ON THE OBERBECK-BOUSSINESQ APPROXIMATION

This paper deals with a derivation (using a perturbation technique) of an approximation, due to Oberbeck(8,9) and Boussinesq,(1) to describe the thermal response of linearly viscous fluids that are mechanically incompressible but thermally compressible. The present approach uses a nondimensionalization suggested by Chandrasekhar(2) and utilizing th e ratio of two characteristic velocities as a measure of smallness, sy stematically derives the Oberbeck-Boussinesq approximation as a third- order perturbation. In the present approach, the material is subjected to the constraint that the volume change is determined solely by the temperature change in the body and uses a novel approach in deriving t he thermodynamical restrictions. Consequently, it is free from the add itional assumptions usually added on in earlier works in order to obta in the correct equations.