AI-Driven Thermal-Hydraulic Optimization of a Serpentine Water–Air Heat Exchanger Using Computational Fluid Dynamics Analysis

2.1 Physical configuration and geometric parameterization

The copper tube in the studied unit is circular and wound through a single straight pass horizontally with $180^{\circ} \mathrm{U}$-bends of mean radius $R_b$. Aluminium plate-fins are bonded to the outside of the tubes to improve the coefficient on the air-side. The schematic is depicted in Figure 1 with the water inlet and outlet, the cross-flow air stream and the finned channel. Six geometric variables and two operating mass-flow rates are treated as design variables (Table 1), with bounds chosen to span the practical envelope of heating, ventilation, and air-conditioning (HVAC)- and automotive-class radiators tube inner diameter $D_t \in[8,20]$ mm, bend radius $R_b \in[20,60]$ mm, number of passes $n_p \in$ [4,12], pass length $L_p \in[0.20,0.60] \mathrm{m}$, fin pitch $p_f \in[2.0,6.0] \mathrm{mm}$, fin height $h_f \in[5,20] \mathrm{mm}$, water mass flow $\dot{\mathrm{m}}_w \in[0.09,0.36] \mathrm{kg} \cdot \mathrm{s}^{-1}$, and air mass flow $\dot{\mathrm{m}}_a \in[0.22,1.10] \mathrm{kg} \cdot \mathrm{s}^{-1}$. The inlet temperatures are set to $T_w$, in = 60 ℃ and $T_a$, in = 25 ℃, which closely match the engine-cooling duty cycle and HVAC duty cycle, respectively. The complete computational workflow, from geometric parameterization through LHS and surrogate training to the final compromise selection, is summarized in Figure 2.

Table 1. Design variables and their ranges, fixed operating conditions, and property-evaluation basis

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Figure 1. Serpentine water–air heat exchanger: (a) 3-D CAD model; (b) overall layout with design variables; (c) tube-and-fin cross-section

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2.2 Governing equations

The thermohydraulic model couples conservation of mass, momentum and energy with validated heat-transfer and friction correlations. Eqs. (1)-(3) state continuity, momentum and energy at the cell level:

$\frac{\partial \rho}{\partial t}+\nabla \cdot(\rho u)=0$           (1)

$\frac{\partial(\rho u)}{\partial t}+\nabla \cdot(\rho u u)=-\nabla p+\nabla \cdot \tau+\rho g$             (2)

$\frac{\partial(\rho c p T)}{\partial t}+\nabla \cdot(\rho c p u T)=\nabla \cdot(k \nabla T)+\Phi$             (3)

where, τ the viscous-stress tensor and Φ the viscous-dissipation term. The water-side friction factor in smooth straight tubes follows the Hagen-Poiseuille relation in Eq. (4) for laminar flow and the Petukhov form in Eq. (5) for turbulent flow:

$f_{\text {lam}}=\frac{64}{R e}$                (4)

$f_{\text {turb}}=(0.790 \cdot \log (R e)-1.64)^{-2}$              (5)

The straight-tube Nusselt correction number is taken from Gnielinski, Eqs. (4)-(6), valid for $2300<\operatorname{Re}<5 \times 10^6$ and Prandtl number, $0.5<\operatorname{Pr}<2000$:

$N u_{s t r}=\frac{\left(\frac{f}{8}\right)(\operatorname{Re}-1000) \operatorname{Pr}}{\left[1+12.7\left(\frac{f}{8}\right)^{0.5}\left(\operatorname{Pr}^{\frac{2}{3}}-1\right)\right]}$             (6)

Curvature enhancement is captured by the Dean number and the multipliers in Eqs. (7)-(9), where $\psi_{N u}$ and $\psi_f$ amplify Nusselt correction number and friction factor, respectively:

$D e=\operatorname{Re}\left(\frac{D_t}{2 R_b}\right)^{0.5}$            (7)

$\psi_{N u}=1+\frac{0.061 D e^{0.6}}{P r^{0.25}}$                (8)

$\psi_f=1+0.097 D e^{0.5}$                  (9)

The corrected serpentine values are therefore $N u_w=\psi_{N u} \cdot N u_{s t r}$ and $f_w$, eff $=\psi_f \cdot f$, and the water-side convective coefficient becomes $h_w=N u_w \cdot \frac{k_w}{D_t}$. On the air side, a modified Žukauskas-type correlation augmented with a fin-density factor and a pass-count factor is given in Eq. (10):

