Ferrofluid bend channel flows for multi-parameter tunable heat transfer enhancement Part 2 Deep Learning and Neural Network Modeling

This work is the second in a series focused on ferrofluid bend channel flows. Here, ferrofluid flows in bend channels are modeled using machine learning methods, based on data generated from the CFD simulation discussed in the first work in this series. Predicting convective heat transfer in ferrofluid flows influenced by magnetic fields is key to advancing thermal management in microscale and energy-intensive systems.

💡 Research Summary

This paper constitutes the second installment in a series investigating ferrofluid flow through bent channels under the influence of external magnetic fields. Building upon a comprehensive CFD database generated in the first study, the authors assemble a high‑dimensional dataset of 15,876 simulation cases that span seven physically meaningful input parameters: ferrofluid volume fraction, bend outer radius, distance between the bend center and the current‑carrying wires, wire‑horizontal angle, the two wire currents, and the Reynolds number. For each case four region‑specific Nusselt numbers are extracted—overall channel, the bend as a whole, and the two sub‑sections of the bend—providing a multi‑output target for surrogate modeling.

Three regression approaches are evaluated: a fully‑connected deep neural network (NN), XGBoost, and Random Forest. All models are trained on an identical 80 %/20 % train‑test split, with the NN architecture consisting of an input layer (7 features), a normalization layer, two dense layers of 128 neurons each (ReLU + 20 % dropout), a third dense layer of 64 neurons (ReLU + dropout), and a four‑neuron output layer. Training employs the Adam optimizer (initial LR = 0.001), mean‑squared‑error loss, early stopping, and learning‑rate reduction on plateau.

Performance metrics on the held‑out test set reveal that the NN outperforms the tree‑based models across all outputs. The NN achieves RMSE values ranging from 0.045 to 0.155, MAE from 0.036 to 0.089, and coefficient of determination (R²) from 0.832 (overall channel) to 0.978 (bend region). The two bend‑section Nusselt numbers attain R² > 0.97, indicating excellent capture of the underlying physics. XGBoost and Random Forest, while useful for baseline comparison, exhibit lower R² (≤ 0.80) and higher errors, reflecting their limited ability to model the highly nonlinear magneto‑hydrodynamic interactions present in the data.

Beyond raw accuracy, the study emphasizes model transparency and reliability. Global feature importance via permutation importance and local explanations via SHAP consistently identify Reynolds number and the two wire currents as the dominant drivers of heat transfer, with wire‑angle and wire‑distance contributing notably to the overall channel Nusselt number. Monte‑Carlo dropout is employed to quantify predictive uncertainty, furnishing confidence intervals for each prediction and highlighting regions of the input space where the surrogate is less certain. Ablation experiments demonstrate that removing Reynolds number or current variables degrades performance dramatically, confirming their physical relevance, while residual analysis shows near‑normal error distributions with only minor systematic bias in sparsely sampled parameter regimes.

The authors conclude that a physics‑informed, multi‑output neural network, complemented by modern interpretability tools, provides a scalable, trustworthy surrogate for magnetically tuned ferrofluid heat‑transfer problems. Such a surrogate enables rapid design space exploration, real‑time control, and optimization for applications ranging from micro‑electronics cooling and energy harvesting to biomedical devices where magnetic field manipulation is integral. Future work is outlined to incorporate experimental data, explore transfer learning to other geometries, and integrate reinforcement‑learning‑based control strategies for closed‑loop thermal management.