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Volume 4, Issue 1
A Note on the Stefan-Boltzmann Problem for Heat Transfer in a Fin

Boris P. Belinskiy, John R. Graef & Lingju Kong

DOI: 10.12150/jnma.2022.103

J. Nonl. Mod. Anal., 4 (2022), pp. 103-113.

Published online: 2022-06

[An open-access article; the PDF is free to any online user.]

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  • Abstract

A fin is traditionally thought of as an extension of a surface to facilitate the transfer of heat away from a larger body to which it is attached. In this paper, the authors study some mathematical properties of a nonlinear heat transfer model for a fin and its relation to an associated linear model. Specifically, they prove that the solution exists and is unique, and they determine bounds for the temperature. Further, they prove the monotonicity of the temperature distribution, and they obtain an estimate for the maximal difference between the temperatures as determined by the nonlinear and linear models.

  • Keywords

Heat transfer, Fin, Stefan-Boltzmann law, Existence and uniqueness, Dependence.

  • AMS Subject Headings

34B15

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JNMA-4-103, author = {Belinskiy , Boris P.Graef , John R. and Kong , Lingju}, title = {A Note on the Stefan-Boltzmann Problem for Heat Transfer in a Fin}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2022}, volume = {4}, number = {1}, pages = {103--113}, abstract = {

A fin is traditionally thought of as an extension of a surface to facilitate the transfer of heat away from a larger body to which it is attached. In this paper, the authors study some mathematical properties of a nonlinear heat transfer model for a fin and its relation to an associated linear model. Specifically, they prove that the solution exists and is unique, and they determine bounds for the temperature. Further, they prove the monotonicity of the temperature distribution, and they obtain an estimate for the maximal difference between the temperatures as determined by the nonlinear and linear models.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2022.103}, url = {http://global-sci.org/intro/article_detail/jnma/20696.html} }
TY - JOUR T1 - A Note on the Stefan-Boltzmann Problem for Heat Transfer in a Fin AU - Belinskiy , Boris P. AU - Graef , John R. AU - Kong , Lingju JO - Journal of Nonlinear Modeling and Analysis VL - 1 SP - 103 EP - 113 PY - 2022 DA - 2022/06 SN - 4 DO - http://doi.org/10.12150/jnma.2022.103 UR - https://global-sci.org/intro/article_detail/jnma/20696.html KW - Heat transfer, Fin, Stefan-Boltzmann law, Existence and uniqueness, Dependence. AB -

A fin is traditionally thought of as an extension of a surface to facilitate the transfer of heat away from a larger body to which it is attached. In this paper, the authors study some mathematical properties of a nonlinear heat transfer model for a fin and its relation to an associated linear model. Specifically, they prove that the solution exists and is unique, and they determine bounds for the temperature. Further, they prove the monotonicity of the temperature distribution, and they obtain an estimate for the maximal difference between the temperatures as determined by the nonlinear and linear models.

Boris P. Belinskiy, John R. Graef & Lingju Kong. (2022). A Note on the Stefan-Boltzmann Problem for Heat Transfer in a Fin. Journal of Nonlinear Modeling and Analysis. 4 (1). 103-113. doi:10.12150/jnma.2022.103
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