Friction-factor and Nusselt-number correlations for low-Reynolds-number flow in curved and helical rectangular channels

This paper derives friction-factor Re f and Nusselt-number Nu correlations for laminar, fully developed, parallel flow in curved rectangular channels. The correlations depend on the channel geometry as characterized by two dimensionless parameters—the channel aspect ratio α and the radius of curvature ξ ( 0 . 1 ≤ α ≤ 5 and 0 . 1 ≤ ξ ≤ 5 ). The analysis shows that the dimensionless correlations can be derived from an eigenvalue of the dimensionless conservation equations. The computational approach solves dimensionless circumferential momentum and thermal-energy equations with a high-resolution finite-element method. The analysis is restricted to parallel flow, with the circumferential velocity being the only velocity component (i.e., there are no radial and axial velocities). This assumption necessarily eliminates the possibility of Dean vortices, which are present in curved channels under flow circumstances that include high Reynolds numbers and small radius of curvature. The results are validated by comparisons with known limiting cases and with three-dimensional computational-fluid-dynamics simulations. The paper reports quantitative fits to the derived correlations (i.e., Re f ( α , ξ ) and Nu( α , ξ ).