Ahmed M. Hassan, Mohammed Azeez Alomari, Luma M. Ahmed, Teeba Ismail Kh, Faris Alqurashi, Omaima Jabbar
• T-shaped rib turbulators with CuO /water nanofluid achieve 121% Nusselt number enhancement. • Thermo-Fluid Efficiency Factor exceeds unity for all cases; peak TFEF = 3.17 at P/e = 12. • Bejan number Be > 0.97 confirms thermal irreversibility dominance across all 40 cases. • First-law and second-law optima coincide at P/e = 12, validating the rib configuration. • Power-law correlations for Nu, f, and TFEF derived with R² ≥ 0.975 and MAPE ≤ 2.26%. This study presents a numerical investigation of turbulent forced-convection heat transfer and entropy generation in a rectangular channel with T-shaped rib turbulators, employing CuO /water nanofluid ( φ = 3% ) as the working fluid. The finite element method (FEM) with the RNG k–ε turbulence model and Enhanced Wall Treatment (EWT) is used to examine the influence of Reynolds number ( Re = 4,000–22,000 ) and relative roughness pitch ( P/e = 6–12 ) at e/Dh = 0.035 on the average Nusselt number ( Nu avgr ), friction factor ( f av ), Thermo-Fluid Efficiency Factor ( TFEF ), and a three-component second-law entropy generation analysis. Results show that Nu avgr increases monotonically with Re and P/e , reaching a maximum of 261.4 at P/e = 12 and Re = 22,000 — a 121% enhancement over the smooth-duct baseline. The friction factor decreases with Re with weak P/e sensitivity, yielding a maximum penalty ratio f av /f s of 2.12. The TFEF exceeds unity across all conditions, peaking at 3.17 ( P/e = 12, Re = 4,000 ), confirming the thermodynamic superiority of the T-shaped rib configuration. Entropy generation analysis reveals that thermal irreversibility dominates throughout, with Bejan number Be > 0.97 across the entire parameter space, validating the nanofluid selection strategy. Power-law correlations for Nu avgr , f av , and TFEF as functions of Re and P/e are derived with R² ≥ 0.975 and MAPE ≤ 2.26%, providing reliable design tools for the investigated configuration.