In this paper, multi-objective optimization of geometric parameters of spirally-cross-corrugated (SCC) tubes is carried out using numerical methods, genetic algorithms (GAs), and artificial neural networks (ANNs). First, the turbulent flow is numerically characterized in various SCC tube geometries using a finite volume method with the realizable k−ε turbulence model. In this approach, the heat transfer coefficient and friction factor f in tubes are calculated. First, two parameters (corrugation pitch-to-diameter ratio (PR = p/D) and corrugation depth-to-diameter ratio (DR = e/D)) are examined in a turbulent flow regime that affects the strength of quadruple longitudinal vortex flows and thermal characteristics. At the final step, using the obtained polynomials for neural networks, multi-objective genetic algorithms (NSGA II) are employed for Pareto based multi-objective optimization of flow parameters in such tubes. This analysis considers two conflicting parameters, f Re and Nusselt number Nu with respect to three design variables, Reynolds number Re, values of PR and DR. Some interesting and important relationships between the parameters and variables mentioned above emerge as useful optimal design principles involved in the heat transfer of such tubes through Pareto based multi-objective optimization. Such important optimal principles would not have been obtained without the use of a combination of numerical techniques, ANN modeling, and the Pareto optimization.

A computational fluid dynamics (CFD) analysis is conducted to systematically investigate heat transfer enhancement in tubes fitted with grooved twisted tapes and to identify the groove geometry that provides the best thermo-hydraulic performance. Three grooved twisted tape configurations—circular-grooved twisted tapes (CGTT), rectangular-grooved twisted tapes (RGTT), and triangular-grooved twisted tapes (TGTT)—are evaluated and compared with a smooth tube and a conventional twisted tape over a Reynolds number range of 5000–20,000 under isothermal wall conditions. The grooved twisted tapes enhance heat transfer through the combined effects of swirl-induced secondary flows and groove-generated flow disturbances, which intensify turbulent mixing and reduce the thickness of the thermal boundary layer. Compared with the plain tube, the grooved configurations increase the Nusselt number by 1.472–1.98 times while increasing the friction factor by 3.21–3.58 times. Relative to the conventional twisted tape, the grooved designs provide an additional 8.0–12.1% enhancement in heat transfer with only a marginal increase of 0.2–1.5% in friction factor. The thermodynamic analysis indicates that the CGTT configuration exhibits the lowest entropy generation rate and exergy loss throughout the investigated Reynolds number range. In particular, the CGTT achieves a Bejan number of 0.999841 at Re = 5000, demonstrating an excellent balance between heat transfer enhancement and frictional losses. Furthermore, the CGTT attains the highest thermal performance factor (TPF) of 1.294 at Re = 5000 and maintains TPF > 1.0 over the entire Reynolds number range. The overall performance ranking is consistently established as CGTT > TGTT > RGTT based on comprehensive analyses of velocity fields, streamline patterns, turbulent kinetic energy distributions, temperature contours, and thermodynamic characteristics. Although the present study identifies the circular-groove configuration as the optimal design for a twist ratio (y/W) of 3.0, further parametric investigations involving variations in twist ratio, groove dimensions, and groove pitch are required to develop generalized design guidelines.

This study reports on heat transfer augmentation by knitted wire coil turbulators in a fully developed turbulent regime. Four knitted wire coil turbulators with different wire loop number densities (N = 6, 8, 10, and 12 loops per pitch, with 1.0 pitch = 6.8 mm) were tested. Each was made by winding a 0.7 mm copper wire around a 1.0 mm core rod. Experiments were conducted under a constant 600 W/m² wall heat flux. The flow behaviors observed through a dye injection technique revealed that the wire coil induced secondary flows and developed shear layers, contributing to enhanced heat transfer. Heat transfer improved with increasing wire loop number density. Application of knitted wire coil turbulators increased the Nusselt number (Nu) by 86, 95.4, 103.2, and 109.3% for N = 6, 8, 10, and 12, respectively. This corresponded to increased friction factors (f) by 1.77, 1.97, 2.15, and 2.31 times, respectively. The tube with coils having N = 12 yielded the highest thermal performance index (TPI), 1.4, at a Reynolds number of 5000. The empirical correlations for Nu, f, and TPI showed deviations within ±2.1, ±0.68, and ±2.28%, respectively.