Search Results (655)

Magnetohydrodynamic (MHD) flow and heat transfer in porous media are central to many engineering applications, including heat exchangers, MHD generators, and polymer processing. This study examines the boundary layer flow and thermal behavior of an electrically conducting viscous fluid over a porous stretching tube. The model accounts for nonlinear thermal radiation, internal heat generation/absorption, and Darcy–Forchheimer drag to capture porous medium resistance. Similarity transformations reduce the governing equations to a system of coupled nonlinear ordinary differential equations, which are solved numerically using the BVP4C technique with Response Surface Methodology (RSM) and sensitivity analysis. The effects of dimensionless parameters magnetic field strength (M), Reynolds number (Re), Darcy–Forchheimer parameter (Df), Brinkman number (Br), Prandtl number (Pr), nonlinear radiation parameter (Rd), wall-to-ambient temperature ratio (rw), and heat source/sink parameter (Q) are investigated. Results show that increasing M, Df, and Q suppresses velocity and enhances temperature due to Lorentz and porous drag effects. Higher Re raises pressure but reduces near-wall velocity, while rw, Rd, and internal heating intensify thermal layers. The entropy generation analysis highlights the competing roles of viscous, magnetic, and thermal irreversibility, while the Bejan number trends distinctly indicate which mechanism dominates under different parameter conditions. The RSM findings highlight that rw and Rd consistently reduce the Nusselt number (Nu), lowering thermal efficiency. These results provide practical guidance for optimizing energy efficiency and thermal management in MHD and porous media-based systems.: Full article

In Liquid Composite Molding (LCM), the high variability present in reinforcement properties such as permeability creates additional challenges during the injection process, such as void formation. Although improved injection strategy designs can mitigate the formation of defects, these processes can benefit from real-time process monitoring and control to adapt the injection conditions when needed. In this study, a machine vision algorithm is proposed, with the objective of detecting and tracking both fluid flow and bubbles in an LCM setup. In this preliminary design, 3D-printed porous geometries are used to mimic the architecture of textile reinforcements. The results confirm the applicability of the proposed approach, as the detection and tracking of the objects of interest is possible, without the need to incur in elaborate experimental preparations, such as coloring the fluid to increase contrast, or complex lighting conditions. Additionally, the proposed approach allowed for the formulation of a new dimensionless number to characterize bubble transport efficiency, offering a quantitative metric for evaluating void transport dynamics. This research underscores the potential of data-driven approaches in addressing manufacturing challenges in LCM by reducing the overall process monitoring complexity, as well as using the acquired reliable data to develop robust, data-driven models that offer new understanding of process dynamics and contribute to improving manufacturing efficiency. Full article

Catalytic upgrading of vacuum residue (VR) is critical for enhancing fuel yield and reducing waste in petroleum refining. This study explores VR cracking over a novel cerium-loaded acidified metakaolinite catalyst (MKA800–20%Ce) prepared via calcination at 800 °C, acid leaching, and wet impregnation with 20 wt.% Ce. The catalyst was characterized using FTIR, BET, XRD, TGA, and GC–MS to assess structural, textural, and thermal properties. Catalytic cracking was carried out in a fixed-bed batch reactor at 350 °C, 400 °C, and 450 °C. The MKA800@Ce20% catalyst showed excellent thermal stability and surface activity, especially at higher temperatures. At 450 °C, the catalyst yielded approximately 11.72 g of total liquid product per 20 g of VR (representing a ~61% yield), with ~3.81 g of coke (~19.1%) and the rest as gaseous products (~19.2%). GC-MS analysis revealed enhanced production of light naphtha (LN), heavy naphtha (HN), and kerosene in the 400–450 °C range, with a clear temperature-dependent shift in product distribution. Structural analysis confirmed that cerium incorporation enhanced surface acidity, redox activity, and thermal stability, promoting deeper cracking and better product selectivity. Kinetics were investigated using an eight-lump first-order model comprising 28 reactions, with kinetic parameters optimized through a genetic algorithm implemented in MATLAB. The model demonstrated strong predictive accuracy taking into account the mean relative error (MRE = 9.64%) and the mean absolute error (MAE = 0.015) [MAE: It is the absolute difference between experimental and predicted values; MAE is dimensionless (reported simply as a number, not %. MRE is relative to the experimental value; it is usually expressed as a percentage (%)] across multiple operating conditions. The above findings highlight the potential of Ce-modified kaolinite-based catalysts for efficient atmospheric pressure VR upgrading and provide validated kinetic parameters for process optimization. Full article

