On the Use and Misuse of the Oberbeck–Boussinesq Approximation

Antonio Barletta, M Celli, D A S Rees

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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.
Original languageEnglish
Pages (from-to)298–309
JournalPhysics
Volume5
Issue number1
Early online date17 Mar 2023
DOIs
Publication statusPublished - 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.

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