Cálculo da condutividade térmica efetiva de meios heterogêneos com múltiplas escalas via homogeneização reiterada e elementos finitos

Detalhes bibliográficos
Ano de defesa: 2017
Autor(a) principal: Mattos, Lucas Prado
Orientador(a): Não Informado pela instituição
Banca de defesa: Não Informado pela instituição
Tipo de documento: Dissertação
Tipo de acesso: Acesso aberto
Idioma: por
Instituição de defesa: Universidade Federal do Rio de Janeiro
Brasil
Instituto Alberto Luiz Coimbra de Pós-Graduação e Pesquisa de Engenharia
Programa de Pós-Graduação em Engenharia Mecânica
UFRJ
Programa de Pós-Graduação: Não Informado pela instituição
Departamento: Não Informado pela instituição
País: Não Informado pela instituição
Palavras-chave em Português:
Link de acesso: http://hdl.handle.net/11422/5962
Resumo: Heat transfer through heterogeneous materials may be modeled using sets of partial differential equations in a microscopic level where there is no heterogeneity. For this reason, the direct numerical study of such equations inside a highly heterogeneous material and with multiple scales can become outstandingly difficult or even impossible to solve. In the case of present interest, materials with multiple scales, one can have small particles at the smallest dimension, scattered throughout a body with the largest dimension, while forming aggregates at the intermediate dimension. The simulation of heat transfer inside this material would require extremely fine and ill-conditioned meshes and, therefore, the success of a numerical implementation becomes extremely unlikely. This is the reason why one proposes to calculate an effective thermal conductivity of a heterogeneous medium with multiple scales. In the present work, a numerical-analytical methodology is developed, based on the variational calculus, the theory of reiterated homogenization and the finite element method, to computationally determine the effective thermal conductivity of composite materials with two homogeneous and isotropic phases, with perfect thermal contact between them. The methodology is then applied to cases with analytical solutions to validate the implementation. Next, geometries that are more complex are considered. The obtained results show that the developed methodology can aid in the explanation of the effective thermal conductivity gain experimentally observed with some classes of heterogeneous media.