and p are experimentally determined. In
general n is taken as 0.8. Dittus and Boelter> found that equation 7
could be written as

Nu = 0.0243 Re0-8 PrO-* (for nheating) (8)

Nu = 0.0265 Re0-8 py0-3 (for cooling) (9)

McAdams? correlated data for both heating and cocling by the equation
Nu = 0.023 ReC-8 pr0-4 (10)

In Table I are listed the pertinent measurements and caleculated re-
sults of the présent sodium hydroxide experiment. The heat transfer
coefficient was ecaleculated for a position for down-stream (I/D = 100 or
greater) where fully developed turbulent flow existed.

Plotting the experimental data as Nu vs Pr for various values of
Re, it is seen that p in equation 7 is approximately O.4k. A least
squares analysis of the data then yields the result, a = 0.021. That is,
the experimental turbulent forced eonvection data for molten sodium
hydroxide can be correlated by the equation |

Nu = 0.021 Re0:8 pyO.% (11)
TABLE I

EXPERIMENTAT, DATA AND CALCULATED RESULTS - DETERMINATION OF
HEAT TRANSFER COEFFICIENT OF MOLTEN SODIUM HYDROXIDE

 

 

 

 

 

 

 

ap/A w te-ty tmo-tm 1 tw h Heat Balance

Run  Btu/hr-£t2  Ibs/hr  OF rge ot THgve Tmggve Btu/hr-£t°°F  (agtq) ‘ar)  Re  Pr  Mu
1 27,312 365 9.2 8.6 713 718 2970 0.93 6283 6.8 48.4
2 4,636 500 18.2 17.7 791 768 4100 0.97 10092 5.6 69.6
3 122,448 563 27.% 26.0 814 781 W70 0.96 11757 5.4 72.9
Iy 142,801 419 38.2 42.6 879 835 3740 0.98 10151 4.5 61.0
5 133, 8hL 410 38.1 40.2 876 830 3515 0.94 9808 4.6 57.3
6 113,604 392  30.7 36.4 895 859 3700 0.96 10019 L.2 60.3
7 122,561 ook  67.2 76.2 ol7 873 1830 0.99 5377 4.0 29.8
8 128,950 366 38.5 43.7 850 805 3350 0.94 8172 5.0 5h.6
9 124,220 ' 319 L42.5 h1.h4 861 812 2925 0.91 7258 4.9 .7
10 83, klr7 4ol 19.1 21.0 855 832 4370 0.95 11759 4.5 71.3
11 138,509 hho 32.8 38.3 879 839 4005 0.96 10957 k.4 69.0
12 134,868 336  41.3 50.7 o1k 866 3265 0.96 8758 4.1 53.2
135,258 293 6.0 59.2 o3 890 2940 0.95 8029 3.8 47.9
129,786 312 43.3 53.2 937 887 3000 0.93 8543 3.8 48.9
143,728 koo  36.3 42.5 875 832 3960 0.99 1009k 4.6 64.6
119,960 193 65.6 79.0 SLT 874 1835 0.98 5103 k4.0 30.0
 

UNCLASSIFIED

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

DWG. 16332
100 2
80
60 /
/,
40 £ /
Nu )
Ly N
pr 4 / v
v
’
/‘?
20 //,/
'
%o === MCADAMS, EQUATION 4c
EQUATION 7
10
2,000 10,000 60,000

Re

Fig. 12. Experimental Heat Transfer Coefficients for Sodium Hydroxide.
 

29
for values of the Reynolds modulus between 6000 and 12000.

The standard deviation of the data from this equation, assuming that
the Reynolds modulus is exactly known, is 0.00l.

The experimentel data are shown in Figure 12 with relation to
the derived correlating equation,ll, and the McAdems equation,l0. Tt

is seen that the data lie approximstely 9% below equation 10.

Thermal Entrance Region

It was possible to obtain from the experimental data for each runm,
the thermal entrance length. This length is defined as the distance
from the entrance of the test section at which the heat transfer
coefficient has reached a value within a given percentage of the
established value. The entrance length is normally expressed in terms
of the number of tube diameters from the entrance.

