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Numerous hydrodynamic processes—such as friction loss and bridge pier scour—depend on identifying dimensionless parameters that quantify system behavior. The Buckingham Π${\\Pi }$theorem offers a principled approach to reducing the number of variables by identifying essential dimensionless groups that govern these processes. While machine learning (ML) algorithms are powerful tools for uncovering complex relationships among variables, they often face limitations in interpretability and physical consistency. In this study, we argue that feature engineering—particularly dimensionality reduction—should precede ML model development to enhance the discovery of physically meaningful hydraulic relationships. We demonstrate this approach using Principal Component Analysis (PCA) applied to two canonical problems: estimating the turbulent friction factor and predicting equilibrium scour depth. Specifically, we integrate PCA with genetic programming and artificial neural networks to derive predictive equations. Our results show that PCA preprocessing improves prediction accuracy, reduces training time, and yields simpler, more interpretable equations. As a practical contribution, we present two concise predictive expressions: one for the friction factor in vegetated open‐channel flows and another for scour depth in turbulent channel flows. These findings highlight the value of PCA‐enhanced ML frameworks for advancing physically informed modeling in hydraulic and sediment transport systems.

The primary objective of this study is to conduct a practical investigation of heat transfer (HT) and friction factor ( f ) characteristics within a double pipe heat exchanger (DPHE) configured in a counter-flow arrangement. To achieve this, a novel approach involving twisted tape (TT) with dimple inserts accompanied by adjacent holes working fluid is water implemented. This dimples, characterized by their concave geometry, are strategically employed to augment the heat exchange process while concurrently mitigating any adverse impact on fluid pressure. A pivotal facet of this study centered on examining the influence of dimple diameter, as well as a consistent dimple-to-depth ratio ( D / H ), on both heat transfer efficiency and friction factor. The performance of TT inserts featuring diverse diameter ( D ) = 2, 4 and 6 mm is meticulously scrutinized in terms of their impact on heat transfer and friction factor characteristics. The outcomes of the study furnished intriguing insights. It is observed that the diameter of the dimples wielded a discernible encouragement on friction factor, revealing a direct correlation. The maximum rate of friction factor is recorded at a 2 mm dimple diameter configuration. When evaluating Nusselt number (Nu) and performance evaluation criteria (PEC), it is revealed that the most favorable results is achieved with the 4 mm dimple diameter configuration. Drawing upon these empirical findings, a significant conclusion can be drawn. Utilization of twisted tape inserts adorned at dimples is a practical, efficient and economically viable approach to heighten HT efficiency within heat exchangers. By optimizing dimple diameter and adhering to a consistent diameter-to-depth ratio, substantial improvements in HT capabilities can be harnessed without disproportionately compromising fluid pressure. This innovative methodology holds the potential to revolutionize heat exchanger design, offering an avenue to enhance HT efficiency with practical and cost-effective solutions.

Over the past century, Blasius (Forschungsheft 131:1–41, 1913) gave empirical power law friction factors λ = 0.3164 Re - 1 / 4 for a turbulent pipe flow and later work published other empirical values of power law indexes. The present work deals with open Reynolds momentum equations by matched asymptotic expansions for large Reynolds number. In the overlap region, a rational dual solutions have power law and log law velocities and friction factor. If outer layer flow is neglected, the power-law friction factor becomes λ = m Re - n in a pipe flow, with power law index n ( Re ) and prefactor m ( Re ) . Further, tangent at a point on power law envelop gives log law at that point. Thus for each value of power index n with prefactor m , the power law theory holds at a point. As an engineering practice, power law at one point is often used in a limited domain of Reynolds number, which compares in that range with experimental and DNS data reported in the literature. The friction factor log law to higher order has been proposed and the second-order effect compares well for lower Reynolds numbers in an entire range of Reynolds numbers for a turbulent pipe flow.

