On the Oberbeck–Boussinesq approximation for fluids with pressure dependent viscosities

We derive, by using a rigorous perturbative approach, the Oberbeck–Boussinesq approximation within the framework of one of the simplest implicit constitutive theories: that of fluids with pressure dependent viscosity. To illustrate an application we use the equations derived here to study the flow of a fluid in a channel with heated walls.