On the Use and Misuse of the Oberbeck–Boussinesq Approximation

Antonio Barletta; M Celli; D A S Rees

doi:10.3390/physics5010022

On the Use and Misuse of the Oberbeck–Boussinesq Approximation

Antonio Barletta
, M Celli
, D A S Rees

Department of Mechanical Engineering

Università di Bologna

Research output: Contribution to journal › Article › peer-review

15 Citations (SciVal)

154 Downloads (Pure)

Abstract

The Oberbeck–Boussinesq approximation is the most commonly employed theoretical scheme for the study of natural or mixed convection flows. However, the misunderstanding of this approximated framework is a possibility that may cause the emergence of paradoxes or, at least, incorrect conclusions. In this paper, the basic features of the Oberbeck–Boussinesq approximation are briefly recalled and three simple examples where this theoretical scheme may be misused are provided. Such misuses of the approximation lead to erroneous conclusions that, in the examples presented in this note, entail violations of the principle of mass conservation. A discussion about the Oberbeck–Boussinesq approximation as an asymptotic theory obtained by letting the product of the
thermal expansion coefficient and the reference temperature difference tend to zero is also presented.

Original language	English
Pages (from-to)	298–309
Number of pages	12
Journal	Physics
Volume	5
Issue number	1
Early online date	17 Mar 2023
DOIs	https://doi.org/10.3390/physics5010022
Publication status	Published - 31 Mar 2023

Bibliographical note

The authors A. Barletta and M. Celli acknowledge the financial support from the Italian Ministry of Education, University and Research (MIUR), grant PRIN 2017F7KZWS.

Publisher Copyright:
© 2023 by the authors.

Funding

This research was funded by Italian Ministry of Education, University and Research (MIUR) grant number PRIN 2017F7KZWS.

Funders	Funder number
Ministry of Education, Universities and Research	PRIN 2017F7KZWS

Keywords

buoyancy force
porous media
thermal convection
variable density

ASJC Scopus subject areas

General Physics and Astronomy

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10.3390/physics5010022Licence: CC BY

paper191Final published version, 283 KBLicence: CC BY

Cite this

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abstract = "The Oberbeck–Boussinesq approximation is the most commonly employed theoretical scheme for the study of natural or mixed convection flows. However, the misunderstanding of this approximated framework is a possibility that may cause the emergence of paradoxes or, at least, incorrect conclusions. In this paper, the basic features of the Oberbeck–Boussinesq approximation are briefly recalled and three simple examples where this theoretical scheme may be misused are provided. Such misuses of the approximation lead to erroneous conclusions that, in the examples presented in this note, entail violations of the principle of mass conservation. A discussion about the Oberbeck–Boussinesq approximation as an asymptotic theory obtained by letting the product of the thermal expansion coefficient and the reference temperature difference tend to zero is also presented.",

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N2 - The Oberbeck–Boussinesq approximation is the most commonly employed theoretical scheme for the study of natural or mixed convection flows. However, the misunderstanding of this approximated framework is a possibility that may cause the emergence of paradoxes or, at least, incorrect conclusions. In this paper, the basic features of the Oberbeck–Boussinesq approximation are briefly recalled and three simple examples where this theoretical scheme may be misused are provided. Such misuses of the approximation lead to erroneous conclusions that, in the examples presented in this note, entail violations of the principle of mass conservation. A discussion about the Oberbeck–Boussinesq approximation as an asymptotic theory obtained by letting the product of the thermal expansion coefficient and the reference temperature difference tend to zero is also presented.

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On the Use and Misuse of the Oberbeck–Boussinesq Approximation

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

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