Natural convection of viscoelastic liquids

Two dimensional natural convection of a nonlinear fluid of the differential type, in an inclined cavity of arbitrary aspect ratio is solved by a regular perturbation for small Grashof numbers. We show that the series are asymptotic in character. Non-Newtonian effects appear at the third order of the analysis even though the Giesekus-Tanner theorem is not valid. The relative contributions of the elastic and shear rate dependent viscosity characteristics of the liquid to the non-Newtonian behavior are investigated through a parametric study, together with the dependence of the Nusselt number on the nonlinear properties of the fluid. The effects of the aspect ratio and the inclination of the enclosure on the flow field and the heat transfer coefficient are also investigated. An interesting instability of the fluid of grade three triggered by elastic effects is discussed together with the implications concerning heat transfer characteristics.