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Knupp D.C.,State University of Rio de Janeiro | Cotta R.M.,Microfluidics | Cotta R.M.,Laboratory of Transmission and Technology of Heat | Naveira-Cotta C.P.,Microfluidics
International Journal of Heat and Mass Transfer

The present work advances a recently introduced approach based on combining the Generalized Integral Transform Technique (GITT) and a single domain reformulation strategy, aimed at providing hybrid numerical-analytical solutions to convection-diffusion problems in complex physical configurations and irregular geometries. The methodology has been previously considered in the analysis of conjugated conduction-convection heat transfer problems, simultaneously modeling the heat transfer phenomena at both the fluid streams and the channels walls, by making use of coefficients represented as space variable functions with abrupt transitions occurring at the fluid-wall interfaces. The present work is aimed at extending this methodology to deal with both fluid flow and conjugated heat transfer within arbitrarily shaped channels and complex multichannel configurations, so that the solution of a cumbersome system of coupled partial differential equations defined for each individual sub-domain of the problem is avoided, with the proposition of the single-domain formulation. The reformulated problem is integral transformed through the adoption of eigenvalue problems containing the space variable coefficients, which provide the basis of the eigenfunction expansions and are responsible for recovering the transitional behavior among the different regions in the original formulation. For demonstration purposes, an application is first considered consisting of a microchannel with an irregular cross-section shape, representing a typical channel micro-fabricated through laser ablation, in which heat and fluid flow are investigated, taking into account the conjugation with the polymeric substrate. Then, a complex configuration consisting of multiple irregularly shaped channels is more closely analyzed, in order to illustrate the flexibility and robustness of the advanced hybrid approach. In both cases, the convergence behavior of the proposed expansions is presented and critical comparisons against purely numerical approaches are provided. © 2014 Elsevier Ltd. All rights reserved. Source

Knupp D.C.,Laboratory of Transmission and Technology of Heat | Naveira-Cotta C.P.,Laboratory of Transmission and Technology of Heat | Ayres J.V.C.,Laboratory of Transmission and Technology of Heat | Cotta R.M.,Laboratory of Transmission and Technology of Heat | Orlande H.R.B.,Laboratory of Transmission and Technology of Heat
International Journal of Thermal Sciences

Theoretical and experimental methodologies for the identification of spatially variable thermophysical properties and for simulating multidimensional heat transfer in heterogeneous materials are illustrated by using plate samples with aluminum oxide nanoparticles dispersed in a polymeric matrix. First, the heterogeneous nanocomposite plate is thermally characterized by means of a fairly simple experimental setup which can be modeled by a one-dimensional heat conduction formulation with space variable properties. Non-intrusive temperature measurements are obtained via infrared thermography, while the direct problem is handled by an error-controlled integral transform solution with an improved lumped-differential formulation, and the inverse analysis is undertaken via Bayesian inference, making use of the Markov Chain Monte Carlo method. Then, in order to illustrate the application of the methodologies here presented, an experimental multidimensional demonstration is provided consisting of a small electrical resistance attached to the plate, simulating a heat generating electronic device installed on the nanocomposite substrate, which in such situation works as a heat spreader modeled by an improved lumped-differential two-dimensional heat conduction formulation. The integral transform solution of the lumped-differential two-dimensional problem is then critically compared against the infrared thermography experimental results.© 2011 Elsevier Masson SAS. All rights reserved. Source

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