The optimization of submerged entry nozzle (SEN) designs plays a pivotal role in achieving stable flow conditions and high-quality steel production during continuous casting. This study presents a comparative analysis of two SEN geometries under identical operational parameters using a combined approach of numerical simulation and physical modeling. A full-scale water model and a validated CFD framework based on the realizable k-$\epsilon$ and VOF models were employed to evaluate velocity distribution, turbulence intensity, free surface behavior, and flow symmetry. Results reveal that the SEN-2 design enhances flow stability near the meniscus region, promotes a consistent double-roll flow pattern (DRF), and reduces surface oscillations and sub-meniscus velocities, thereby minimizing the risk of mold flux entrapment. The proposed dimensionless KE number effectively quantifies the energy dissipation behavior of both designs, highlighting SEN-2’s superior hydraulic performance. This integrated methodology offers a robust evaluation framework for future nozzle development aimed at improving product quality without compromising productivity. Full article

In this paper, the electromagnetohydrodynamic (EMHD) flow and heat transfer of a fluid are analytically investigated. The flow and heat transfer occur in a horizontal channel filled with a porous medium, where the permeabilities of the upper and lower halves of the channel are different. The lower half of the channel is saturated with a hybrid nanofluid, while the upper half is saturated with a nanofluid. The base fluids of the nanofluid and the hybrid nanofluid are different. The channel walls are impermeable. The channel is subjected to external magnetic and electric fields. The problem is analyzed under the inductionless approximation. By introducing dimensionless variables and physical parameters that characterize the flow and heat transfer, the governing equations are transformed into their dimensionless forms. These equations are solved analytically, and the velocity and temperature distributions of the fluid in the channel are obtained. The distributions are graphically illustrated for the case in which the upper half of the channel contains the Al₂O₃/oil nanofluid and the lower half contains the Cu–TiO₂/water hybrid nanofluid, considering various values of the Hartmann number, the external electric load factor, the porosity factor, and the nanoparticle volume fractions. The numerical values of the dimensionless shear stresses and Nusselt numbers at the channel walls are presented in a table. The analysis of the results indicates that an increase in the Hartmann number leads to higher temperatures within the channel. The findings also demonstrate that, in this case, the flow velocities are lower and the temperatures decrease, while the shear stresses and Nusselt numbers at the channel walls are higher compared to those observed for pure fluid (oil and water) flow through the channel. This indicates the advantage of employing the model investigated here over the classical model (water and oil) in engineering practice. Full article

Submerged vanes offer a promising solution for reducing scour depth around hydraulic structures such as bridge piers by modifying near-bed flow patterns. However, temporal changes in bed profiles around a cylindrical pier remain insufficiently quantified. This study employs three machine learning models (MLMs), gene expression programming (GEP), support vector regression (SVR), and an artificial neural network (ANN), to simulate the temporal evolution of the bed profile around a cylindrical pier under constant subcritical flow. We use a published laboratory flume dataset (106 observations) obtained for a pier of diameter $D=6\mathrm{cm}$ and uniform sediment with median size $D_{50}=0.43\mathrm{mm}$. Geometric/layout parameters of the submerged vanes (number n, transverse offset z, longitudinal spacing e, and distance from the pier base a) were fixed at their reported optima, and subsequent tests varied installation angles $\alpha$ to minimize scour. Models were trained on $70\%$ of the data and tested on $30\%$ using dimensionless inputs $(t/t_e,{\alpha }_1,{\alpha }_2,{\alpha }_3)$ with t the elapsed time from the start of the run and $t_e$ the equilibrium time at which scour growth becomes negligible and response $s/D$ with s the instantaneous scour depth at time t. The GEP model with a three-gene structure achieved the best accuracy. During training and testing, GEP attained $(\mathrm{RMSE}, \mathrm{MAE}, R^2, {(D_s/D)}_{\mathrm{DDR}\left(\max \right)})=(0.0864,0.0681,0.9237,4.25)$ and $(0.0729,0.0641,0.9143,4.94)$, respectively, where $D_s$ denotes scour depth at equilibrium state, D is the pier diameter, and $\mathrm{DDR}\left(\max \right)\equiv max(D_s/D)$ is the maximum dimensionless depth ratio observed/predicted. Full article

