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 - <p style="text-align: justify;">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.</p>