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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 NameAffiliation
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.