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INVERSE PROBLEM ANALYSIS FOR HEAT FLUX ESTIMATION IN CONJUGATED CONDUCTION-EXTERNAL CONVECTION

DOI: 10.1615/ICHMT.2008.CHT.2160
20 pages

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

Helcio R. B. Orlande
Department of Mechanical Engineering, Federal University of Rio de Janeiro – POLI/COPPE, Centro de Tecnologia, Caixa Postal: 68503, Cidade Universitária, Rio de Janeiro, 21941-972, Brazil

Abstract

This work presents an inverse problem analysis for the estimation of the net heat flux to or from the solid wall in forced convection over flat plates of non-negligible thickness, subjected to arbitrary variations of applied wall heat flux at the interface fluid-solid wall. A function estimation approach is implemented, based on the maximum likelihood objective function without and with Tikhonov regularization of zeroth and first orders. Different optimization methods are critically investigated and compared, including Newton, Levenberg-Marquadt, and Simulated Annealing. The provided data for the heat flux estimation is restricted to a few temperature measurements at the fluid-solid interface. The algorithm is constructed in the Mathematica 5.2 platform and is first tested with simulated data for a prescribed heat flux with linear variation along the longitudinal coordinate. Then, the conjugated conduction-external convection formulation is considered and solved by a hybrid numerical-analytical approach to yield a more realistic set of data for the heat flux partition estimation.

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