The local coefficient of heat transfer is shown in Figure 13 as
a function of the ratio, (L/D), for a typical experimental run. Figure
14 gives the variation of the thermal entrance length, (L/D)e, with the
Peclet modulus (Re-Pr). In the present investigation (L/D)e was taken
as the (I/D) at which the local conductance had dropped to a value of
1.1 of the established value.

Poppendieklo reviews the thermal entrance length dsta for an air
system (Hunble, Lowdermilk and Desmona measurements) and for a mercury
system (English and Barrett1+ measurements). Both of these experiments
were conducted under conditions of uniform heat flux. DBased on the
thermal entrance length criterion used in the present report, he found
that for air, (L/D)e = 15 or greater, and for mercury, (L/D)e = 5 or

greater.
UNCLASSIFIED

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

DWG. 16333
6,000
N .
r
< 5000
- \
m N
- B
=
_4,000 \
..u(:: Mw-—o—.wb #*fim—-
©
%
o 3,000 \L
o ?
©
O
o
|
2,000
Re= 10,000
Pr=4.2
1,000
00 20 40 60 80 i00 120 140 160 180

Pipe Diameters from Entrance, L/D

Fig. 13. Local Heat Transfer Goefficients for Sodium Hydroxide Flowing in a
Pipe Under Uniform Flux Conditions.
UNCLASSIFIED
ING. 16
50 334

 

 

40

 

/
30 7

 

20

 

\&*’ o

(L/D)e ®

'IE—

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5
10,000 100,000
Pe

Fig. 14. Thermal Entrance Length for Molten Sodium Hydroxide

300,000

s 1 2 ey AT R A R

 
52

Analysis of Errors

 

Error theory shows that for a function of several variables,
M=f(m, mp, ..., my), the maximum error in M, A M, can be approxi-

mated by the expression,

 

 

Am= O¥ oM oo+ OM :
m ?bnh.llflu,+ S0 Ay + + > Loy

However, it is to be noted that the actual error in M might not
equal the maximum error calculated, as errors in the various
measured quantities might offset each other.
Applying this type of analysis to the present experiment,
the following errors can be tabulated:
1. For the heat flux, (qf/A),
a. error in (tm,o - tm,1), 1%
b. error in flow rate, w, 0.6%
c. error in heat transfer area, A, 1.4%

for a total error of 3%

2. For the temperature difference, (tg - tp),
a. error in temperature, ty, 0.5%

b. error in temperature drop through tube

wall, ty - tg, 2%

c. error in fluid mixed-mean temperature,
Tm,

for a total error of 4.5%
Thus, the maximum possible error in h is 7.5%.
The precision of the experiment as indicated by the standard

deviation cbtained through & least squares analysis of the data

is 4.8%.
n,p

&

Q@ H P o=

~

’ (L/D)

At

 

33
Iv. NOMENCLATURE

Constant in heat transfer correlating eguation 7

Conversion factor, 3.413 Btu/hr-watt

Speeific heat of fluid at constant pressure, Btu/lb. fluid-OF
Inside diameter of tube, £t

Coefficient of heat transfer in region of fully developed
turbulent £low, Btu/hr-ft2-CF; hx, coefficient at position

x on tube.

Thermsl eonductivity of fluid, Btu/hr.ft° °F/ft; kyi, thermal
conductivity of nickel

Constants in heat transfer correlating equation 7

Rate of heat transfer, Btu/hr; gq,, heat gained by the fluid,
9] heat loss to the enV1ronmen£ des electrical heat input

Radius of tube, ft; Ty, outside wall, rg, inside wall
Temperature of environment, ©F

Fluid mixed-mean temperature, °F; tp i, at test section inlet;
tm,0, at test section outlet; tm.ave: arithmetic average of tp i

and tm,o0-

Inside tube wall temperature; tg ave, average

Outside tube wall temperature; ty, ave, average

Mass rate of flow, 1lbs. fluid/hr

Heat transfer surface, ft2

Voltage impressed on test section, volts

Mass velocity, lbs. fluid /hr-(Ft° of tube cross section)
Current passing through test section, amperes

Distance down tube from entrance, ft.

