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International Heat Transfer Conference 15

ISSN: 2377-424X (online)
ISSN: 2377-4371 (flashdrive)

Unified Integral Transforms in Single Domain Formulation for Internal Flow Three-Dimensional Conjugated Problems

Diego C. Knupp
Polytechnique Institute, State University of Rio de Janeiro, Brazil

Carolina Palma Naveira-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; Mechanical Engineering Department, University College London, UCL, United Kingdom

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

DOI: 10.1615/IHTC15.nsm.009729
pages 5867-5880


PALABRAS CLAVE: Conjugated problem, Hybrid methods, Integral transforms, Micro-channel, Laminar flow

Sinopsis

The Integral Transform Method is employed in the hybrid numerical-analytical solution of three-dimensional conjugated conduction-convection problems for internal flow situations based on a single domain formulation for both the solid and fluid regions. The transition between the solid and fluid domains is accounted for through space variations of the energy equation coefficients. Then, this information is carried along to the associated eigenvalue problem which supports the eigenfunction expansion of the temperature field. The Generalized Integral Transform Technique (GITT) is then employed to yield a hybrid solution of this eigenvalue problem with space variable coefficients, resulting in an algebraic eigenvalue problem. The approach is here illustrated for steady three-dimensional laminar convection within a rectangular micro-channel with participating walls. Convergence behavior of the proposed eigenfunction expansions is then critically examined and physical interpretation of the obtained numerical results is provided.

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