Three-dimensional thermal convection of viscoelastic fluids

The influence of inertia and elasticity on the onset and stability of three-dimensional thermal convection is examined for highly elastic polymeric solutions with constant viscosity. These solutions are known as Boger fluids, and their rheology is approximated by the Oldroyd-B constitutive equation. The onset and the stability of steady convective patterns, namely rolls, hexagons and squares, are studied in the post-critical range of the Rayleigh number by using an amplitude equation approach. The square pattern is found to be unstable. In contrast to Newtonian fluids, the hexagonal pattern can be stable for a certain range of elasticity.