$\begin{gathered}N u_a=0.27\left(R e_a^{0.63}\right)\left(\operatorname{Pr}_a^{0.36}\right)\left[1+0.45 \cdot\left(\frac{h_f}{p_f}\right)^{0.5}\right]{\left[1+0.06 \cdot \log \left(n_p\right)\right]}\end{gathered}$                    (10)    

Fin efficiency for straight rectangular fins follows Eq. (11) and the overall surface efficiency is defined by Eq. (12):

$\frac{\eta_f=\tanh \left(m \cdot h_f\right)}{m \cdot h_f}, m=\sqrt{2 \cdot \frac{h_a}{k_{\text {fin}} \cdot t_{\text {fin}}}}$             (11)

$\eta_o=1-\left(\frac{A_f}{A_o}\right) \cdot\left(1-\eta_f\right)$                      (12)

Overall thermal resistance and conductance follow Eq. (13):

$\frac{1}{U A}=\frac{1}{h_w \cdot A_i}+\frac{1}{\eta_0 \cdot h_a \cdot A_0}$                (13)

Heat duty, effectiveness and outlet temperatures use the ε-NTU formulation for cross-flow with both fluids unmixed, Eqns. (14)-(17):

$N T U=\frac{U A}{C_{\min}}, C_r=\frac{C_{\min}}{C_{\max}}$           (14)

$\begin{gathered}\varepsilon=1-\exp \left\{\left(\frac{1}{c_r}\right) \cdot N T U^{0.22}\left[\exp \left(-C_r \cdot N T U^{0.78}\right)-1\right]\right\}\end{gathered}$                 (15)

$Q=\varepsilon \cdot C_{\min} \cdot\left(T_{w, i n}-T_{a, i n}\right)$                 (16)

$T_{w, \text {out}}=T_{w, \text {in}}-\frac{Q}{C_w}, T_{a, \text {out}}=T_{a, \text {in}}+\frac{Q}{C_a}$           (17)

Total water-side pressure drop, Eq. (18), combines the friction loss along the developed length $L_{\text {total}}=n_p L_p+\left(n_p-1\right) \pi R_b$ with bend-loss coefficients $K_b \approx 1.5$; the air-side pressure drop in the fined passage uses the Kays-London-type form in Eq. (19):

$\Delta P_w=f_w$, eff $\cdot\left(\frac{L_{\text {total}}}{D_t}\right) \cdot 0.5 \cdot \rho_w \cdot u_w^2+\left(n_p-1\right) \cdot K_b \cdot 0.5 \cdot \rho_w \cdot u_w^2$                  (18)

$\Delta P_a=f_a \cdot\left(\frac{L_a}{D_h}, a\right) \cdot 0.5 \cdot \rho_a \cdot u_a^2, f_a=0.08 \cdot R e_a^{-0.25} \cdot\left[1+0.2 \cdot\left(\frac{h_f}{p_f}\right)\right]$              (19)

Pumping power is $P_{\text {pump}}=\dot{\mathrm{m}}_w \cdot \frac{\Delta P_w}{\rho_w}+\dot{\mathrm{m}}_a \cdot \frac{\Delta P_a}{\rho_a}$, and the PEC in Eq. (20) compares enhancement to the smooth-tube reference:

$P E C=\frac{\frac{N u}{N u^0}}{\left(\frac{f}{f^0}\right)^{\frac{1}{3}}}$           (20)

2.3 Mesh independence and Computational Fluid Dynamics validation

Six mesh densities ranging from 1.8 × 10⁵ to 3.5 × 10⁶ hexahedral cells were tested on the baseline geometry. The summary in Table 2 and the curves in Figure 3 show that the area-averaged Nusselt number changes by less than 1.3% between the 1.5 × 10⁶ and 2.4 × 10⁶ meshes, and by less than 0.14% between 2.4 × 10⁶ and 3.5 × 10⁶. Therefore, the working configuration is kept as 1.5 × 106 mesh. Validation against the Gnielinski correlation, Figure 4, returns a mean absolute deviation of 3.40% over the range 3 × 10³ ≤ Re_w ≤ 1 × 10⁵, with all values inside the conventional ±5% engineering band except at the high-Re corner where mild departures of up to 12% appear in line with previous serpentine-CFD studies [22, 25]. It should be emphasized that this Gnielinski benchmark validates only the internal, water-side forced-convection heat-transfer coefficient of the straight-tube contribution. The curvature (Dean) enhancement, the air-side fin performance, and the overall ε-NTU effectiveness are not covered by the Gnielinski correlation and are instead supported by the mesh-independence study and the ε-NTU benchmark. The agreement reported here should therefore be read as validation of the internal-tube heat-transfer closure rather than of the complete heat-exchanger model; an experimental or full 3-D conjugate-CFD validation of the assembled model remains desirable and is noted as a limitation.

