Theoretical analysis for axisymmetric mixed convection between rotating coaxial disks

Abstract

This paper deals with a similarity analysis of axisymmetric mixed convection between two horizontal infinite coaxial disks. Governing equations with respect to a rotating frame of reference are formulated, and Boussinesq approximation is invoked to explore centrifugal-buoyancy effects. The rotational conditions of two disks rotating at different rates are mainly concerned. Upon considering Reynolds number up to 2000 and the buoyancy parameter ( B = βΔT) of | B | ⩽ 0.1, the rotational effects on the flow and heat transfer characteristics are examined. Analytic features of the high-Re solution behaviors are also studied. By using the present similarity model, flow structure patterns of co-rotating, counter-rotating and rotor-stator systems under the influence of buoyancy effect are disclosed. Furthermore, the results also reveal the significance of centrifugal buoyancy in flow and heat transfer characteristics. For co-rotating disks, the centrifugal-buoyancy effects are reflected in the velocity field and skin friction. In the case of counter-rotating disks, remarkable buoyancy effects exert on the temperature field, heat transfer rate, and the radial skin friction. For rotor-stator systems, the buoyancy effects on boundary derivatives are insignificant, while those on core-flow in high-Re cases are noticeable.