Numerical solution for fully developed flow in heated curved tubes

Fully developed laminar flow for a horizontal heated curved tube is studied numerically. The tube is heated so as to maintain a constant axial temperature gradient. A physical model is introduced that accounts for the combined effects of both buoyancy and centrifugal force. Results, for a Prandtl number of one, are presented for a moderate range of Dean numbers and the product of the Reynolds and Rayleigh numbers. Detailed predictions of the flow resistance, the average heat-transfer rate and the secondary-flow streamlines are given. Also presented are results on the position of the local maxima of shear stress and heat-transfer rate. The numerical results reveal that the mass-flow rate is drastically reduced owing to the secondary flow for a given axial pressure gradient. Consequently, the total heat- transfer rate decreases for a more-curved tube as well as for a larger axial temperature gradient. A flow-regime map is provided to indicate the three basic regimes where (i) centrifugal force dominates, (ii) both buoyancy and centrifugal forces are important, and (iii) buoyancy force dominates.