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Hybrid Methods in Engineering

ISSN Imprimir: 1099-2391
ISSN On-line: 2641-7359

Archives: Volume 1, 1999 to Volume 4, 2002

Hybrid Methods in Engineering

DOI: 10.1615/HybMethEng.v3.i4.60
14 pages

INTEGRAL TRANSFORMS FOR HEAT AND FLUID FLOW IN TWO- AND THREE-DIMENSIONAL POROUS MEDIA

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
H. Luz Neto
Instituto Nacional de Tecnologia — INT, Rio de Janeiro, Brazil
Leonardo Alves
Departamento de Engenharia Mecânica - TEM Universidade Federal Fluminense - UFF
Joao N. N. Quaresma
School of Chemical Engineering, Universidade Federal do Para, FEQ/UFPA, Campus Universitario do Guama, 66075-110, Belem, PA, Brazil

RESUMO

Hybrid numerical—analytical algorithms, based on the generalized integral transform technique, are developed and reviewed to handle transient two-and three-dimensional heat and fluid flow in cavities filled with a porous material. A general formulation and solution methodology for horizontal and vertical cavities is developed. To illustrate the algorithm computational behavior, specific situations are more closely considered, under the Darcy model for natural convection in porous medium filled cavities. The problem is analyzed with and without the time derivative term in the flow equations, using a vorticity-vector potential formulation, which automatically reduces to the stream-function-only formulation for two-dimensional situations. Results for rectangular (2-D) and parallelepiped (3-D) vertical cavities are presented to demonstrate the convergence behavior of the proposed eigenfunction expansion solutions, and comparisons with previously reported numerical solutions are critically performed.


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