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Computational-Analytical Integral Transforms and Lumped-Differential Formulations: Benchmarks and Applications in Nuclear Technology

DOI: 10.1615/THMT-18.80
pages 125-140

Renato M. Cotta
Laboratory of Nano- and Microfluidics and Microsystems, LabMEMS, Mechanical Engineering Department and Nanotechnology Engineering Dept., POLI & COPPE, Universidade Federal do Rio de Janeiro, Cidade Universitária, Cx. Postal 68503, Rio de Janeiro, RJ, CEP 21945-970, Brazil; Interdisciplinary Nucleus for Social Development—NIDES/CT, UFRJ, Brazil; Mechanical Engineering Department, University College London, UCL, United Kingdom

Jian Su
Interdisciplinary Nucleus of Fluid Dynamics, NIDF, Mechanical Eng. Dept., POLI & COPPE, Universidade Federal do Rio de Janeiro, Brazil; Nuclear Eng. Dept., POLI & COPPE, Universidade Federal do Rio de Janeiro, Brazil

A. Pontedeiro
General Directorate of Nuclear and Technological Development, DGDNTM, Brazilian Navy, Rio de Janeiro, Brazil

K.M. Lisboa
Interdisciplinary Nucleus of Fluid Dynamics, NIDF, Mechanical Eng. Dept., POLI & COPPE, Universidade Federal do Rio de Janeiro, Brazil

Abstract

A mixed lumped-differential reformulation strategy, known as the Coupled Integral Equations Approach (CIEA), and a unified integral transforms solution methodology, known as the Generalized Integral Transform Technique (GITT), are reviewed in the computational-analytical handling of nonlinear diffusion and convection-diffusion problems. The aim of the CIEA is to reduce the number of space variables in the associated partial differential equations, by improved averaging processes through Hermite integration formulae. On the other hand, the GITT is aimed at providing hybrid numerical-analytical solutions to partial differential equations, by eliminating all but one of the independent variables through analytical eigenfunction expansions, followed by an integral transformation process that yields a transformed ordinary differential system to be numerically solved for the transformed potentials. The two approaches can be used independently or in combination and are here illustrated for problems associated with nuclear technology applications, such as the thermal analysis of high burnup nuclear fuel rods and the wet storage of spent nuclear fuel elements with passive pool cooling.

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