Numerical analysis of entropy generation and optimal Reynolds number for developing laminar forced convection in double-sine ducts with various aspect ratios

In the present paper, the entropy generation in a double-sine duct, which is frequently used in plate heat exchangers, is investigated by numerical methods. The Reynolds number (Re) at inlet covers ranges from 86 to 2000, and wall heat flux (q″) varies as 160, 320 and 640 W/m2. Three aspect ratio (Λ/a) cases, including Λ/a = 2, 4 and 8, are investigated. The results indicate that the entropy generation, image, in cases with larger Re and smaller q″ is dominated by the entropy generation due to frictional irreversibility (image); whereas the entropy generation is dominated by the entropy generation due to heat transfer irreversibility (image) in cases with smaller Re and larger q″. There is no monotonic relationship between Λ/a and image or image. For all cases with different Re and q″, image is found to be minimal in Λ/a = 2 case, whereas image is minimal in Λ/a = 4 case. The optimal aspect ratio, (Λ/a)opt, with which the minimal image can be obtained, is found to be dependent on Re and q″. In q″ = 160 W/m2 case, (Λ/a)opt = 2 when Re > 540; (Λ/a)opt = 4 when Re < 540. In q″ = 320 W/m2 case, (Λ/a)opt = 2 when Re > 662; (Λ/a)opt = 4 when Re < 662. In q″ = 640 W/m2 case, (Λ/a)opt = 2 when Re > 1008; (Λ/a)opt = 4 when Re < 1008. An optimal Re, which is found to increase with q″, exists for every case with specific Λ/a and q″ to induce the minimal image. These results provide important information for the heat exchanger design since the thermal system could have the least irreversibility and best exergy utilization if the optimal Re and optimal aspect ratio is used according to the practical design conditions.