Numerical investigation on laminar forced convection and entropy generation in a curved rectangular duct with longitudinal ribs mounted on heated wall

Three-dimensional laminar forced convective flow and entropy generation in a 180-deg curved rectangular duct with longitudinal ribs equipped on the heated wall are investigated by numerical methods. The development of secondary vortices, temperature and local entropy generation distributions as well as the overall entropy generation in whole flow fields, including the entrance and fully developed region, are analyzed. The effects of rib size are particularly highlighted in the present paper. Calculations of cases with various rib sizes under different Dean numbers and external heat fluxes are carried out to examine the influence of rib on the flow field and entropy generation. The entropy generated from frictional irreversibility and heat transfer irreversibility is investigated separately in detail. The results reveal that the addition of rib can effectively reduce the entropy generation from heat transfer irreversibility since the secondary vortices are augmented by the rib, through which the heat transfer performance is enhanced, in turn making the temperature gradient become smoother. Nevertheless, the entropy generation due to frictional irreversibility is raised at the same time because larger fluid friction is resulted from the wider solid walls and the complex flows disturbed by ribs. Due to the opposite influences of rib on the entropy generations from irreversibilities, the analysis of the optimal trade-off is carried out based on the minimal entropy generation principle. The optimal rib size which induces the minimal entropy generation in the flow fields is found to be dependent on the external heat flux and Dean number. Even under some flow conditions, the resultant entropy generation could not be reduced but becomes worse when ribs are added. These results provide worthwhile information for considerations of adding ribs on a curved duct and the determinations of rib sizes from view point of thermodynamic second law.

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