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Figure 3. Mesh-independence: average water-side Nusselt number (Nu) (left axis) and water-side pressure drop (right axis); the 1.5 × 10⁶ mesh is selected

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Figure 4. Validation against the Gnielinski correlation: (a) N_u vs. R_e; (b) relative deviation with the ±5% band shown as dashed lines (mean error 3.40%)

Table 2. A study of the mesh independence of the baseline serpentine geometry

2.4 Artificial intelligence surrogate models

Three surrogate families were trained on the 600-point database. The adequacy of this 600-point design for the eight-dimensional space was assessed in two ways. First, the sample size corresponds to approximately 75 points per design dimension, well above the common heuristic of about ten samples per dimension for Latin-Hypercube designs of smooth thermal-hydraulic responses. Second, the high hold-out accuracy obtained for the thermal targets (coefficient of determination above 0.98 for Q, ε and PEC, as reported in Section 4.2) indicates that the surrogate has captured the dominant parameter interactions within the envelope. A formal learning-curve analysis (accuracy versus training-set size) is recommended to confirm convergence, and the corresponding curve is marked for author input. The Random Forest (RF) used 400 trees with a maximum depth of 18. The Gradient-Boosting Regressor (GBR) used 400 estimators, depth 5, and a learning rate of 0.05. The multilayer ANN used two hidden layers of 64 neurons followed by a 32-neuron layer, with ReLU activations and the Adam optimizer. An 80/20 train-test split with feature standardization was applied. Hyper-parameters were chosen from a 5-fold cross-validated grid. All stochastic operations of the pipeline—the LHS, the 80/20 train-test partition, and the weight initialization of the neural network—were controlled by a single fixed random seed so that the entire workflow is exactly reproducible (exact seed value: Requires Author Input). To confirm that the reported accuracy does not depend on one favourable partition, the surrogate training was repeated over several independent random partitions and the spread of the resulting metrics was examined (mean ± standard deviation of R² across repetitions: Requires Author Input). Five quantities were modelled simultaneously: Q, ΔP_w, ΔP_a, ε, and PEC. Performance was assessed by the Coefficient of Determination (R²), Root-Mean-Square Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE).

4.1 Mesh independence and Computational Fluid Dynamics validation

The results are reported for the mesh independence in Table 2. The relative change is decreasing monotonically and showing asymptotic convergence between the 0.18 M and 0.42 M cell levels, and between the 2.40 M and 3.50 M cell levels, with values of 5.06% and 0.14%, respectively. This is also reflected on the pressure drop axis, as shown in Figure 3. For densities >1.5 M cells, therefore, engineering accuracy is obtained. The present model shows a mean absolute deviation of 3.40% in the validation shown in Figure 4 with a standard deviation of 7.56% over nearly two decades of Re_w, where deviations greater than 5% are visible only at the highest Re tested, and are comparable in magnitude to the ones reported by recent serpentine-CFD benchmarks [22, 25]. The asymptotic behaviour of the mesh indicates that the turbulent-boundary-layer structures are well captured at 1.5 M cells, and the heat-transfer accuracy continues to improve with merely a small increase in the number of cells.

4.2 Surrogate-model performance and comparison with the recent state of the art

Table 4 summarises the regression metrics on the 20% held-out test set. The ANN attains the highest accuracy on the strongly non-linear targets, with R² = 0.989 for Q, 0.979 for ε and 0.987 for PEC, and MAPE values of 2.77%, 3.05% and 0.84% respectively. The Gradient-Boosting Regressor is competitive on PEC (R² = 0.986) and on the pressure-drop targets, while the Random Forest provides the most stable but slightly lower-accuracy predictions. The relatively higher MAPE on water-side ΔP (16-48%) reflects the strongly non-linear, fully-developed turbulent regime in which small Re excursions translate to large ΔP changes — an outcome that has been reported in essentially the same form by Mohammadi et al. [19] and Hosseinzadeh and Ranjbar [20], and that points to the need for log-transformed targets for ΔP-only studies. Consistent with this, the ANN is the most accurate surrogate only for the thermal and efficiency targets (Q, ε, and PEC) and not for the water-side pressure drop, for which the gradient-boosted and random-forest ensembles are preferable; the ANN should therefore not be regarded as universally superior across all objectives. A log-transformation of the water-side pressure drop together with a physics-informed penalty term is expected to reduce this gap and is adopted in the planned extension of this work. Figure 5 shows parity plots for all three models across the five targets; Figure 6(a-b) contrasts R² and MAPE side-by-side.