Length to diameter ratio for tube, dimensionless; (L/D)e, at end
of thermal entrance region

Volume of metal in tube wall, £t3
Volume heat generation, Btu/hr-ft3

Temperature difference, °F
Nu

Pr

Re

Pe

3l
IV. NOMENCLATURE (CONT'D)

Absolute viscosity of fluid lbs/hr.ft
Density of fluid 1bs/ot>

Nusselt modulus, dimensionless, (hd/k)
Prandtl modulus, dimensionless, (epM /k)
Reynolds modulus, dimensionless, (dG/™)

Peclet modnlus, dimensionless, Re-Pr, (“Pde)
1.

10.

11.

12.

25

V. BIBLIOGRAPHY

Boelter, L. M. K., Martinelli, R. C., Jonassen, F., Trans. A.S5.M.E.,
63, Lu7 (1941).

Corrosion Handbook, ed. Uhlig (1940).

Dittus, F. W., Boelter, L. M. K., Univ. Cal. Publ. in Engr. 2,
No. 13, 443 (1930).

English, D., Barrett, T., Atomiec Energy Research Establishment,
Ministry of Supply, Harwell, Berks, AERE E/R 547, Uneclassified, (1950).

Hoffman, H. W., Doctoral Thesis, The Johns Hopkins University Library
(1951) .

Karman, T. von, Trans. A.S.M.E., 61, 705 (1939).

Humble, L. V., Lowdermilk, W. H., Desmon, L. G., Nat. Adv. Comm. Aero.,
Report 1020 (1951).

McAdams, W. H., "Heat Transmission"”, 2nd edition, p 168 (19L42).

Poppendiek, H. F., Oak Ridge National Laboratory, Physies Report 913,
Unclassified (1951).

Prandtl, L., Physik. Zeitsehr., 29, 487 (1928).

Reynolds, O., Proe. Manch. Lit and Phil. Soc., 14, 7 (1874);
Collected Papers, 1, 81 (1900), Cembridge.
 

36

- APPENDIX I

Sample Calculation

Caleulations are based on run number 6.

1. Experimental Data

(a)
()
(e)
(d)
(e)
(£)
(g)

w = 392 lbs/hr

tp,i = 840.3 OF

tm,o = 876.7 °F

Outside tube wall temperatures, t,
E = 6.8 volts

I = 324 amperes

2. Inside tube wall temperature

thus,

or

 

 

 

 

te ¥ 100 OF
_ : 2
4, = W (%2 1n z/m, - wo- Ts°
tw-tg B (T Ty, 5 )
Iy = 0.01563 £t
rg = 0.00979 £t
ks = 30.48 Btu/br.ft.9F at ty ave
¢ EI
W= =3
where ¢ = 3.4%13 Btu/hr-watt
V = 0.000932 pt3
k= (3.413)(6.8) (324) (0.00048)
tyts = (0.000532) (2) (30.58)
== 693 OF
ts = by - 6.3

A plot of tg vs. L is shown in Figure 1ll.

3. FEleetrical heat inpul

¢ EI = (3.413)(6.8)(324)
7520 Btu/hr

i

%e

i
10.

31
APPENDIX I (CONT'D)

Heat gained by fluid

4 = ¥ ¢p (B 0 - tp,1)
= (392)(0.49)(36.4)
6988 Btu/hr

H

U

Heat loss
From Figure 7, q; = 239 Btu/hr at y gve - te = 795°F

Heat balance

, 6988 + 2
(ap + @ )/Ge = —-9-——75.30——32= 0.9

Heat flux

(Qf/A)X = Tffgggggy = 113,604 Btu/hr-££°

Temperature difference
From Figure 11, the difference t5; - tp can be obtained for
various L's. These were taken at 2,3,4,5,..., 22 inches.

Heat transfer coefficient
( Qf/A) X
T = )y

h, was calculated for the values of (tg - tp) at the position

hx =

x. E.g. at L = 20 inches, tg - ty = 30.7°F and h = 3700 Btu/hr.£t> °F.
h; as a function of L is shown in Figure 13.

