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ENCIT 2020
18th Brazilian Congress of Thermal Sciences and Engineering
SOME EXACT SOLUTIONS FOR A CLASS OF NONLINEAR DIFFERENTIAL EQUATIONS ARISING FROM THE MATHEMATICAL DESCRIPTION OF POROUS FINS
Submission Author:
Maria Laura Martins-Costa , RJ , Brazil
Co-Authors:
Vinícius Vendas Sarmento, Maria Laura Martins-Costa, ROGERIO GAMA
Presenter: Vinícius Vendas Sarmento
doi://10.26678/ABCM.ENCIT2020.CIT20-0249
Abstract
This article presents two analytical solutions for a rectangular profile porous fin, assumed to have an infinite length. These solutions are proved to be unique and are associated with a convex functional. The original fin is subjected to natural convection and thermal radiation. The closed-form analytical solutions stand for the limiting cases, namely: 1) no thermal radiation and 2) no convection (the fin confined in an atmosphere-free space). The obtained results are compared with results obtained numerically via minimization of a functional that accounts for both natural convection and thermal radiation simultaneously, showing excellent agreement.
Keywords
Nonlinear Ordinary Differential Equations, porous fins, exact solutions
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