Numerical analysis of different fluted fins for condensation on a vertical tube

Abstract A numerical analysis of laminar film condensation of pure vapor on an isothermal vertical fluted tube surface is presented using a surface-fitted orthogonal curvilinear coordinate system. Based on the assumptions employed in Nusselt's analysis on a flat plate, a liquid film thickness equation for film-wise condensation on fluted surface is obtained by simplifying the Navier-Stokes equations. By defining the fluted fin surface curvatures, different fin shapes can be obtained. A relationship between curvature parameters of the sinuous fluted tube such as fin height and fin arc length is obtained. A general condensation performance comparison method for different fin geometries which is set up using the Fourier's series approximation is presented by defining the fin surface curvature parameters. By solving the liquid film thickness equation, the curvature variation effects on a condensing surface and the stable film profiles are investigated. The calculations show that the standard sinuous fin's crest region area is crucial for total condensation heat transfer. It is demonstrated that the effect of surface tension because of curvature change on fluted sinuous fins is important in heat transfer enhancement as compared to other rectangular, triangular and other sinuous fin surfaces. For a constant base diameter tube, it was determined that heat transfer enhancement of the sinuous fins can be achieved by increasing the number of fins and the fin length. However, it is not a valid method to lengthen the fin height for rectangular or triangular fin when the liquid flow does not reach flooding. A more useful outside tube fin arrangement, which takes full advantage of fin tip effect and flooding flow characteristic, is presented.