Estimation of slip flow parameters in microscale conjugated heat transfer problems

In this work, it is proposed the direct and inverse analyses of the forced convection of an incompressible gas flow within rectangular channels in the range of the slip flow regime by taking into account the wall conjugation and the axial conduction effects. The Generalized Integral Transform Techni...

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Bibliographic Details
Published in:Journal of the Brazilian Society of Mechanical Sciences and Engineering 2020-05, Vol.42 (5), Article 263
Main Authors: Silva, Géssica R., Knupp, Diego C., Naveira-Cotta, Carolina P., Cotta, Renato M., Silva Neto, Antônio J.
Format: Article
Language:English
Subjects:
Biot number
Computational fluid dynamics
Conjugation
Eigenvalues
Engineering
Fluid flow
Forced convection
Gas flow
Incompressible flow
Integral transforms
Inverse problems
Mechanical Engineering
Operators (mathematics)
Parameter estimation
Slip flow
Technical Paper
Wall thickness
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Summary:In this work, it is proposed the direct and inverse analyses of the forced convection of an incompressible gas flow within rectangular channels in the range of the slip flow regime by taking into account the wall conjugation and the axial conduction effects. The Generalized Integral Transform Technique (GITT) combined with the single-domain reformulation strategy is employed in the direct problem solution of the three-dimensional steady forced convection formulation. A non-classical eigenvalue problem that automatically accounts for the longitudinal diffusion operator is here proposed. The Bayesian framework implemented with the maximum a posteriori objective function is used in the formulation of the inverse problem, whose main objective is to estimate the temperature jump coefficient, the velocity slip coefficient, and the Biot number, using only external temperature measurements, as obtained, for instance, with an infrared measurement system. A comprehensive numerical investigation of possible experimental setups is performed in order to verify the influence of the Biot number, wall thickness, and Knudsen number on the precision of the unknown parameters estimation.
ISSN:1678-5878
1806-3691
DOI:10.1007/s40430-020-02328-z