Numerical Investigation of Thermodynamic Performance in Gradient-Pitch Twisted Square Ducts with Variable Aspect Ratio

This study numerically investigates heat transfer and thermodynamic behavior in twisted square and rectangular air ducts while keeping a constant hydraulic diameter (Dh = 30 mm). Three aspect ratios are considered (AR = 1.00, 0.75, and 0.50). The heated test section (900 mm) is divided into three equal segments, and three pitch patterns are examined: a uniform pitch (400–400–400 mm, P444) and two axial gradients (300–400–500 mm, P345; 500–400–300 mm, P543). All results are compared to a standard reference, the straight square duct (SD-AR1.00), to ensure fair comparisons across all cases with Reynolds numbers between 5000 and 20,000. Among the twisted ducts, the strongest rectangularity combined with the increasing pitch sequence, TSD-AR0.50-P345, provides the best overall balance. Its heat transfer rises from Nu = 39.39 to 88.62, giving Nu/Nu0 = 1.493 → 1.433, while the pressure penalty increases to f/f0 = 1.345 → 1.405. Under cube-root weighting of friction, this case maintains the highest thermal performance factor, TPF = 1.352 at Re = 5000 and TPF = 1.279 at Re = 20,000. Second-law trends support the same ranking: exergy destruction decreases from 12.81 W (baseline) to 8.44 W at Re = 5000 (≈34% reduction) and from 6.54 W to 4.84 W at Re = 20,000 (≈26% reduction). The Bejan number remains high at low Reynolds numbers (≈0.998), indicating heat-transfer irreversibility dominance, but drops at higher Reynolds numbers (≈0.87) as frictional effects become more important. In general, the results show that adding a small axial pitch increase to rectangularity can improve near-wall mixing while reducing losses downstream. This leads to a clear improvement in both first-law performance and exergy-based measures.