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MICROCOPY RESOLUTION TEST CHART
NATIONAL BUREAU OF STANDARDS -1963
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1
ORNUD 1945
Cont: 660305-9.
DRNL - AEC - OFFICIAL
HEAT TRANSFER IN THE DESIGN OF LARGE RADIOISOTOPIC HEAT SOURCES
ORNI - AEC - OISICIAL
J. C. Posey and R. E. McHenry
PEB 23 BS

Isotopes Development Center
Oak Ridge National Laboratory
Oak Ridge, Tennessee
RELEASED FOR ANNOUNCEMENT
IN MUCLEAR SCIENCE ABSTRACTS.
This paper contains methods of estimating the internal temperatures of radio-
isotope heat sources and suggests methods by which these temperatures may be
held to reasonable levels. It is emphasized that the most common design, a
single geometric configuration of compact shape, is not always the best and
in many cases is not practicable.
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Radioisotopic sources, whetier radiation or heat sources, must meet a single
universal criterion. The effects produced by the ionized radiation resulting
from the decay of the isotope must be suitably contained or released under :-
...controlled conditions. Since a large fraction of the decay energy is inevi-
tably converted to heat by absorption within the source material, the single.
criterion is usually considered in two parts: one, the control of the ioniz-
ing radiation containment and shielding); the other, the transfer of heat
from the source. In the design of the most efficient heat source (minimum:
weight, minimum volume, and maximum utilization of heat energy), however, the
'containment and shielding and heat transfer must be considered together because
of the many factors which mutually affect both. For example, all of the require-
ments placed on the properties of the materials in the source container are more
easily met as the temperatures are reduced. The minimum temperature at the sur-
face from which the heat is to be removed from a heat source assembly is defined
by the designer of the apparatus into which the source assembly must be incor-
porated, while the maximum temperature is fixed by the source design and the
properties of materials. It is essential that the increase in temperature :::
from the surface to the interior of a source assembly be minimized, since the
. list of candidate materials for both the source and the container are limited
for high temperature environments.
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PROBLEMS CAUSED BY HIGH TEMPERATURE
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Most radioisotopic heat sources must operate at the comparatively high temper-
:..atures required at the hot junction of thermoelectric generators or at the
emitting surfaces of thermionic devices. Materials are being sought which are
useful at the highest temperature; however, the search for higher temperature
materials will not always solve the heat source design problems. It is unfor-
tunate that essentially all the desirable physical properties which affect the
container integrity and heat transfer in a source or its container deteriorate
with increasing temperatures higher than a few hundred degrees centigrade. :
......ORNL - AEC - OFFICIAL
"Research sponsored by the U. S. Atomic Energy Commission under contract ::
with the Union Carbide Corporation.
LEGAL NOTICE .
ORNL - AEC - OFFICIAL
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This report mo prepared as an account of Government sponsored work, Nolther the United
Statos, por the Commission, nor any person soting on behalf of the Commissions
A. Makes any warranty or representation, expressed or implied, with respect to the accu
racy, completeness, or unotalpeus of the information contained in this report, or that the man
of any information, apparatus, method, or proceso discloud in this report may not latriar
printoly owned to or
B. Assume, any liabilues with roopoot to the use of, or for damague remitting from the
um of aay Information, apparatus, method, or pronou disclosed in this report.
As und in the above, "person soting on behall of the Commisalon" includes wy om-
ploys or contractor of the Commission, or employee of much contrmotor, to the extent that
such employee or contractor of the Commission, or employer of mon contractor prepares,
disseminates, or provides noceso to, any laformation pur munt to Mo employment or contrnot
with the Commission, or bin employment with mob opatrnotor.
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Alimentandora
Many of the otherwise desirable heat source materials have comparatively
thermal conductivities. This problem becomes especially severe in large....
sources, or in sources with high power density, because of the large high. :.
heat fluxes at the working surfaces. The mechanical properties of material
are also considerably altered by increasing temperatures. In heat sources
using alpha emitters, the increase in temperature not only decreases the ti
strength of the container but also increases the stress by producing higher
helium pressures.
OPNE - All - OFFICIAL
higher temperatures, the problems of compatibility of materials are greater
due to higher reaction and diffusion rates in addition to possible changes in
... equilibria which cannot be predicted from data taken at moderate temperatures.
