Eigenfunction Expansions for Coupled Nonlinear Convection-Diffusion Problems in Complex Physical Domains

Cotta, Renato M.; Naveira-Cotta, Carolina P.; Knupp, Diego C.; Zotin, José Luiz Zanon; Pontes, Péricles C.

doi:10.1088/1742-6596/745/2/022001

Cited by 3 publications

(2 citation statements)

References 10 publications

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“…The algebraic eigenvalue problem (11) can be readily solved numerically to provide results for the eigenvalues µ and corresponding eigenvectors w È É which are then combined by the inverse formula given in Equation (10b) to provide an explicit representation of the desired original eigenfunctions, ψ(y,z). Then, the transformed system solution, given by Equation 7, can be readily substituted into Equations (8), together with the calculated eigenfunctions, yielding the temperature field T representation at any desired position (x, y, z).…”

Section: Problem Formulation and Solution Methodologymentioning

confidence: 99%

Analysis of conjugated heat transfer in micro-heat exchangers via integral transforms and non-intrusive optical techniques

Knupp

Naveira-Cotta

Renfer

et al. 2015

Int Jnl of Num Meth for HFF

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Purpose-The purpose of this paper is to employ the Generalized Integral Transform Technique in the analysis of conjugated heat transfer in micro-heat exchangers, by combining this hybrid numerical-analytical approach with a reformulation strategy into a single domain that envelopes all of the physical and geometric sub-regions in the original problem. The solution methodology advanced is carefully validated against experimental results from non-intrusive techniques, namely, infrared thermography measurements of the substrate external surface temperatures, and fluid temperature measurements obtained through micro Laser Induced Fluorescence. Design/methodology/approach-The methodology is applied in the hybrid numerical-analytical treatment of a multi-stream micro-heat exchanger application, involving a three-dimensional configuration with triangular cross-section micro-channels. Space variable coefficients and source terms with abrupt transitions among the various sub-regions interfaces are then defined and incorporated into this single domain representation for the governing convection-diffusion equations. The application here considered for analysis is a multi-stream micro-heat exchanger designed for waste heat recovery and built on a PMMA substrate to allow for flow visualization. Findings-The methodology here advanced is carefully validated against experimental results from non-intrusive techniques, namely, infrared thermography measurements of the substrate external surface temperatures and fluid temperature measurements obtained through Laser Induced Fluorescence. A very good agreement among the proposed hybrid methodology predictions, a finite elements solution from the COMSOL code, and the experimental findings has been achieved. The proposed methodology has been demonstrated to be quite flexible, robust, and accurate. Originality/value-The hybrid nature of the approach, providing analytical expressions in all but one independent variable, and requiring numerical treatment at most in one single independent variable, makes it particularly well suited for computationally intensive tasks such as in optimization, inverse problem analysis, and simulation under uncertainty.

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Section: Problem Formulation and Solution Methodologymentioning

confidence: 99%

Analysis of conjugated heat transfer in micro-heat exchangers via integral transforms and non-intrusive optical techniques

Knupp

Naveira-Cotta

Renfer

et al. 2015

Int Jnl of Num Meth for HFF

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“…This work is an extended version of the plenary lecture presented by R.M. Cotta in the 7th European Thermal Sciences Conference, EUROTHERM 2016, Krakow, Poland, June 2016 [32].…”

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confidence: 99%

Recent advances in computational-analytical integral transforms for convection-diffusion problems

et al. 2017

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An unifying overview of the Generalized Integral Transform Technique (GITT) as a computational-analytical approach for solving convection-diffusion problems is presented. This work is aimed at bringing together some of the most recent developments on both accuracy and convergence improvements on this well-established hybrid numericalanalytical methodology for partial differential equations. S p e c i a l e m p h a s i s i s g i v e n t o n o v e l a l g o r i t h m implementations, all directly connected to enhancing the eigenfunction expansion basis, such as a single domain reformulation strategy for handling complex geometries, an integral balance scheme in dealing with multiscale problems, the adoption of convective eigenvalue problems in formulations with significant convection effects, and the direct integral transformation of nonlinear convection-diffusion problems based on nonlinear eigenvalue problems. Then, selected examples are presented that illustrate the improvement achieved in each class of extension, in terms of convergence acceleration and accuracy gain, which are related to conjugated heat transfer in complex or multiscale microchannel-substrate geometries, multidimensional Burgers equation model, and diffusive metal extraction through polymeric hollow fiber membranes. Numerical results are reported for each application and, where appropriate, critically compared against the traditional GITT scheme without convergence enhancement schemes and commercial or dedicated purely numerical approaches.

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Integral transform solution of eigenvalue problems within irregular geometries: Comparative analysis of different methodologies

Pinheiro

Sphaier

Knupp

2019

Numerical Heat Transfer, Part B: Fundamentals

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Eigenfunction Expansions for Coupled Nonlinear Convection-Diffusion Problems in Complex Physical Domains

Cited by 3 publications

References 10 publications

Analysis of conjugated heat transfer in micro-heat exchangers via integral transforms and non-intrusive optical techniques

Analysis of conjugated heat transfer in micro-heat exchangers via integral transforms and non-intrusive optical techniques

Recent advances in computational-analytical integral transforms for convection-diffusion problems

Integral transform solution of eigenvalue problems within irregular geometries: Comparative analysis of different methodologies

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