ISSN 0018-151X, High Temperature, 2008, Vol. 46, No. 5, pp. 731–733. © Pleiades Publishing, Ltd., 2008. Original Russian Text © S.V. Stankus, I.V. Savchenko, A.V. Baginskii, O.I. Verba, A.M. Prokop’ev, R.A. Khairulin, 2008, published in Teplofizika Vysokikh Temperatur, Vol. 46, No. 5, 2008, pp. 795–796.
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Thermal Conductivity and Thermal Diffusivity Coefficients of 12Kh18N10T Stainless Steel in a Wide Temperature Range S. V. Stankus, I. V. Savchenko, A. V. Baginskii, O. I. Verba, A. M. Prokop’ev, and R. A. Khairulin Kutateladze Institute of Thermophysics, Siberian Division, Russian Academy of Sciences, Novosibirsk, 630090 Russia Received May 16, 2007
PACS numbers: 72.15.Eb, 81.05.Bx DOI: 10.1134/S0018151X08050222
supports was placed in a high-temperature electric furnace with inert atmosphere (99.992% by volume argon). The lower surface of the sample was heated by a 0.8-ms pulse from an Nd:YAG laser with wavelength of 1.064 µm. The overall heating of the sample did not exceed 1–3 K. The variation of temperature of the upper surface was registered by a liquid nitrogencooled IR detector (InSb). The samples of 12Kh18N10T steel (according to the data of chemical analysis, their composition in percent by mass was as follows: 0.06% C, 16.6% Cr, 9.0% Ni, 0.5% Ti, 0.4% Si, and 1.1% Mn) were shaped as cylinders 12.6 mm in diameter and 1.5 and 2.5 mm thick with plane-parallel ground end faces. No additional coating was applied for increasing the absorption of laser radiation. The thermal diffusivity was calculated in view of all heat losses from all surfaces of the sample by the model of Cape and Lehman [4]. A correction was introduced for the finite duration of laser pulse and its real shape [5].
High-alloy austenitic 12Kh18N10T (chrome-nickeltitanium) steel (GOST [State Standard] 5632-72) exhibits a complex of properties which enable one to use this steel as the structural material for vacuum systems, corrosion-resistant, cold-resistant, heat-resistant, and other articles. Data on the coefficients of thermal conductivity λ and thermal diffusivity a are required for the calculation of thermal stresses in articles and of thermal fields. Precise and reliable data on λ at temperatures below 300 K are given in [1]. The majority of reference books in the range of high temperatures employ data identical to those of [2], for which no error was determined. Measuring the thermal conductivity coefficient in the high-temperature range is a complicated problem, because it is difficult to correctly include the heat transfer between sample and environment. In this situation, instead of measuring λ, this coefficient may be found by the results of measurements of thermal diffusivity of the material (for which no measurements of heat fluxes are required) and by the data on heat capacity CP and density ρ, using the relation λ = aρC p .
The measurement results are given in Fig. 1 and Table 1. The thermal expansion of samples was ignored in determining the thermal diffusivity. Each point in
(1)
As a rule, the data on CP and ρ are much more precise than those on thermal diffusivity; therefore, the error of determination of λ almost coincides with that for a. It was the objective of this study to experimentally investigate the thermal diffusivity of 12Kh18N10T steel in a wide temperature range and to determine the thermal conductivity coefficient using the literature data on density and heat capacity. The measurements were performed using the laser flash method in an LFA-427 automated experimental setup by NETZSCH [3] rated for the maximal working temperature of 2250 K. A sample mounted on needle
Table 1. Results of measurements of thermal diffusivity of 12Kh18N10T steel (disregarding thermal expansion)
731
T, K
a, mm2/s
294.0 294.2 377.9 473.0 571.6 673.3 772.4
3.93 3.99 4.13 4.33 4.52 4.71 4.89
T, K 872.8 973.5 1070 1172 1275 1375 1475
a, mm2/s 5.04 5.28 5.41 5.54 5.72 5.91 6.00
732
STANKUS et al.
a, mm2/s
λ, W/(m K)
6.0
30 25
5.5 20 1 2
5.0
15 1 2 3
10
4.5
5 4.0 0 0
200
400
600
800
1000 1200 T–273.15, ä
Fig. 1 is an averaged value over three “shots”. The data were obtained in three series of measurements with both heating and cooling of samples in the temperature range from 295 to 1475 K. No significant difference was observed in the results for samples of different thicknesses and thermal histories. The approximation of experimental data resulted in the equation (2)
where a is in mm2/s, ∆T = T – 273.15, and T is the temperature in K. The mean-square deviation of experimental points from Eq. (2) does not exceed 0.5%. The overall error of determination of thermal diffusivity (2% at 300 K and 4% at 1500 K) was estimated by the results of measurements of a for molybdenum and standard samples of Inconel and Pyroceram. In calculating λ by formula (1), we used the data on heat capacity [6], temperature coefficient of linear expansion [7], and density [8] and our data on thermal diffusivity. The approximation in the temperature range of 300–1500 K gave the equation λ(T) = 13.9 + 0.0185∆T – 5 × 10–6∆T2,
250
500
750
1000
1250
1500 T, ä
Fig. 2. The temperature dependence of thermal conductivity coefficient of 12Kh18N10T steel: (1) [1], (2) [2], (3) Eq. (3).
