Heat transfer enhancement in helical tubes using iron oxide nanofluid and spring turbulators with different pitches: Experimental and neural network study

The effect of simultaneously using nanofluid (NF) and spring turbulators on heat transfer in straight tubes has been repeatedly studied, whereas this effect in helical tubes has received little attention. Since the quality and quantity of the impact of these turbulators in spiral tubes and straight tubes are naturally different due to the presence of centrifugal forces and vortices, this study experimentally investigates the thermal performance of iron oxide nanofluid in a helical coil tube equipped with spring-wire inserts under a constant heat flux of 1000 W. Experiments were conducted with nanoparticle volume fractions ranging from 0.1 to 0.5% and wire pitches of 0.003, 0.006 and 0.009 m. Results indicated that increasing the nanoparticle concentration and decreasing the wire pitch significantly enhanced the Nusselt number. A maximum heat transfer improvement of approximately 40% was observed compared to water. Two artificial neural network (ANN) models, namely Multi-Layer Perceptron (MLP) and Self-Organizing Map (SOM), were employed to predict thermal behavior. The MLP model outperformed SOM, achieving an R² greater than 0.99 and lower error rates. To predict the Nu number with a self-organizing map (SOM) ANN with the number of 21 winning neurons with a 3–21–1 topology (including three inputs of Reynolds number, volume fraction, turbulator pitch, and one Nu number output), the obtained data were evaluated. According to the findings, at a pitch of 0.003 m and with a Reynolds number of 10,594, the convection heat transfer coefficient and the Nusselt number are 8200 (W/m²/K) and 110, respectively. This results in the optimal mode of increase for the helical tube. It should be noted that the circular motion of the fluid around the tube axis in spiral tubes is the result of centrifugal force, which causes the flow to transform from laminar to transient and then into turbulent. The experimental results showed that increasing the nanoparticle volume fraction from 0.1% to 0.5% and reducing the turbulator pitch from 0.009 m to 0.003 m significantly enhanced the Nu number by up to 38%, although the pressure drop also increased. The thermal performance evaluation criterion (PEC) reached a maximum value of 1.38 under optimal conditions. Furthermore, an ANN model with a 3–21–1 architecture and a sigmoid activation function was trained, achieving high predictive accuracy with an R-squared value (R²) of 0.989 and a mean square error (MSE) of 7.2434. Using the known enhancement techniques, this study's contribution lies in its systematic integration and multi-objective optimization within a helical coil system. The development of a high-precision ANN model provides a practical framework for designing compact heat exchangers.