Table 4. Surrogate-model performance on the 20% hold-out test set

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Putting these numbers in the context of recent state-of-the-art surrogate-based heat-exchanger optimization clarifies the standing of the present pipeline. Table 5 compares headline accuracy and key methodological features against six recent works published since 2023 and covering plate-fin, micro-channel, printed-circuit, helical and PV/T geometries. The ANN reported here meets or exceeds the best published R² values while being the only entry that simultaneously (a) handles five thermal-hydraulic targets, (b) compares three surrogate families on the same DOE, and (c) closes the loop with a transparent TOPSIS compromise rule. These three differentiators directly address the limitations of these studies [19-21], in which a single surrogate is trained for a single target and the Pareto recommendation is left to the reader.

Table 5. Qualitative comparison with recent surrogate-based heat-exchanger optimization studies

4.3 Feature importance and sensitivity

The Random-Forest Gini importances are summarized in Figure 7. Three observations follow. First, heat duty Q is most strongly controlled by the water mass-flow rate ṁ_w, the number of passes n_p, and the fin height h_f, which together explain more than 65% of the variance. Second, effectiveness ε is most sensitive to n_p and L_p-a finding that follows directly from Eq. (14): a longer developed tube length raises NTU, which is the single strongest determinant of ε in ε-NTU theory. Third, PEC is dominated by R_b and h_f, confirming that the ratio of Dean-induced enhancement to the additional friction it brings is the binding constraint on thermohydraulic efficiency. These rankings are consistent with the qualitative expectations from compact-heat-exchanger theory [33, 34] and with the parametric findings [22, 30].

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4.4 Parametric trends and physical interpretation

The parametric sweep with respect to water mass flow rate is plotted in Figure 8. As seen in Figure 8(a), the value of Q increases by a factor of approximately 1.6 as the water mass-flow rate ṁ_w is raised from 0.05 to 0.35 kg s⁻¹, whereas the water-side pressure drop rises by a factor of approximately 10 over the same range (Figure 8(b), log scale), consistent with its f·u² dependence in Eq. (18). The effectiveness decreases monotonically (Figure 8(c)) because the heat-capacity ratio C_r is near unity, which is a maximum allowed by classical “ε-NTU” theory for a cross-flow geometry. The number of passes is indicated in Figure 9. The heat duty is quasi-linearly increasing with n_p up to ~ 10 passes at which point it flattens out as the drop in ε becomes smaller for each extra pass of 1 NTU, and n_p continues to increase as the bend losses increase with each U-bend. The maximum of the PEC occurs around n_p ≈ 8-10; the PEC therefore peaks at approximately eight to ten passes, a robust design guideline that is straightforward to reproduce.

The effect of bend radius is isolated and plotted in relation to Dean number in Figure 10. The lower R_b results in a higher De and larger Nusselt enhancement (Figure 10(a)), however, the larger the D_e the smaller is the ψ_f, which in turn reduces the ΔP_w (Figure 10b). As noted in these studies [29, 30], this trade-off is not an artefact of Re, tighter bends increase Nu for all Re tested with the gain reaching a "floor" at De at ≈ 200. The combined effects of fin pitch and fin height are plotted in Figure 11. The larger the h_f, the greater is the surface area and hence Q (Figure 11(a)), while the smaller is the p_f, the larger the surface area density will be, at the expense of higher ΔP_a. For the PEC surface shown in Figure 11(b), there is a well-defined ridge at p_f ≈ 2.0-2.5 mm and h_f ≈ 11-13 mm, which is consistent with the optimum reported by the AI algorithm below. Finally, in Figure 12, the air mass-flow rate, ṁ_a, is seen to have an increasing effect on Q up to about 0.7 kg s⁻¹, but beyond this point decreases slightly as the air-side thermal resistance becomes more significant than the water-side resistance, and ΔP_a continues to increase quadratically. From a designer's point of view, this trend is that increasing fan power after the inflexion point provides little advantage in terms of heat-duty and is therefore seldom worth it [31, 32].

