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.
Hessam Mirgolbabaei (Fri,) studied this question.