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CALCULATIONS OF TEMPERATURES IN SIMPLE GEOMETRIC SHAPES
The temperature difference between the center and surface of the source itself
• can be calculated for sources of simple geometric forms if adequate data are
available. Qualitative generalizations can be made from these calculations
which will apply to all shapes of radioisotopic heat sources. Calculations
concerning three basic cases are covered in this paper: (1) the long cylinder,
2) the flat slab, and (3) the sphere. Both mathematical equations and nomo-
graphs are given (Figs. 1, 2, and. 3). The equations are derived readily by
elementary calculus. The assumption is made in these methods that the thermal
conductivity and the power density are constant throughout the source and that
the surface temperature of the source is uniform.
Figure 1. is a nomograph for the calculation of the maximum (centerline) temper-
ature in a cylinder, the height of which is much greater than the diameter....
This nomograph is based on Equation (1):
AT - PD2
AT - 66,
(1)
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where AT = difference between the centerline and surface temperature,
.: P = rate of heat generation per unit volume,
D = diameter,
A k = thermal conductivity.
The values AT, P, D, and k can be in any system of consistent units.
The difference between the maximum internal temperature and the surface temper..
ature of a thin planar source of uniform thickness can be determined from Fig. 2
... Which is based on Equation (2):
12)
::. AT e
where I = thickness of the slab.
The other symbols have been defined.
The nomographs are used as follows: first establish a line from P to D which
intersects the reference line, then draw a line from k to the intersection of
. the first line with the reference line to find AT.
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NOMOGRAPH FOR COMPUTING THE CENTERLINE TEMPERATURES OF LONG CYLINDERS
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OF THIN SLAB OR SHORT CYLINDRICAL SOURCES
NOMOGRAPH FOR CALCULATING THE MAXIMUM INTERNAL TEMPERATURE ...
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NOMOGRAPH FOR CALCULATING THE MAXIMUM INTERNAL
TEMPERATURE OF SPHERICAL SOURCES
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The case of the spherical source is covered by Fig. 3 which is based
Equation (3):
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ORNI - AEC - OFFICIAL
The symbols have the same meaning as in the previous equations.
mewn memoria commencompas.com imagine
In most cases, it has been found that the primary reason for uncertainty in
calculations of this type is the lack of adequate thermel conductivity data:
High-temperature thermal conductivity data are lacking for most of the source
materials which are under consideration. Furthermore, thermal conductivities
are affected to an appreciable degree by impurities and porosity; thus, nom
inally identical samples may differ in conductivity. It is unlikely that ;
high-temperature data which can be applied with confidence to specific radio-
active sources will be available any time soon.
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In the absence of reliable data, the thermal conductivity is estimated from
that of a similar material in the same temperature range. This is generally
preierable to the use of a value obtained by measurement at a temperature :
greatly different from the one of intended application.
In many instances, the use of a single geometrically compact source of pure
material is not practicable. As an example, let us assume that a spherical
::source of pure, dense 242Cm20s is to be used where the surface temperature
is 1000°C.. If the melting point, 1950°C, is fixed as the maximum allovable :
temperature, the maximum size of spherical source which can be used is deter
mined as follows: Using values of 1,230 watts/cc for P and 0.025* watts/cmºc :
for k, one finds that the maximum diameter is only 0.68 cm and the total power,
is 204 watts. Since the thermal conductivity was estimated, not even this
comparatively small size can be considered safe:
REDUCTION OF TEMPERATURES BY SOURCE DESIGN
The problem of overheating in the center of a large source can be overcome: ";
by proper design. Three general approaches are available: (1) the source :
material can be diluted so as to reduce the power density, P; (2) the thermal
conductivity of the source can be improved by mixing the radioactive substance
with a material of higher conductivity such as a metal or by fabricating veins
. or rods of metal into the source to form highly conducting paths from the
interior to the surface; and (3) the source can be divided into several
smaller units which are placed in a matrix of highly conducting material.
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Dilution
Dilution with materials which do not appreciably affect the thermal co
often is not advisable. Even in cases where the melting point is not lowered,
no gain may occur. As an example, in some thermionic devices & defined power
per unit area of a surface is required. Dilution will require thickening of
: the source if constant power per unit area is maintained. By application of
Equation (2), it can be shown that the difference in temperature between the
ORNL - AEC - OFFICIAL
:: This is the value given for Thoz, a similar material, at 1400°C by Kingery
.... Franci, and Cobbled and was converted to the units of this report. ::
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center and surface will be increased by dilution with a material which does.
he thermal conductivity. Equation (1) in combination with common
:: geometric formulas shows that if the source is in the form of a tall cylinder,
:the diameter of which is varied' to maintain constant total power at various
dilutions, the center to surface At is independent of dilution.
:,:.