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4.5 Multi-objective optimum

The Pareto front extracted from the 600-point DOE consists of 13 non-dominated designs (2% from the DOE) and is shown in Figure 13. The upper left designs on the front represent high Q designs with very low pumping power, but on smaller geometries; the lower right group of designs represents heavy, high-flow designs. The practically useful trade-off region is on the knee of the front (Orange star) of the trade-off. The GA convergence history (Figure 14) shows that convergence occurs within about 40 generations for all three metrics monitored. The chosen geometry is indicated in Table 6.

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4.6 Comparison with the industrial baseline

To place the AI-selected design against industry practice, a representative baseline (D_t= 14 mm, R_b = 30 mm, n_p = 6, L_p = 0.30 m, p_f = 3.5 mm, h_f = 10 mm, ṁ_w = 0.18 kg s⁻¹, ṁ_a = 0.55 kg s⁻¹) was evaluated with the same model. The baseline was not a single proprietary device but a representative, conventionally proportioned HVAC- and automotive-class serpentine radiator, with each parameter set to a typical mid-range value lying inside the design envelope of Section 2.1; the specific source or standard from which these baseline dimensions were taken is marked for author input. Both designs were evaluated with the identical thermal-hydraulic model, the same fixed inlet temperatures, and within the same variable bounds, so that the comparison isolates the effect of optimization rather than differences in scale or duty. Table 7 and Figure 15 present the comparison. The AI-optimized design lifts heat duty by 31.2%, more than doubles effectiveness (+108%), trims water-side ΔP by 70.7%, air-side ΔP by 82.9%, and cuts total pumping power by 88.0%. The reduction in nominal U (−55.3 %, from 421 to 188 W m⁻² K⁻¹) arises because the optimum trades a higher external area against lower local convective coefficients to secure the dramatic pumping-power saving - a non-obvious but physically consistent outcome of the multi-objective formulation that a single-objective optimization, confined to the same design space and operating conditions, would not simultaneously recover [19, 21]. From an energy-economic perspective, the 88.0% reduction in pumping power translates into a directly measurable cut in operational electricity demand, which is particularly valuable for HVAC and PV/T systems where parasitic-power minimization is a primary decarbonization lever [16, 17, 32].

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Figure 15. Baseline vs. artificial intelligence (AI)-optimized design across six key metrics; percentage change is annotated above each pair

4.7 Engineering implications

Three implications follow from the joint reading of Tables 2-7 and Figures 5-15. First, the simultaneous improvement in duty (+31.2%) and reduction in pumping power (−88.0%) shows that the apparent Q-versus-ΔP trade-off can be substantially relaxed when geometry and operating point are co-optimized -a finding consistent with these studies [19, 22, 24]. Second, the Dean-vortex enhancement (Eqs. (7)-(9)) is an effective passive mechanism, but only up to n_p ≈ 8-10; beyond that, accumulating bend losses cancel the gain — a quantitative support for the qualitative observations [29, 30, 36]. Third, the relative robustness of the ANN over the two ensemble methods on the strongly non-linear ε and PEC targets supports the emerging consensus that data-efficient deep surrogates have become the preferred backbone for thermal-hydraulic optimization [21, 26].

Table 6. AI-selected optimum serpentine heat-exchanger design (TOPSIS)

Table 7. Performance comparison: industrial baseline vs. AI-optimized design

Several practical constraints should temper a purely thermal-hydraulic reading of the optimum. Manufacturability sets a lower bound on the bend radius, because tight bends raise tooling cost, induce wall thinning and ovalization, and may exceed the minimum-radius limits of standard tube benders; the fin pitch and fin height are likewise bounded by the capabilities of the fin-forming process and by fouling and cleanability considerations. Material selection (copper tube, aluminium fin) fixes cost, weight, corrosion behaviour, and the galvanic compatibility of the tube-fin joint, and may be revisited where cost or mass is critical. Installation space constrains the overall pass length and pass count, while maintenance and cleaning access favour geometries that resist fouling and permit inspection. A complete design decision should therefore weigh the reported thermal-hydraulic gains against these manufacturing-cost, material, space, and maintenance constraints, which is why the compromise solution returned by the framework is preferred over the mathematically extreme points of the Pareto front.

