TY - JOUR
T1 - Radiative heat transfer in curved specular surfaces in czochralski crystal growth furnace
AU - Guo, Zhixiong
AU - Maruyama, Shigenao
AU - Tsukada, Takao
N1 - Funding Information:
Received 13 May 1997; accepted 7 June 1997. Part of this work is the result of "Technology for Production of High Quality Crystal," which is supported by the New Energy and Industrial Technology Development Organization (NEDO) through the Japan Space Utilization Promotion Center (JSUP) in the program of the Ministry of International Trade and Industry (MITI) of Japan. Address correspondence to Professor Shigenao Maruyama, Institute of Fluid Science, Tohoku University, Aoba-ku, Katahira 2-1-1, Sendai 980, Japan. E-mail: [email protected]
PY - 1997/11
Y1 - 1997/11
N2 - A numerical investigation of radiative heat transfer constructed by curved surfaces with specular and diffuse reflection components is carried out. The ray tracing method is adopted for the calculation of view factors, in which a new ray emission model is proposed. The second-degree radiation ring elements are introduced, which are of engineering importance and numerical efficiency. The accuracy of the method is analyzed and verified using a simple configuration. The present computation using the proposed ray emission model is in good agreement with the analytical solution. As a numerical example and engineering application, the effects of the specular reflection and the meniscus of the melt surface in Czochralski (CZ) crystal growth are investigated. A marked temperature decrease in the melt surface is found by introducing specular reflection and the meniscus. The combined effects of the specular reflection and the meniscus should be considered in precision heat transfer control of a CZ apparatus.
AB - A numerical investigation of radiative heat transfer constructed by curved surfaces with specular and diffuse reflection components is carried out. The ray tracing method is adopted for the calculation of view factors, in which a new ray emission model is proposed. The second-degree radiation ring elements are introduced, which are of engineering importance and numerical efficiency. The accuracy of the method is analyzed and verified using a simple configuration. The present computation using the proposed ray emission model is in good agreement with the analytical solution. As a numerical example and engineering application, the effects of the specular reflection and the meniscus of the melt surface in Czochralski (CZ) crystal growth are investigated. A marked temperature decrease in the melt surface is found by introducing specular reflection and the meniscus. The combined effects of the specular reflection and the meniscus should be considered in precision heat transfer control of a CZ apparatus.
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U2 - 10.1080/10407789708913908
DO - 10.1080/10407789708913908
M3 - Article
AN - SCOPUS:0031558619
SN - 1040-7782
VL - 32
SP - 595
EP - 611
JO - Numerical Heat Transfer; Part A: Applications
JF - Numerical Heat Transfer; Part A: Applications
IS - 6
ER -