Flow and free surface of a non-Newtonian fluid between concentric cylinders maintained at unequal temperatures

The motion and the shape of the free surface of a non-Newtonian liquid which fills the open space between two concentric cylinders maintained at different temperatures were analyzed. Under the effect of the temperature gradient the liquid circulates, driven by buoyant forces due to density variations and the free surface can not maintain its static shape. The analysis is set within the framework of Noll's concept of simple fluids. The motion is governed by the Oberbeck-Boussinesq equations. The non-linear problem is posed on a domain which must be determined as part of the solution. The Lagrangian theory of domain perturbations, which involves simultaneous perturbations of the field equations and the unknown flow domain, is used and the stress is assumed to be Frechet differentiable and expanded in a series in terms of the perturbation parameter, the temperature difference of the cylinder walls. The solution in the physical domain is represented as a power series, whose coefficients are the partial derivatives evaluated the rest state.