Natural convection in narrow-gap, spherical annuli

The subject of this paper is natural convection of fluid contained within narrow-gap, spherical annuli. The flows are presumed to be steady and the fluid is assumed to follow the Oberbeck-Boussinesq model. With the gap being very small relative to the outer sphere's radius, the dependent variables are solved for by using a regular perturbation method in powers of the relative gap width, epsilon. Solutions were found for a heated outer spere through terms of order epsilon to the 11th. The results include Nusselt numbers, and contours of streamlines and isotherms as functions of the Grashof and Prandtl numbers, epsilon and Q, the dimensionless uniform energy generation rate parameter. The value of epsilon ranged from 0.1 to 0.001, Pr from 0.01 to 10, and Gr 7 x 10 to the 6th to 5 x 10 to the 12th.