Acerca de la homogeneización y propiedades efectivas de la ecuación del calor
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Universidad Distrital Francisco José de Caldas
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Este es un trabajo de divulgación científica, dedicado a recorrer el problema de la conductividad térmica efectiva de un material heterogéneo bifásico tipo matriz inclusión con microestructura periódica. El material compuesto es macroscópicamente isótropo y presenta contacto perfecto en las fases. El problema se estudia en el contexto de la homogeneización periódica. Las propiedades efectivas se determinan como resultado del Método de Homogeneización Asintótica (MHA). Se utilizan conocidas herramientas de la teoría de variable compleja para la resolución del problema sobre la celda periódica. Se presentan los casos límites.
This is a work of scientific circulation intended to introduce the homogenization process from the heat equation. An example is studied for a medium made of two conducting materials, matrix and fibers. The fibers are periodically distributed and embedded within the matrix. The composite is isotropic on the macroscopic scale and perfect inter-facial contact conditions are considered. The problem is studied in the context of periodic homogenization. The effective conductivity tensor is calculated as a result of the application of the asymptotic homogenization method. The solution of the problem on the periodic cell is based on well-known tools of Complex Variable Theory. Some limit cases are also presented.
This is a work of scientific circulation intended to introduce the homogenization process from the heat equation. An example is studied for a medium made of two conducting materials, matrix and fibers. The fibers are periodically distributed and embedded within the matrix. The composite is isotropic on the macroscopic scale and perfect inter-facial contact conditions are considered. The problem is studied in the context of periodic homogenization. The effective conductivity tensor is calculated as a result of the application of the asymptotic homogenization method. The solution of the problem on the periodic cell is based on well-known tools of Complex Variable Theory. Some limit cases are also presented.
Palabras clave
Periodic composites, asymptotic homogenization, effective properties, perfect contact, Compuesto periódico, homogeneización asintótica, propiedades efectivas, contacto perfecto.