Boussinesq-type approximation for second-grade fluids

We derive the equivalent of the Oberbeck-Boussinesq approximation for second-grade fluids. We find that two new non-dimensional numbers (in comparison to the Newtonian model) have to be taken into account in order to arrive at the approximation. In addition we deduce a system which does not neglect dissipative heating together with criteria which qualify the system to be suitable.