In the present work, an outdoor experimental investigation for solar air heater with arc-shape apex upstream flow by the use of circular cross-sectional wires as roughness elements has been carried out. The roughness elements have been expressed in non-dimensionalizing geometric parameters as relative roughness pitch ( P / e ), relative roughness height ( e / D ), and flow attack angle ( α /60), and the range of these parameters varies from 8 to 15, 0.0454, and 0.75 to 1.25, respectively. For evaluation of performance of the roughened SAH, a novel parameter has been proposed and introduced in the present investigation which is thermo-hydraulic improvement parameter (THIP). With the use of present roughness geometry, considerably, Nusselt number enhancement ratio (NNER) and friction factor enhancement ratio (FFER) have been observed. The maximum NNER and FFER values obtained experimentally are about 2.83 and 1.79 times, respectively, while the maximum THIP obtained is 157.49% higher than the smooth SAH. Using the experimental results, correlations for the output parameters (Nusselt number and friction factor) as a function of input parameters (flow and roughness) have been developed.

This study aims to identify the Coulomb friction coefficient and shear friction factor in aluminum forming processes at high temperatures by using the warm and hot upsetting sliding test (WHUST). The presence of pile-up material in front of the contactor when performing the WHUST on aluminum alloys at elevated temperatures modified the contact geometry. Thus, in this study, the pile-up material was derived as a parameter in the analytical equations. It was found that the analytical equation allows to identify the Coulomb friction coefficient directly from the experimental data, while the analytical equation for the shear friction factor requires the yield stress at the contact surface in addition to the experimental data. For the experiment, the WHUST was performed on AA6082-T6 aluminum alloy against AISI H13 hot work tool steel under dry contact conditions at 400 °C. To precisely control the testing temperature, the WHUST apparatus was installed into the heating chamber of the Bruker UMT TriboLab. Finite Element Analysis (FEA) was used to determine the yield stress at the contact surface. In this study, three commercial FEA software, ABAQUS, DEFORM, and FORGE NxT, with two different sets of material data based on Hansel-Spittel material behavior law were carried out to demonstrate the variations in the computational results of the yield stress and its impact on the identification result of the shear friction factor. Finally, the Coulomb friction coefficient was 0.57, and the shear friction factor ranged between 0.76 and 0.90, depending on the yield stress obtained from the FEA software.

This experimental study aimed to intensify the aerothermal performance index (API) in a round tube heat exchanger employing twisted tapes in rib and sawtooth forms (TTRSs) as swirl/vortex flow generators. The TTRSs have a constant twist ratio of 3.0, a constant rib pitch ratio (p/e) of 1.0, and six different sawtooth angles (α = 20°, 30°, 40°, 50°, 60°, and 70°). Experiments were carried out in an open flow using air as the working fluid for Reynolds numbers between 6000 and 20,000 in the current study, which was conducted in a heated tube under conditions of uniform wall heat flux. A typical twisted tape (TT) was also tested for comparison. The experimental results suggest that TTRSs yield Nusselt numbers ranging from 1.42 to 2.10 times of those of a plain tube. TTRSs with larger sawtooth angles (α) offer superior heat transfer. The TTRSs with α = 20°, 30°, 40°, 50°, 60°, and 70° respectively, enhance average Nusselt numbers by 158%, 162%, 166%, 172%, 180%, and 187% with average friction factors of 3.51, 3.55, 3.60, 3.67, 3.75 and 3.82 times higher than a plain tube. Additionally, TTRSs with sawtooth angles (α) of 20°, 30°, 40°, 50°, 60°, and 70° offer APIs in the ranges of 0.99 to 1.19, 1.01 to 1.21, 1.03 to 1.26, 1.05 to 1.31, 1.07 to 1.42, and 1.09 to 1.48, respectively, which are higher than those of the typical twisted tape (TT) by around 5%, 7%, 11%, 16%, 25%, and 31%, respectively. This demonstrates that twisted tapes in rib and sawtooth form (TTRSs), with appropriate geometries, give a promising trade-off between enhanced heat transfer and an increased friction loss penalty.