This paper reveals a counterintuitive, non-monotonic dependence of terahertz coded-aperture imaging (TCAI) performance on the imaging range. This phenomenon stems from phase-induced spatiotemporal correlations in the reference-signal matrix (RSM), governed by the wavefront phase interactions between the coded-aperture elements and scatterers on the imaging plane. Image quality deteriorates noticeably when a specific dimensionless criterion, which is defined mathematically and physically in this work, precisely reaches integer values. Under such conditions, the relative phase difference concentrates or clusters into discrete values determined by the imaging range, leading to strong column and row correlations in RSM that compromise the spatiotemporal independence essential for high-quality reconstruction. For imaging ranges exceeding the critical threshold determined by the number of grid points along one dimension of the imaging plane, two degradation mechanisms emerge: increased correlation between RSM columns mapping to directly adjacent scatterers and phase coverage reduction in wavefront encoding. Both effects intensify as the imaging range increases, resulting in a monotonic deterioration of imaging performance. Crucially, reconstruction fails primarily when strong correlations involve dominant scatterers, whereas correlations among non-dominant (dummy) scatterers have a negligible impact. The Two-step Iterative Shrinkage/Thresholding (TwIST) algorithm demonstrates superior robustness under these challenging conditions compared to some other conventional methods. These insights provide practical guidance for optimizing TCAI system design and operational range selection to avoid performance degradation zones. Full article

The optimization of polymer extrusion processes is crucial for improving product quality and manufacturing efficiency in plastic industries. This study aims to investigate the viscoelastic flow behavior of high-density polyethylene (HDPE) through an extrusion die with an internal mandrel, focusing on the effects of die geometry and flow parameters. A two-dimensional (2D) numerical model is developed in COMSOL Multiphysics using the Oldroyd-B constitutive equation, solved using the Galerkin/least-square finite element method. The simulation results indicate that the Weissenberg number (Wi) and die geometry significantly influence the dimensionless drag coefficient (Cd) and viscoelastic stress distribution along the die wall. Furthermore, filleting sharp edges of the die wall surface effectively reduces stress oscillations, enhancing flow uniformity. These findings provide valuable insights for optimizing die design and improving polymer extrusion efficiency. Full article

Evaluating power consumption in stirred media mills over a wide range of process parameters is crucial for analyzing breakage kinetics and milling efficiency. Despite considerable research efforts, existing models predominantly rely on power-law approaches and fail to provide a holistic understanding of the relationship between process parameters and power consumption. The aim of this study is to introduce a new mathematical model that accurately captures this relationship, across all bead filling ratios (φ), using dimensionless numbers including power number (Ne) and Reynolds number (Re). First, we considered experimental data from literature and discriminated various models to correlate either Ne or Re separately for each φ (Class 1 models) or Ne to Re–φ simultaneously (Class 2 models). The best performing model (Model 2.6 with SSR = 36.71, RMSE = 0.591, R² = 0.99) was subsequently applied to a new set of experimental data, confirming that this model is highly robust and reliable across various conditions. To the best of our knowledge, in stirred media mill research, this work is the first to show that a simple four-parameter nonlinear model provides a robust fit for Ne data across varying rotor Re (200 to 1 × 10⁶) and bead filling ratios (0.35–0.90). Full article

