Thermophysical properties of atjs graphite at high temperatures

Carbon

1970, Vol. 8, pp. 665-671.

Pergamon

Press.

Printed

in Great

Britain

THERMOPHYSICAL PROPERTIES OF ATJS GRAPHITE AT HIGH TEMPERATURES R. E. TAYLOR and W. D. RIMBROUGH Thermophysical Properties Research Center, Purdue University, West Lafayette, Indiana 47906, U.S.A. (Received 29 August 1969) Abstract -The spectral emittance (0.65 p) , total hemispherical emittance, electrical resistivity and thermal conductivity of Grade ATJS Graphite from about 1200 to 2400°K has been measured using a multi-purpose thermophysical properties apparatus. 1. EXPERIMENTAL

is the electrical resistivity, P is the circumference, E,., is the total hemispherical emittance, cr is the Stefan-Boltzmann constant, To is the ambient temperature, T is the temperature at any position Z, M is the Thomson coefficient, c, is the specific heat, and D is the density. At steady state the right hand side is zero. For an infinitely long sample (i.e. dzT/dZ2 = dT/dT = 0) the electrical resis-

will be discussed in detail in a separate publication [l] and only a brief description will be given here. The apparatus consists of an automatic high vacuum facility capable of attaining 2 X lo-* torr, a bell jar with optical windows, feed-through collar, sample holder with a sliding electrode to allow thermal expansion, several regulated DC power supplies, an automatic optical pyrometer and an instrumentation console including a guarded six-dial potentiometer and digital voltmeter. A sample in the form of a long thin rod or tube is mounted between two electrodes and Joulean heated by the passage of DC current from a regulated power supply. Temperatures are measured optically and /or with Pt/PT-10% Rh thermocouples. The differential equation which describes the temperature distribution along a thin homogeneous current-carrying rod of material radiating to its surroundings is: The

experimental

apparatus

IdT

x(T1-To4)-M2z=cpDdt

dT

tivity and emittance

can be obtained:

AE P=ET

Pp ‘” = APm (p

- To4)

where E is the potential drop between two voltage probes which are separated by a distance “L”. Alternately, the electrical resistivity may be measured while the sample is heated by a tantalum tube heater. This procedure eliminates the need for measuring true temperature under non-black body Accuracies for resistivity and conditions. emittance measurements at 2000°K are usually within 0.6 per cent and 2 per cent respectively. After the resistivity and emittance determinations, the electrode positions are moved closer together and temperature profiles are obtained. Typical temperature profiles are shown in Fig. 1. By reversing the current

(1)

where A is the thermal conductivity, I is the current, A is the cross-sectional area, p 665

R. E. TAYLOR and W. D. KIMBROLJGH

Fig. 1. 86 A temperature

profiles for ATJS Grade Graphite.

flow, the magnitude of the term containing the Thomson coefficient can be determined. The thermal conductivity can be computed from the knowledge of the temperature at any three positions along the profile. Thus, from a set of data consisting of temperature measurements at 16 locations, over 500 separate conductivity values can be obtained. A significant improvement in the computed thermal conductivity values are obtained when calculation procedures using all the experimental data (multiple point calculations) are used instead of the S-point method which uses only 3 data points per calculated value. These multiple point methods, which will be described in another article [2] employ spline programs [3] for smoothing and differentiating. As a result of these methods, it is now possible to obtain thermal conductivity values accurate within

24 per cent above 2300°K. The numerical solution of equation (1) without the use of restrictive. assumptions was one of the important accomplishments of the present work. The spectral emittance of metals is usually determined in the multiple purpose apparatus by comparing the brightness temperature (measured with a sensitive automatic optical pyrometer) and the true temperature determined from the electrical However, resistivity. temperature the coefficient of graphite is too small for an accurate spectral emittance determination by this technique. Therefore, the spectral emittance (0.65 p) of ATJS Graphite was determined by measuring the brightness temperature of the surface of electrically heated thin walled tubes and the temperature of the black body hole drilled through the

ATJS GRAPHITE

667

AT HIGH TEMPERATURES

Only samples machined perimmersion. pendicular to the molding direction were received and investigated. Thus, the physical property data reported in the present paper (except for emissivity) apply only to the perpendicular direction.

thin wall into the interior. Calculations indicated that the temperature drop across the thin walls was less than two degrees below 2500°K. The samples of Grade ATJS Graphite were obtained from the Air Force Materials Laboratory of Wright-Patterson Air Force Base. Grade ATJS Graphite is an improved version of ATJ Graphite produced by Union Carbide Corporation, Like ATJ Graphite, it is molded graphite having a maximum particle size of O+lO6”, but differs in that it is impregnated after the carbonization cycle, with the material being carbonized again and then graphitized. Thus, Grade ATJS Graphite has a higher density (nominally 1.8 g cmp3) than ATJ (about 1.7 g cmm3) and is more uniform. The densities of the l-806- 1.809 g cmw3 samples tested were when measured by water immersion and l-902- 1 a910 g cmp3 when measured by alcohol

4. RESULTS AND DISCU!SSION Two thin walled tubes were used (gin. OD by bin ID and #in. OD by Qin. ID) for the spectral emittance (E*) measurements. The spectral emittance results for the two samples are shown in Fig. 2. These results are believed accurate within al per cent, and the two curves are separated by an amount equal to their combined uncertainty. It should be noted that changing the spectral emittance by 1 per cent at 1600°K corresponds to changing the “true temperature” of the graphite surface by 1.4”K. Because the values of lA for graphite were not measured on the

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2400

2800

2800

(K)

Fig. 2. Spectral emittance (O-65 p) of Grade ATJS Graphite.