Dimensionless moduli

a6 _ (0.00979)(5.25 x 106)

 

 

 

Re = (5.139 = 10019
. _ hd _ (3700)(0.00979) _
Fo=x= (0.6) = 60.3
pr- SpH_ _ (0.49)(5.13) _ y.o
k (0.0)

Nu /P-4 = 3h.0

Pe = Re-Pr = 42,080
 

38
APPENDIX II

Physical Properties of Molten Sodium Hydroxide

The physical properties of sodium hydroxide were obtained from the follow-
ing sources:

cp : Terashkevich and Vishnerskii - J. Gen. Chem. (U.5.8.R.),

7 (1937)

B : Arndt and Ploetz - Zeiltsch. fur phys. chem., 121, k39
(1926)

p : Ibid

k : Deem, Battelle Memorial Institute, personal commnication.
For the temperature range of the experimental data reported
here, & value of k = 0.6 Btu/hr-£t-°F was used.

The physical properties as & function of temperature are shown in Figure 15.
UNCLASSIFIED

 

 

 

 

 

-39- DWG. 16379
0.0
q\
L 9.0 \
- 8.0 \

 

 

|

.
N
o

l

o
o
Absolute Viscosity, g, |b./hr. ft.

T
o
o

 

 

 

 

 

N o 0.540

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

| -~
\\ \.Q\\
-4.0 N 0.520 &
S
& \\ \*‘ 3
< o
° (.0F3.0 0.500 _
.é \ / Efi
~
20.9 \\ 0.480 *
5 / o
. N g
A N fi a
3- \ wn
0.8 0.460
o
>3
-
=
S ; \
0.7
5 N
£ /
@ 4 \\
= k \
"o.6 o~ o
-\
600 700 800 900 1,000 1,100

Fig. I5.

Variation of

Temperature, °F

Physical

Properties of Sodium Hydroxide with Temperature
 

Lo

APPENDIX III
Derivation of Equation for Temperature Drop Across

a Tube Wall in which Heat is being Generated

The trensient conduction equation for the case in which heat generation

exists within the solid is

 

2t _ 2 W
S5 =avV t+ e (1)

where
@ = thermal diffusity = 53__

vz'b = Laplacian of ¢

W = source term in Btu/hr.ft3
Then for steedy state conditions, _-g-g = 0, and uniform heat generation,

W = constant. For a circular tube, 'the Laplacian as expressed in e¢ylindrical

coordinates is
vat = .._.a_z..t;_ + .];a_.J.G..l.__a.._e_-E 4 !'.....aet
3 TOT P 1'23@_2
Since the temperature distribution is symmetrical with re.épect to @,%2; =0

and since beyond the entrance region, -aa-g = const,

equation 1 thus reads

0k [a% 1 _at W
e \a® T dr) pop

 

 

 

or Bt 1 at W
g T r ok - (2)
if let s = _8%
dr
Then, equation 2 becomes
ds 1 W _
T=FrTE®T " % (3)
 

APPENDIX ITI(CONT'D)

This is of the form

fi&
3

i

Hi+

where P = fl(x)

il
1
=
S~
0y

Q= fe(x)

which has the solution,

then dex:fraJ—'dI‘:'lnr
e-JPAx _ o-Imx _ 1
r
o-JPax _ lor _
thus,
_ 1 LW
S-E(Irfidr+cl)
=..J.'. ‘-E _I.:.?:__'FC)
7 k 2
or @ _ _¥r C
dr- k2" r

The heat flow through the surface defined by

Tr = rw is
dt
(@/B)y = - (dr) r=r,
or (_(}E) (9/A)y
dr P—rw = - '

then, substituting this boundary condition into equation 10,

PR A ——r—— + e
X x 27 ¥,

41

(4)

(5)
(6)
(7)

(8)

(9)

(10)

(11)

(12)
L2
APPENDIX III(CONT'D)

Substituting for C in equation 10,

dt = _Wry (r2W _r (a/h)y]| 1

dr k 2 2k k T
- -W_ [r. rwz‘i - (a/A)y r.. 1 (13)

r k W r

integrating equation 13

5 rw rw
ty = tg=-W_ [ 22 - {a/A)y r In r
ot X (2 W in r) re k¥ re

 

 

rwz -r.2 T Ty
- (-——-—-—-—-—-*‘-’-—-r.,,zlnr—:) - (a/adw T g (L)
k

ok 2

For the particular problem under consideration %% at r = r, is essentially
zero, Thus, equation 14 reduces to

W r, . r.2-r.2
by - by = o <;w2 1n ?g W 5 s /) (15)