The often used analytical representation of the Maxwell–Boltzmann classical speed distribution function (F) for elastic, indivisible particles assumes an infinite limit for the speed. Consequently, volume and the number of particles (n) extend to infinity: Both infinities contradict assumptions underlying this non-relativistic formulation. Finite average kinetic energy and temperature (T) result from normalization of F removing n: However, total energy (i.e., heat of the collection) remains infinite because n is infinite. This problem persists in recent adaptations. To better address real (finite) systems, wherein T depends on heat, we generalize this one-parameter distribution (F, cast in energy) by proposing a two-parameter gamma distribution function (F*) in energy which reduces to F at large n. Its expectation value of kT (k = Boltzmann’s constant) replicates F, whereas the shape factor depends on n and affects the averages, as expected for finite systems. We validate F* via a first-principle, molecular dynamics numerical model of energy and momentum conserving collisions for 26, 182, and 728 particles in three-dimensional physical space. Dimensionless calculations provide generally applicable results; a total of 10⁷ collisions suffice to represent an equilibrated collection. Our numerical results show that individual momentum conserving collisions in three-dimensions provide symmetrical speed distributions in all Cartesian directions. Thus, momentum and energy conserving collisions are the physical cause for equipartitioning of energy: Validity of this theorem for other systems depends on their specific motions. Our numerical results set upper limits on kinetic energy of individual particles; restrict the n particles to some finite volume; and lead to a formula in terms of n for conserving total energy when utilizing F* for convenience. Implications of our findings on matter under extreme conditions are briefly discussed. Full article

Overfall flow, characterized by high Froude numbers and intense turbulence, generates boundary shear stress on vertical surfaces, which is considered the direct cause of headcut erosion. This study aims to analyze the hydraulic characteristics of nappe flow over a vertical or near-vertical overfall. Detailed experiments using hot-film anemometry were conducted in an indoor flume to examine the shear stress distribution on vertical surfaces under varying flow rates, overfall heights, and backwater depths. The results show that when the jet dynamic pressure head is less than the backwater depth, the dimensionless relative shear stress and relative depth relationship can be fitted with a beta probability density function. When the dynamic pressure head exceeds the backwater depth, the distribution follows a cubic polynomial form. Dimensional analysis and flow trajectory calculation methods were used to establish shear stress distribution formulas, with determination coefficients of 0.829 and 0.652, and the mean absolute percentage error (MAPE) between the measured and predicted values being 0.106 and 0.081, respectively. The findings provide valuable insights into the effects of complex flow structures on shear stress and offer essential support for the development of scour models for overfall structures. Full article

