Comprehensive Numerical Investigation of Helically Coiled Tube’s Thermal Efficiency Through Morpho-Hydrodynamic Variations and Global E-NTU Correlation

Helically coiled tube heat exchangers (HCTHEXs) are widely deployed in compact thermal systems, yet reliable effectiveness–NTU (ε–NTU) correlations for realistic fluid to fluid operation remain scarce. This work presents a comprehensive three dimensional numerical study of a vertical tube in annular shell HCTHEX under laminar flow on both coil and shell sides, with water as the working fluid in all cases. More than 2400 steady state CFD simulations in ANSYS Fluent are performed to systematically vary morpho hydrodynamic parameters, including coil pitch ratio, flow rates, and thermal boundary conditions. The numerical model is verified against established correlations for coil side Nusselt number and pressure drop, with discrepancies typically below 10%, and is then used to construct a global ε–NTU database. For each pitch ratio, three candidate ε–NTU correlations are evaluated: a power law relation in log–log space, a log quadratic polynomial in log(NTU), and a nonlinear exponential form of the type ε=1-exp⁡(-a NTU^b). The log quadratic and exponential models consistently reproduce the characteristic rising–plateau ε–NTU behavior with R²values between 0.90 and 0.98, whereas simple power laws underpredict the curvature. A global log based regression model log⁡(ε)=f[log⁡(NTU),P]captures the overall monotonic trends but attains only moderate accuracy (R²≈0.59 in ε space), highlighting the intrinsic nonlinearity of the ε–NTU–pitch surface. To overcome this limitation, generalized additive models (GAM) and bagged decision tree ensembles are trained using log⁡(NTU)and pitch as predictors. These machine learning regressors yield substantially improved agreement with the CFD data, with R²≈0.94for GAM and R²≈0.91for the ensemble, while a simple average of both predictions achieves the highest fidelity (R²≈0.95). The resulting pitch specific closed form correlations and global GAM/Ensemble surrogate provide practical tools for predicting the effectiveness of helically coiled tube heat exchangers over a broad range of morpho hydrodynamic conditions.