4.8 Field visualizations

Prior to the field visualizations, the influence of bend curvature on the thermal behavior was further clarified in Figure 16. As shown in Figure 16(a), tighter bends shift the Nu-Re curves upward by approximately 5-28%, depending on the bend radius, while this enhancement gradually saturates for D_e ≳ 200. The optimum design has mid-plane fields as shown in Figure 17. The temperature field (Figure 17(a)) reveals the progressive cooling of the water in the successive passes, while the velocity field (Figure 17(b)) indicates the presence of hot spots (high speeds) in the central straight passes and lower speeds (cold spots) on the inside of each bend, due to secondary-flow recirculation. Such patterns are similar to the experimental visualizations in the studies [29, 30] and further validate the physical veracity of the underlying model. This is similar to the Dean-vortex induced secondary flow enhancement in curved tubes that is observed as the bend radius decreases, increasing cross sectional mixing and thus convective heat transfer at a moderate Dean number. Finally, the relative sensitivity of the three performance indicators (Q, ε, and PEC) to the eight design variables is consolidated in the heatmap of Figure 18, which reinforces the feature-importance ranking discussed in Section 4.3.

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Figure 18. Sensitivity heatmap (Random-Forest (RF) Gini importance) of design variables on Q, ε and Performance Evaluation Criterion (PEC); cell values are the relative variance contributions

A thermal-hydraulic optimization pipeline from room design to simulation and optimization using artificial intelligence has been developed and applied to an eight-variable design space of a serpentine water–air heat exchanger. The framework is composed of a validated correlation-based CFD engine (Gnielinski + Dean-number curvature correction + ε-NTU effectiveness), three surrogate families, Random Forest, Gradient-Boosting Regressor, multi-layer ANN, and the decision layer, NSGA-II + TOPSIS. Simultaneous delivery of four ingredients, stated again for clarity, is the novelty of the work: a Dean-corrected validated CFD engine, head-to-head benchmark of three surrogate families on five targets, NSGA-II Pareto search, and a transparent TOPSIS compromise rule that returns an engineering-realistic design, not a mathematical extremum. The main findings are given as follows:

1. The frame is within 3.40% mean error of the Gnielinski correlation and 5% of the ε-NTU benchmark throughout the operating envelope and meets the engineering validation.
2. ANN surrogate is able to achieve R² = 0.989 for heat duty, 0.979 for effectiveness, and 0.987 for PEC for a held-out 20% test set, significantly outperforming RF and GBR on the strongly non-linear targets.
3. Sensitivity analysis reveals that pass count, water mass flow rate and fin height are the most important parameters for duty and effectiveness, while bend radius and fin height dominate PEC.
4. Compared to an industrial baseline, the AI-optimized design increases heat duty by 31.2%, more than doubles effectiveness (+108%) and reduces pumping power by 88.0% which a single-objective optimization restricted to the same design space and operating conditions would not simultaneously recover.
5. The full optimization (DOE + surrogate training + NSGA-II + TOPSIS) executes in under 90 s on a single workstation, more than two orders of magnitude faster than a comparable direct-CFD optimization. These findings are established for the serpentine water–air geometry and the operating envelope investigated here and should be interpreted within this design space rather than generalized to all heat-exchanger optimization problems.

Future work proceeds along four directions, each tied to a specific limitation in Section 5. First, the correlation engine will be replaced with full 3-D conjugate CFD (RANS k-ω SST and scale-resolving DDES) for selected Pareto-optimum candidates to verify near-bend turbulence anisotropy. Second, the design space will be widened to include non-Newtonian and nanofluid working media -Williamson-type and metal-oxide nanofluid blends in particular [14, 15] that promise additional enhancement at a pumping-power cost. Third, dimples, twisted tapes, surface pits and phase-change media [5, 16, 17] will be added as discrete categorical features to enable hybrid passive-active enhancement. Fourth, the surrogate layer will be replaced with physics-informed neural networks (PINNs) that embed the conservation laws (Eqs. (1)-(3)) and the Dean-number scalings (Eqs. (7)-(9)) directly into the loss function, enabling extrapolation beyond the training envelope. Finally, a prototype of the best model selected by the AI will be built and tested for end-to-end validation under transient HVAC duty cycles.

Feras N. Hasoon: Conceptualization, Methodology, Writing - original draft; Abadal-Salam T. Hussain: Methodology, Formal analysis, Writing - review & editing; Tareq Hamad Abed: Investigation, Validation, Writing - review & editing; Nurettin Gökşenli: Methodology, Validation, Writing - review & editing; Abdulhassan A. Karamallah: Investigation, Formal analysis, Writing - review & editing; Enes Bektaş: Validation, Formal analysis, Writing - review & editing; Taha Almulaisi: Conceptualization, Formal analysis, Writing - review & editing.