Natural convection in an annulus between two rotating vertical cylinders

A numerical study is conducted to understand the effect of rotation on the axisymmetric flow driven by buoyancy in an annular cavity formed by two con centric vertical cylinders which rotate about their axis with different ang ular velocities. The inner and outer side walls are maintained isothermally at temperatures theta (c) and theta (h), respectively, while the horizonta l top and bottom walls are adiabatic. The vorticity-stream function form of the Navier-Stokes equations and the energy equation have been solved by mo dified Alternating Direction Implicit method and Successive Line Over Relax ation method. Numerical results are obtained for a wide range of the Grasho f number, Gr nondimensional rotational spends Omega (i) Omega (o) of inner and outer cylinders and for different values of the Prandtl number Pr. The effects of the aspect ratio, A, on the heat transfer and now patterns are o btained for A = 1 and 2. The numerical results show that when the outer cyl inder alone is rotating and the Grashof number is moderate, the outward bou nd flow is confined to a thin region along the bottom surface while the ret urn now covers a major portion of the cavity. For a given inner or outer cy linder rotation the temperature field is almost independent of the now in t he annulus for fluids with low Prandtl number, while it depends strongly fo r high Prandtl number fluids. At a high Grashof number, with moderate rotat ional speeds, the dominant now in the annulus is driven by thermal convecti on, and hence an increase in the heat transfer rate occurs. In the case of unit aspect ratio, the now pattern is unicellular for the rotation of the c ylinders in the same direction, and when they rotate in the opposite direct ion two or more counter rotating cells separated by a stagnation surface ar e formed. The rate of heat transfer at the hot cylinder is suppressed when its speed of rotation is higher than that of the cooler cylinder. The compu ted heat transfer and now patterns are compared with the available results of a nonrotating cylindrical annulus, and good agreement is found.