Flow transitions and combined free and forced convective heat transfer in a rotating curved circular tube

Abstract

The simultaneous effects of curvature, rotation and heating/cooling of the tube complicate the flow and heat transfer characteristics beyond those observed in the tubes with simple curvature, rotation or heating/cooling. The phenomena encountered are investigated for steady, hydrodynamically and thermally fully developed laminar flow in circular tubes. A full second-order perturbation solution is obtained under the condition that the wall heat flux is uniform with peripherally uniform wall temperature. The results cover both the nature of flow transitions and the effect of these transitions on temperature distribution, friction factor and Nusselt number. When the rotation is in the same direction as the main flow imposed by a pressure gradient and the fluid is heated, the flow and heat transfer remain similar to those observed in stationary curved tubes, radially rotating straight tubes or mixed convection in stationary straight tubes. There are, however, quantitative changes due to the combined effects of centrifugal, Coriolis and buoyancy forces. A more complex behaviour is possible when the rotation is opposite to the flow due to the pressure gradient or when the fluid is cooled. In particular, the inward Coriolis force and/or buoyancy force may cause the direction of the secondary flow to reverse. The flow reversal occurs by passing through a four-cell vortex flow region where overall, the centrifugal, Coriolis and buoyancy forces just neutralize each other.