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Hybrid Methods in Engineering

ISSN Print: 1099-2391

Archives: Volume 1, 1999 to Volume 4, 2002

Hybrid Methods in Engineering

DOI: 10.1615/HybMethEng.v2.i4.40
28 pages

ERROR ANALYSIS OF MIXED LUMPED-DIFFERENTIAL FORMULATIONS IN DIFFUSION PROBLEMS

Leonardo Alves
Departamento de Engenharia Mecânica - TEM Universidade Federal Fluminense - UFF
Leandro A. Sphaier
Department of Mechanical Engineering – PGMEC, Universidade Federal Fluminense, Rua Passo da Patria 156, bloco E, sala 216, Niteroi, RJ, 24210-240, Brazil
Renato M. Cotta
Laboratory of Transmission and Technology of Heat, LTTC, Department of Mechanical Engineering, Universidade Federal do Rio de Janeiro, POLI&COPPE/UFRJ, Cidade Universitaria, Cx. Postal 68503, 21945-970, Rio de Janeiro, RJ, Brazil

ABSTRACT

Mixed lumped-differential formulations for diffusion problems are formally analyzed, with particular emphasis on heat transfer applications The main interest in these formulations resides in the task of modeling problems, prior to the choice of solution strategies, trying to reduce, as much as possible, and within prescribed accuracy requirements, the number of dimensions of any particular partial differential problem. This article illustrates appropriate integration strategies developed within a symbolic computation environment, which are employed to deduce mathematical formulations of comparable simplicity and improved accuracy in comparison with the classical well—established lumping procedures. Besides, approximate error expressions, based on the known boundary and/or initial conditions of the solutions, are readily obtained, for both steady and transient states formulations.