Laminar Forced Convection Heat Transfer in Spherical Annuli

An analysis is presented of forced convection heat transfer in spherical annuli bounded by isothermal surfaces at different temperatures. Flow enters the annulus through a port in the outer sphere and exits through a diametrically opposite port. The conservation equations of mass, momentum, and energy are reduced to dimensionless form, and the governing parameters of the problem are identified. Solutions are obtained for several values of each of the governing parameters via a numerical finite-difference procedure. It is found that very complex flow patterns can prevail within the annulus, particularly at high Reynolds numbers. Details of the flow field are presented by means of velocity and pressure profile plots. The effect of the flow patterns on the heat transfer phenomena is discussed by examining temperature profiles and variations of the local Nusselt number along the spherical surfaces. In addition, the circumferential average Nusselt numbers at the two spherical surfaces are presented as functions of the governing parameters of the problem. These graphs of average Nusselt numbers constitute information that could be used in the design of spherical annulus heat transfer equipment.