MIXED-CONVECTION FLOWS WITHIN A HORIZONTAL CONCENTRIC ANNULUS WITH A HEATED ROTATING INNER CYLINDER

Abstract

Numerical analysis is performed for two-dimensional mixed convection in the annulus between horizontal concentric cylinders with a heated rotating inner cylinder. The ratio of the annulus gap width to the inner cylinder radius is held fixed at 1.6. The Grashof number range is taken from 1.39 × 10 2 D. Coles , Transition in Circular Couette Flow , J. FluidMech. , vol. 23 , part 3 , pp. 385 – 425 , 1965 .[Crossref] , [Google Scholar] to 1.39 × 10 5 J. Lis , Experimental Investigation of Natural Convection Heat Transfer in Simple and Obstructed Horizontal Annuli , Proc. 3rd Int. Heat Transfer Conf. , paper 61 , vol. 2 , pp. 196 – 204 , 1966 . [Google Scholar] and the rotational parameter σ ( = Gr/Re 2 D. Coles , Transition in Circular Couette Flow , J. FluidMech. , vol. 23 , part 3 , pp. 385 – 425 , 1965 .[Crossref] , [Google Scholar]) varies from ∞ ( pure natural convection) to 1. The flow and temperature fields and heat transfer characteristics are presented over this parameter range where effects of both buoyancy and centrifugal force due to rotation are significant. A relatively novel formulation of the Navier-Stokes equations is employed in the present study. A vorticity transport equation, two Poisson equations for the velocity components, and the energy equation are solved by a finite-difference scheme. A direct method is used to solve simultaneously for the dependent variables along a grid line via a block tridiagonal matrix algorithm. The formulation is found to be stable over the entire range of σ studied and appropriate for investigating fluid flow and heat transfer problems in multiply connected domains where the net flow rate is not known a priori.