This work proposes a method for evaluating the Darcy friction factor and the Nusselt number for fully developed laminar convective flow of Carreau fluids through straight circular tube under a constant heat flux. General mathematical formula for the Darcy fiction factor and the Nusselt number has been derived. This work has found that both the Darcy friction factor and the Nusselt number vary along with the flow rate from their Newtonian to Power law values in a similar way. Then, they have been evaluated for the Carreau fluids with various constants.

This study compares the predictive performance of standard Neural Networks (NNs) and Physics-Informed Neural Networks (PINNs) in estimating pressure drops across laminar and turbulent flow regimes. The proposed PINN framework integrates the Hagen–Poiseuille and Darcy–Weisbach equations, incorporating multiple friction factor correlations (Blasius, Swamee–Jain, and Haaland) to evaluate the impact of physical constraints and regularization on model generalization. The dataset, generated from established analytical models, covers a wide range of industrially relevant parameters (pipe diameter 0.005–0.1 m, velocity 0.5–20 m/s). Results show that PINNs substantially outperform standard NNs, achieving up to 41% lower Mean Absolute Error (MAE) while maintaining strong generalization across unseen data. The optimal PINN configuration (α = 0.0001, Blasius model) achieved an MAE of 1.31, compared to 2.23 for the best NN optimized by Bayesian search. These findings demonstrate that embedding physical laws enhances predictive accuracy and interpretability, especially under limited data conditions. The developed framework offers a robust and computationally efficient tool for mechanical system design, pipeline optimization, and fluid transport analysis.

In this work, the performance of an inline dimpled-based absorber plate solar air heater (IDPSAH) is studied in relation to pitch, a system parameter, and air flow rate ( M air ), an operating parameter. In this regard, two alternative IDPSAH with pitch ratios 0.88 and 1.33 have been experimentally evaluated on alternative days by altering the M air from 0.010 to 0.053 kg s -1 (Proportional Re range: 1971.66–11,113.24) and the result are compared with flat plate solar air heater (FPSAH). For performance evaluation and comparative research, various parameters have been studied, including air temperature difference, efficiencies ( η inst , η eff , η daily ), global heat loss coefficient, heat removal factor, collector efficiency, top loss, area averaged Nusselt number (Nu avg ), and friction factor ( f avg ), among others. The effective efficiency reaches its maximum at a particular M air and then begins to decline, but the instantaneous and daily efficiency of IDPSAH and FPSAH increases continuously. Due to a decrease top loss, the efficiency of IDPSAH is higher than FPSAH. The instantaneous efficiency of IDPSAH at pitch ratio 0.88 is 1.13–1.53 times greater than the instantaneous efficiency of IDPSAH at pitch ratio 1.33 and it is 1.21–1.86 times higher than FPSAH. With an increase in Re, the f avg value decreases; while, the Nu avg of both the FPSAH and IDPSAH increases. In comparison with IDPSAH with pitch ratio 1.33, the Nu avg of IDPSAH at pitch ratio 0.88 is 1.23–1.41 times higher, and it is 1.68–2.12 times higher than FPSAH. In comparison with IDPSAH at pitch ratio 1.33 and FPSAH, the f avg of IDPSAH at pitch ratio 0.88 is higher. However, there is a significant enhancement in overall performance of IDPSAH than the FPSAH.

In this experimental study, twisted tape insert and nanofluid turbulent flow (passive techniques) are considered to increase the heat transfer in the curved tube. The curved tube and twisted tape are fabricated from the copper. The test section (curved tube) is submerged inside a pool filled with hot water. To prepare water/Al 2 O 3 nanofluid, a three-step procedure is utilized. The influences of volume flow rate, nanoparticles concentration, and twisted tape insert on the convective heat transfer coefficient, Nusselt number, and Darcy friction factor are studied. The results show that the curved tube with twisted tape insert improves the convective heat transfer coefficient up to 31%. But enhancing Al 2 O 3 concentration from 0 to 1% increases convective heat transfer coefficient up to 21%. On the other hand, the twisted tape and adding nanoparticle affect Darcy friction factor, and it is greater than that without twisted tape and base fluid. In addition, the Darcy friction factor declines by increment of volume flow rate. Ultimately, the current article presents a new twisted tape as passive enhancement technique.