Holow 1-D cylinders with heat generation: a sufficiently general approach to solving problems with a time variable Dirichlet condition

• Autor(a) principal: Araújo, Jorge Corrêa de
• Data de Publicação: 2021
• Outros Autores: Márquez, Rosa María García
• Tipo de documento: Artigo
• Idioma: por; eng
• Título da fonte: Remat (Bento Gonçalves)
• Texto Completo: https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/4638
• topic: Hollow Cylinder; Bessel Functions; Green’s Function Method; Approximated General Solution; Cilindro Oco; Funções de Bessel; Método de Funções de Green; Solução Geral Aproximada

In this work, a sufficiently approximated general solution to transient heat conduction problems in 1-D cylindrical geometry, with heat generation and time variable Dirichlet conditions, was presented using the Green’s function method. An important integral involving Bessel functions, that is part of the solution, has been solved in detail here. The results obtained from the use of this solution, when applied in some particular cases of practical interest, were aligned with the solutions reported by the literature. We have adopted, in this sense, a methodology that consists of addressing a non-homogeneous problem solution with non-homogeneous boundary conditions in a non-homogeneous problem solution with homogeneous border conditions and two more stationary solutions related to the given Dirichlet conditions. As a result, the solution obtained has no problems of convergence at the boundaries of the cylindrical region with the temperature prescribed conditions.