668

R. E. TAYLOR and W. D. KIMBROUGH

identical samples used for the resistivity, total hemispherical emittance and thermal conductivity measurements, the uncertainty as to which EAvalues to use causes uncertainties in the value of these properties. Consequently, p, lH and A values were calculated using both lA curves shown in Fig. 2. The resulting lH values differed by almost 1 per cent but both p and A values were changed by less than O-2 per cent. Thus, the uncertainty in lA of graphite did not seriously affect the thermal conductivity results. Electrical resistivity and total hemispherical emittance were measured simultaneously on two Qin. diameter rods used for the conductivity determinations. The electrical resistivity results are shown in Fig. 3. The electrical resistivity from 1200 to 2400 K of the first sample can be expressed in ohm cm as:

The resistivity of the second sample from 1300 to 2600°K is about 1 per cent less and is given by: p = 4.7419 x 1O-4 + 1.8055 X lo-‘T-6.8767 x lo-12T2. Additional resistivity measurements were obtained on a bin. diameter rod. These results (not shown), which were very close to the lower curve shown in Fig. 3, further demonstrated that the electrical resistivity exhibits a minimum below 1100°K and that the values then increase to about 860 X 10e6 ohm cm near room temperature. The total hemispherical emittance results for the two samples are given in Fig. 4. The data for the first sample were obtained during seven separate runs (including runs both before and after temperature profile measurements) and can be expressed as:

p = 5.2195 x 1O-4 + 1.3296 x 10-7T+ 6.6049 x IO-12T2.

l,z,= 0.7308 + 2.738 x 10-5T (T > 1200°K).

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Fig. 3. Electrical resistivity of Grade ATJS Graphite.

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AT HIGH TEMPERATURES

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Fig. 4. Total hemispherical emittance of Grade ATJS Graphite. As shown in Fig. 4, the values for the total hemispherical emittance of the second sample were within 1 per cent of those measured for the first sample. Thermal conductivity values for the two graphite samples are given in Fig. 5. Conductivity data on the first sample were obtained from 10 different profiles. Over 500 conductivity values were calculated from these profiles. Since this is too many values to plot conveniently, mainly results from the “multiple-point” methods are given in Fig. 5. Although fewer profiles were obtained on the second sample, the results indicated that the conductivity of the second sample was about 6 per cent below that of the first sample (Fig. 5). Smoothed conductivity values for the two samples are given in Table 1. The recommended curve[4] for Grade ATJ Graphite is included on Fig. 5. From that the conthis figure, it is deduced

carbon-Vol.8.No.5-G

ductivity of Grade ATJS Graphite is from 10 to 20 per cent greater than that of ATJ Graphite. This observation indicates that the difference in conductivity values between the two grades of graphite is greater than the difference in densities (about 6 per cent). Conductivity values were also calculated from several of the profiles using the Krishnan and Jain[5] and the Lebedev[6] techniques. These results were usually more than 10 per cent above the values given in Fig. 5 or Table 1. Also included in Table 1 are values of the Lorenz function calculated using the resistivity and the conductivity values for sample number 1. The values of the Lorenz function are much greater than the theoretical value for metals (2443 X lo-* watt-ohm K+‘) and are also greater than the usual values published for graphite[7]. These results demonstrate that the lattice component of the

R. E. TAYLOR

670

and W. D. KIMBROUGH

ATJ (I)

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TEMPERATURE ( K)

Fig. 5. Thermal Table

conduction in graphite

1. Thermal

conductivity of Grade ATJS Graphite.

conductivity and Lorenz ATJS Graphite (I)

Temp. (“K)

A(Wcm-I K-r) (Smoothed) Sample 1

1500 1600 1700 1800 1900 2000 2100 2200 2300 2400

0.567 0.544 0.525 0.508 0.492 0.477 0.464 0.451 0.439 0.425

mechanism is still important at high temperatures and/or

that the electronic component is considerably different from that observed in metals.

X(Wcm-‘K-l) (Smoothed) Sample 2

function

of grade

Lorenz function (lo-%’ 0 K-*) Sample 1

0.541 0.513 0.490 0.471 0.456 0.441 0.429 0.419 0.409 0.402

27.8 25.6 23.7 22.1 20.7 19.4 18.3 17.4 16.4 15.5

This work was supported by the Air Force Materials Laboratory of WrightPatterson Air Force Base and was monitored

Acknowledgments-

by Do. M. Minges. The efforts of Mr. H. Groat

and

Mr.

D. Rhine

are

sincerely

appreciated.

ATJS GRAPHITE

AT HIGH TEMPERATURES

REFERENCES 1. Taylor R. E., Powell R. W. and Dewitt D. P., In preparation. 2. Taylor R. E. and Davis F. F., In preparation. 3. Rice J. R., Pyodynamics 6,231 (1968). 4. Ho C. Y., Powell R. W. and Liley P. E., NSRDSNBS 16, U.S. Government Printing Office (1968).

671

5. Krishnan K. S. and Jain S. C., hit. J. ApPl. Phys. 5,426 (1954). 6. Lebedev V. V., Phys. Metals Metallog. USSR, lo,31 (1960). 7. Powell R. W. and Schofield F. H., Proc. Phys. Sot. 51, 153 (1939).