On the laminar free convection and instability of grade fluids in enclosures

Free convection of rate fluids of the grade type in an inclined cavity of arbitrary aspect ratio is investigated in two dimensions by a regular perturbation in terms of the Grashof number. Fluids of grade N are assumed to be Fourier and Boussinesq fluids. 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 non-linear 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 with a negative first Rivlin–Ericksen constant triggered by elastic effects is identified and the implications concerning heat transfer characteristics are discussed.