Radiative heat transfer in curved specular surfaces in czochralski crystal growth furnace

Zhixiong Guo; Shigenao Maruyama; Takao Tsukada

doi:10.1080/10407789708913908

Radiative heat transfer in curved specular surfaces in czochralski crystal growth furnace

Zhixiong Guo, Shigenao Maruyama, Takao Tsukada

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	595-611
Number of pages	17
Journal	Numerical Heat Transfer; Part A: Applications
Volume	32
Issue number	6
DOIs	https://doi.org/10.1080/10407789708913908
State	Published - Nov 1997
Externally published	Yes

All Science Journal Classification (ASJC) codes

Numerical Analysis
Condensed Matter Physics

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title = "Radiative heat transfer in curved specular surfaces in czochralski crystal growth furnace",

abstract = "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.",

author = "Zhixiong Guo and Shigenao Maruyama and Takao Tsukada",

note = "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: maruyama@ifs.tohoku.ac.jp",

year = "1997",

month = nov,

doi = "10.1080/10407789708913908",

language = "English (US)",

volume = "32",

pages = "595--611",

journal = "Numerical Heat Transfer; Part A: Applications",

issn = "1040-7782",

publisher = "Taylor and Francis Ltd.",

number = "6",

}

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: maruyama@ifs.tohoku.ac.jp

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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Radiative heat transfer in curved specular surfaces in czochralski crystal growth furnace

Abstract

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