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| A Note on the Stefan-Boltzmann Problem for Heat Transfer in a Fin |
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| KeyWord:Heat transfer Fin Stefan-Boltzmann law Existence and uniqueness Dependence |
| Author Name | Affiliation | | Boris P. Belinskiy | Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, Tennessee 37403, USA | | John R. Graef | Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, Tennessee 37403, USA | | Lingju Kong | Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, Tennessee 37403, USA |
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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. |
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