CFD-derived ε–NTU correlations for a vertical tube-in-annular-shell helically coiled heat exchanger: pitch and capacity-rate effects

Purpose The purpose of this study is to develop Effectiveness–number of transfer units (ε–NTU) correlations for vertical helically coiled tube-in-annular-shell heat exchangers (HCTHEXs) under laminar water–water operation and to quantify the effect of coil pitch. Design/methodology/approach Three-dimensional steady-state conjugate computational fluid dynamic (CFD) is performed for >2,400 cases, varying pitch ratio, coil/shell flow rates and thermal boundary conditions. Pitch-specific ε–NTU fits (power law, log-quadratic and ε = 1 − exp(−a · NTUb) and global models using {log(NTU), P} [log-linear regression, generalized additive models (GAM), bagged trees] are developed. Findings Pitch specific ε–NTU fits confirm that log quadratic and bounded exponential models reproduce the characteristic rising–plateau behavior with high fidelity (R2 = 0.90–0.98), whereas simple power law fits underpredict curvature and yield lower agreement (R2 ≈ 0.81–0.95). A compact global log linear regression in log(ε) captures the monotonic ε–NTU–pitch trend but remains only moderately accurate (R2 = 0.5883 in ε-space). Incorporating the capacity rate ratio Cr into the bounded exponential global correlation improves performance and reduces systematic residual structure with respect to Cr, increasing global accuracy from Rε2 = 0.6546–0.7225. For maximum fidelity global prediction, machine learning surrogates (GAM and bagged ensembles trained on log(NTU) and pitch) further improve agreement, achieving R2 up to 0.9453 with RMSE ≈ 0.078. Research limitations/implications Results are limited to laminar single-phase water and the studied geometry/pitch range; future work should test turbulence, other fluids and experiments. Practical implications The correlations/surrogates enable rapid prediction of effectiveness for design and optimization without repeated CFD. Originality/value A large validated ε–NTU database for fluid-to-fluid HCTHEXs is provided and high-fidelity global surrogate modeling of the nonlinear ε–NTU–pitch relationship is demonstrated.