The analytical benchmark solution of a spatial diffusion kinetics in source driven systems for homogeneous media

• Autor(a) principal: Oliveira, Fernando Luiz de
• Data de Publicação: 2007
• Outros Autores: Maiorino, José Rubens, Santos, Rubens Souza dos, Instituto de Engenharia Nuclear, Instituto de Pesquisas Energéticas e Nucleares
• Tipo de documento: Artigo de conferência
• Idioma: eng
• Título da fonte: Repositório Institucional do IEN
• Texto Completo: http://carpedien.ien.gov.br:8080/handle/ien/2521
• topic: INAC 2007; Analytical solution; Numerical methods; Driven systems

This paper describes a closed form solution obtained by the expansion method for the general time dependent diffusion model with delayed emission for source transients in homogeneous media. In particular, starting from simple models, and increasing the complexity, numerical results were obtained for different types of source transients. Thus, first an analytical solution of the one group without precursors was solved, followed by considering one precursors family. The general case of G-groups with R families of precursor although having a closed form solution, cannot be solved analytically, since there are no explicit formulae for the eigenvalues, and numerical methods must be used to solve such problem. To illustrate the general solution, the multi-group (three groups) time-dependent without precursors was also solved and the results inter compared with results obtained by the previous one group models for a given fast homogeneous media, and different types of source transients. The results are being compared with the obtained by numerical methods.