DOI QR코드

DOI QR Code

Heat Transfer between Substrate and Substrate-heater in Low Vacuum

저진공 내 시료가열판과 시료의 열전달

  • Park, Hyon-Jae (Division of Energy Systems Research, Ajou University) ;
  • Oh, Soo-Ghee (Division of Energy Systems Research, Ajou University) ;
  • Shin, Yong-Hyeon (Center for Vacuum Technology, Korea Research Institute of Standards and Science) ;
  • Chung, Kwang-Hwa (Center for Vacuum Technology, Korea Research Institute of Standards and Science)
  • 박현재 (아주대학교 에너지시스템학부) ;
  • 오수기 (아주대학교 에너지시스템학부) ;
  • 신용현 (한국표준과학연구원 진공센터) ;
  • 정광화 (한국표준과학연구원 진공센터)
  • Published : 2008.07.30

Abstract

Heat transfer between substrate and substrate-heater in low vacuum was investigated. The convection related with gas flow and pressure, the heat conduction considering surface roughness and contact pressure, and the heat loss by radiation depending on the surface emissivity were considered. The coefficient of heat conduction $h_c$ in the Fourier's law were determined experimentally from the temperature difference between the substrate and the substrate-heater in the range of substrate-heater temperature $100\;-\;500^{\circ}C$, in the pressures of 300 mTorr - 1 Torr. The temperature difference was then calculated in the reverse way for the purpose of verification, using the heat flow and the experimentally determined coefficients. The verified temperature differences were thus obtained within 0.33 % error.

진공 챔버 내부에서 열접촉된 시료가열장치와 시료 사이의 열전달 현상을 고찰하였다. 열전달은 가스 유량과 기체 압력에 따른 대류현상, 시료와 접촉하는 기판가열장치의 표면 거칠기 및 접촉압력에 따른 전도현상, 기판가열장치의 표면 방사율에 따른 복사현상으로 나누어 푸리에 식과 슈테판-볼츠만 식을 이용하여 열흐름 값을 분석하였다. 실험은 시료가열장치의 온도를 $100\;-\;500^{\circ}C$ 사이에서 일정하게 유지하면서 300 mTorr - 1 Torr 사이의 압력에 따른 시료의 온도를 측정하고, 푸리에 식과 슈테판-볼츠만 식을 이용하여 열흐름 값을 계산하였다. 열흐름 값의 산출에 사용된 푸리에 계수의 정확성을 확인하기 위해, 역으로 열흐름 값으로부터 온도차를 구하는 방법을 사용하였으며 0.33 % 오차 내에서 재현됨을 확인하였다.

Keywords

References

  1. Hyeok-Cheol Choi and Chun-Yeol You, J. Kor. Vac. Soc. 16, 433 (2007) https://doi.org/10.5757/JKVS.2007.16.6.433
  2. J. S. Lee, G. C. Kim, H. H. Jeon, S. J. Hwangboe, D. H. Kim, C. M. Seong, M. H. Jeon, J. Kor. Vac. Soc. 17, 23 (2008) https://doi.org/10.5757/JKVS.2008.17.1.023
  3. Siegel-Howell, Thermal radiation heat transfer (McGraw-Hill, 1971)
  4. N. V. Tsederberg, Thermal conductivity of gases and liquids (M.I.T. Press,1965)
  5. 정서긴, 이진원, 박종윤 공저, 진공 과학 입문
  6. C. V. Madhusudana, Int. Comm. Heat Mass Transfer 20, 123-132 (1993) https://doi.org/10.1016/0735-1933(93)90013-L
  7. F. Boeschoten and E. F. M. Van der Held, Physica 23, 37-44 (1957) https://doi.org/10.1016/S0031-8914(57)90236-7
  8. P. M. Lang, Nucleonics 20, 62-63 (1962)
  9. J. P. Hollman, Heat Transfer, 8th edition
  10. V. W. Antonetti, Statistical Variability of Thermal Interface Conductance. NSF/DITAC (Workshop, Melbourne, Australia, 1992), pp. 37-45
  11. E. H. Kennard, Kinetic Theory of Gases. (McGraw- Hill, New York, 1938 ) pp. 311-327
  12. Yu. G. Semyonov, S. E. Borisov and P. E. Suetin, Int. J. Heat Mass Transfer 27, 1789 (1984) https://doi.org/10.1016/0017-9310(84)90161-3
  13. H. Y. Wachman, ARS Journal 32, 2-12 (1962) https://doi.org/10.2514/8.5939
  14. M. L. Wiedmann, and P. P. Trumpler, Trans. ASME, 68, 57-64 (1946)
  15. G. Dharmadurai, J. App. Phys. 54, 5990 (1983) https://doi.org/10.1063/1.331777
  16. Smoluchowski, Phil. Mag. and Jour. Sci. 5, 192-206 (1898)
  17. M. Knudsen, The Kinetic Theory of Gases, (Methuen, London, 1934) pp. 46-61
  18. J. K. Roberts, The Exchange of Energy Between Gas Atoms and Solid Surfaces II, (Proc. R. Soc, London, 1932), Ser. A, 135:192-205