  The Oberbeck-Boussinesq approximation is the most widely 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 note,
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.
