Effect of curvature on the thermal stability of a fluid between two long vertical coaxial cylinders

The effects of curvature on the stability of natural convection between two long vertical concentric cylinders at constant but different temperature with a hot inside cylinder are studied in the conduction regime by using the linear theory of stabililty over a range of radius ratio from 0.1 to 0.75 , and the Prandtl number from 0.1 to 1000. For all Prandtl numbers considered in the study, the instability sets in as a travelling wave moving in the direction opposite to the gravity. For low Prandtl numbers (i.e., Pr less than 0.71), increasing the curvature stabilizes the flow. This effect is reversed for Prandtl numbers in the range 10-100. For moderate Prandtl numbers (i.e., (5.6-10) the increase of curvature first stabilizes the flow then destabilizes it. For Prandtl numbers above 100, the curvature does not effect the stability.