Some reduction in A1 can be obtained when the size of the source is increased
in all three dimensions at constant total power. In the typical case of a :
sphere, it is found that it is proportional to the cube root of the concentre-
tion of radioactive material at constant total power. The same relationship
will apply to any change in power density at constant thermal conductivity
· and total power.
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Use of Intrasource Conductors
The formation of a cermet by dilution of the radioactive source with a good
.conductor results in substantial lowering of the maximum internal temperature.
The metal in the cermet not only lowers the power density by dilution but :
also substantially increases the thermal conductivity. Methods of estimating
the thermal conductivity have been summarized by Powers.
The use of solid metallic conductors as heat paths inside the heat source has
: theoretical advantages over the use of a cermet. In a well-designed source
the amount of metal necessary to achieve a given lowering of AT is less than
that for a cermet, and a wider range of ratios of metal to oxide can be used
efficiently because a comparatively high ratio of metal to oxide is usual.ly :
required to assure that the metallic phase is the continuous phase in a cermet.
If the oxide phase is continuous, i.e., the source consists of metal particles
suspended in an oxide matrix, the improvement in thermal conductivity is much
less than when the reverse is true.
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At the present, there is no experience with sources having built-in metallic
beat paths. Practical difficulties with respect to the adherence of the oxide
to the metal may be encountered. Cracking because of differences in coefficients ...
of expansion may also be a problem.
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Separation into Smaller Units
The separation of the source into several smaller units has an advantage in :
applications where internal helium pressure is a problem. This can be vis-..
: ualized from a specific example where small, closely spaced holes are drilled
into a metal block and the radioactive material is placed in the holes which
::...are then sealed separately. If volume must be allowed for helium produced by
:. the decay of the radioactive material, the material can be used in the form .
:: Of a powder without an increase in the overall volume of the encapsulated ..
source. The advantage of this design is that the metal between the holes
'not only acts as a high conductivity heat path but makes an appreciable con-
tribution to the strength of the overall structure.
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The optimum design from the viewpoint of operation alone for this type of
capsule would not contain circular holes. A more nearly optimum arrangement
would consist of a close-packed array of small polyhedral cavities. However,
a complex capsule of this type would be very difficult to fabricate and fuel.
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The use of deep hexagonal or square holes (a honeycomb-like arrangement)
would make more, efficient use of the space occupied by the metal partitions.
.than would an array of circular holes and could be fabricated and filled ,
without excessive difficulty. However, the relative ease of construction and
sealing suggests that the circular hole design will be preferred in most cases.
Container Design
:
The temperature difference between the surface of the heat source and the
actual working hot surface of the thermoelectric or thermionic source also:
should be held to a minimum. This is done by usual methods of design. Struc..
tural materials of high thermal conductivity are chosen and discontinuities :
path are kept to a minimum.. If any layers of material of
unusual resistance to heat flow are required, their influence will be minimized
if they are placed where the cross section of the heat path is large, i.e., at
a distance from the center. This also applies to discontinuities if the primary
mode of heat transfer is conduction.
In many designs the heat source is surrounded by two or more separate shells
of material. Since these shells are not likely to fit perfectly, much of the
heat must pass between the surfaces by radiation and conduction through a :
layer' of gas. At high temperature, radiation is the dominant mode of transfer.
Therefore, it is advantageous to treat the surfaces to obtain high emissiv;
This is particularly true in the case of shiny metals such as platinum. It
is also advantageous to seal the apparatus in an atmosphere of helium. to:
assure that any gaps are filled with this highly conducting gas..
SUMMARY
... Very high temperatures can occur inside of radioactive heat sources in thermo-
:: electric generators or in thermionic devices. It is desirable that these
temperatures be held to the minimum consistent with the required operating
temperature of the apparatus, since high temperature creates problems such
as increased chemical reactions, melting, vaporization, and weakening of
structural materials. The difference between the maximum internal temper-
ature and the surface temperature of heat sources of simple geometric shape
can be calculated. These calcrilations show that a source of pure material :
and simple compact geometric shape is not always optimum or even usable. :o
Three general methods of designing sources so as to avoid extreme internal:
temperatures are discussed.
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REFERENCES
1. W. D. Kingery, J. Franc., and R. L. Cobble, Thermal conductivity: X, Data
for several pure oxides corrected to zero porosity, J. Am. Ceram. Soc. 37
: 107-10 (February 1954).
:
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2.A. E. Powers, Conductivity in aggregates, Report No. KAPL-2145, Knolls
: .Atomic Power Laboratory, General Electric Company (Mar. 6, 1961).
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