Free convection between horizontal concentric cylinders in a slightly-thermally stratified fluid

Abstract

The present paper considers the steady, two-dimensional Flow of a vertically stratified viscous fluid in the annulus between two concentric horizontal cylinders in a uniform gravity field. The outer cylinder is assumed to be maintained at a variable temperature such that conditions for vertical stratification are satisfied. Theoretical solutions are obtained in a power series of (modified) Grashof number G up to G 3. Two cases are considered: when the inner cylinder is either thermally insulated or when its surface temperature is kept constant. Results are presented mostly in the form of graphs of the streamlines and isotherms. A dimensionless stratification parameter S governs the flow. For S equal to zero, the solutions tend to the unstratified case. When S approaches infinity, the flow has both vertical and horizontal symmetry. When the inner cylinder is thermally insulated, the streamline pattern is almost the same as in the isothermal case ( S = ∞), but the directions of the flow are reversed.