Fig. 1. The temperature dependence of thermal diffusivity of 12Kh18N10T steel: (1) experimental data, (2) Eq. (2).
a(T) = 3.91 + 2.1 × 10–3∆T – 3 × 10–7∆T2,
0
(3)
where λ is in W/(m K). The overall error of determination of thermal conductivity coefficient (3% at 300 K and 5% at 1500 K) somewhat exceeds that in the case of thermal diffusivity due to the contribution by the errors of density (up to 0.5%) and heat capacity (up to 1.5%). Figure 2 gives comparison of the results with available literature data. One can see that our results agree very well with the recommendations of [1] for the
room temperature range. The difference from the data of [2] above 300 K does not exceed 4.5%, i.e., is likewise within the errors being estimated. Table 2 gives the temperature dependence of λ in the temperature range Table 2. Thermal conductivity coefficient of 12Kh18N10T steel: 4 to 300 K [1]; 300 to 1475 K (our results) (disregarding thermal expansion) T, K λ, W/(m K) 4 10 20 30 40 50 60 70 80 100 125 150 175 200 225 250 275 300 350 400 450
0.28 0.85 2.08 3.37 4.58 5.68 6.66 7.50 8.23 9.37 10.36 11.10 11.78 12.46 13.12 13.72 14.25 14.91 15.3 16.1 17.0
∆, % 2.6 1.5 1.2 1.1 1.0 1.0 1.0 0.9 0.9 1.1 1.2 1.2 1.3 1.4 1.3 1.4 1.5 1.7 3 3 3
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∆, % 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 2008
THERMAL CONDUCTIVITY AND THERMAL DIFFUSIVITY COEFFICIENTS
from 4 to 1475 K, constructed by the data of [1] and Eq. (3). The approximation equation for the “true” coefficient of thermal conductivity of 12Kh18N10T steel (in view of thermal expansion) has the form λ(T) = 13.9 + 0.019∆T – 4.4 × 10–6∆T2.
(4)
The errors of determination of λ by Eqs. (3) and (4) are the same, because the error in the overall coefficient of linear expansion of steel (up to 2 × 10–7 K–1) makes a negligible (less than 0.1%) contribution to the value of thermal diffusivity. ACKNOWLEDGMENTS This study was supported in part by the Russian Foundation for Basic Research (project no. 07-0800071).
3.
4. 5. 6.
7.
REFERENCES 1. GSSSD 67-84. Stal’ nerzhaveyushchaya 12Kh18N10T. Koeffitsient teploprovodnosti v diapazone temperatur 4−300 K (State Service of Standard and Reference Data 67-84. 12Kh18N10T Stainless Steel. Thermal Conductivity Coefficient in the Temperature Range of 4–300 K), Moscow: Izd. Standartov, 1985. 2. Chirkin, V.S., Teplofizicheskie svoistva materialov yadernoi tekhniki. Spravochnik (The Thermophysical Prop-
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erties of Materials in Nuclear Engineering: A Reference Book), Moscow: Atomizdat, 1968. NETZSCH-Gerätebau GmbH. Metod lazernoi vspyshki v shirokom intervale temperatur (LFA427) (The Laser Flash Method in a Wide Temperature Range (LFA427)), (http://www.ngb-ta.ru/ru/products/detail/pid,24.html). Cape, J.A. and Lehman, G.W., J. Appl. Phys., 1963, vol. 34, no. 7, p. 1909. Blumm, J. and Opfermann, J., High Temp. High Pressures, 2002, vol. 34, p. 515. GSSSD 32-82. Stali 12Kh18N9T i 12Kh18N10T. Udel’naya ental’piya i udel’naya teploemkost’ v diapazone temperatur 400-1380 K pri atmosfernom davlenii (State Service of Standard and Reference Data 32-82. 12Kh18N9T and 12Kh18N10T Steels. Specific Enthalpy and Specific Heat capacity in the Temperature Range of 400–1380 K), Moscow: Izd. Standartov, 1991. GSSSD 59-83. Molibden, monokristallicheskaya okis’ alyuminiya, stal’ 12Kh18N10T. Temperaturnyi koeffitsient lineinogo rasshireniya (State Service of Standard and Reference Data 59-83. Molybdenum, Single-Crystal Alumina, 12Kh18N10T Steel. Temperature Coefficient of Linear Expansion), Moscow: Izd. Standartov, 1984. Basin, A.S., Revenko, M.A., and Stankus, S.V., The Variation of Density of Kh18N10T Steel in Melting and Crystallization, in Kristallizatsiya i protsessy v kristallizatorakh (Crystallization and Processes in Crystallizers), Novosibirsk: Inst. of Thermophysics, Siberian Div., USSR Acad. Sci., 1979, p. 109.