Kirchhoff’s current law was originally derived for systems such as telegraphs that switch in 0.1 s. It is used widely today to design circuits in computers that switch in ~0.1 nanoseconds, one billion times faster. Current behaves differently in one second and one-tenth of a nanosecond. A derivation of a current law from the fundamental equations of electrodynamics—the Maxwell equations—is needed. Here is a derivation in one line: $\mathbf{d}\mathbf{i}\mathbf{v} \mathbf{c}\mathbf{u}\mathbf{r}\mathbf{l}\mathbf{B}/{\mathsf{\mu }}_0=0=\mathbf{d}\mathbf{i}\mathbf{v}\left(\mathbf{J}+({\mathsf{\epsilon }}_{\mathit{r}}-1){\mathsf{\epsilon }}_0\mathbf{\partial }\mathbf{E}/\mathbf{\partial }\mathbf{t}+{\mathsf{\epsilon }}_0\mathbf{\partial }\mathbf{E}/\mathbf{\partial }\mathbf{t}\right)=\mathbf{d}\mathbf{i}\mathbf{v}{\mathbf{J}}_{\mathbf{t}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}}$. Maxwell’s ‘true’ current is defined as ${\mathbf{J}}_{\mathbf{t}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}}$. The universal displacement current found everywhere is ${\mathsf{\epsilon }}_0\partial \mathbf{E}/\partial \mathrm{t}$. The conduction current $\mathbf{J}$ is carried by any charge with mass, no matter how small, brief, or transient, driven by any source, e.g., diffusion. The second term $({\mathsf{\epsilon }}_r-1){\mathsf{\epsilon }}_0\partial \mathbf{E}/\partial \mathrm{t}$ is the usual approximation to the polarization currents of ideal dielectrics. The dielectric constant ${\mathsf{\epsilon }}_r$ is a dimensionless real number. Real dielectrics can be very complicated. They require a complete theory of polarization to replace the $({\mathsf{\epsilon }}_r-1){\mathsf{\epsilon }}_0\partial \mathbf{E}/\partial \mathrm{t}$ term. The Maxwell current law $\mathrm{d}\mathrm{i}\mathrm{v}{\mathbf{J}}_{\mathbf{t}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}}=0$ defines the solenoidal field of total current that has zero divergence, typically characterized in two dimensions by streamlines that end where they begin, flowing in loops that form circuits. Note that the conduction current $\mathbf{J}$ is not solenoidal. Conduction current $\mathbf{J}$ accumulates significantly in many chemical and biological applications. Total current ${\mathbf{J}}_{\mathbf{t}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}}$ does not accumulate in any time interval or in any circumstance where the Maxwell equations are valid. ${\mathbf{J}}_{\mathbf{t}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}}$ does not accumulate during the transitions of electrons from orbital to orbital within a chemical reaction, for example. ${\mathbf{J}}_{\mathbf{t}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}}$ should be included in chemical reaction kinetics. The classical Kirchhoff current law $\mathrm{d}\mathrm{i}\mathrm{v} \mathbf{J}=0$ is an approximation used to analyze idealized topological circuits found in textbooks. The classical Kirchhoff current law is shown here by mathematics to be valid only when $\mathbf{J}\gg {\mathsf{\epsilon }}_0\partial \mathbf{E}/\partial \mathrm{t},$ typically in the steady state. The Kirchhoff current law is often extended to much shorter times to help topological circuits approximate some of the displacement currents not found in the classical Kirchhoff current law. The original circuit is modified. Circuit elements—invented or redefined—are added to the topological circuit for that purpose. Full article

A time-domain semi-empirical simulation model based on the wake oscillator approach is developed to investigate the coupled in-line (IL) and cross-flow (CF) vortex-induced vibration (VIV) of a flexible riser in uniform oscillatory flow. A novel nondimensionalization method is introduced by utilizing the dimensionless parameter $StKC$, which effectively replicates the fundamental lift frequency caused by the complex vortex motion around the riser. The structural responses of the riser are described using the Euler–Bernoulli beam theory, and the van der Pol equations are used to calculate the fluid forces acting on the riser, which can replicate the nonlinear vortex dynamics. The coupled equations are discretized in both time and space with a finite difference method (FDM), enabling iterative computations of the VIV responses of the riser. A total of six cases are examined with four different Keulegan–Carpenter ($KC$) numbers (i.e., $KC=31$, 56, 121, and 178) to investigate the VIV characteristics of small-scale and large-scale risers in uniform oscillatory flow. Key features such as intermittent VIV, amplitude modulation, and hysteresis, as well as the VIV development process, are analyzed in detail. The simulation results show good agreement with the experimental data, indicating that the proposed numerical model is able to reliably reproduce the riser VIV in uniform oscillatory flow. Overall, the VIV characteristics of the large-scale riser resemble those of the small-scale riser but exhibit higher vibration modes, stronger traveling wave features, and more complex energy transfer mechanisms. Full article

Heating, ventilation, and air-conditioning (HVAC); domestic and commercial buildings; district energy; industrial processes and water treatment; municipal wastewater and water supply; and agriculture and irrigation, among others, represent a wide breadth of domains where pumps are used. From this perspective, the number of pumps that will be required to ensure future human demands is expected to increase significantly; accordingly, power consumption is also expected to increase sharply. Therefore, the energy efficiency of pumps will become an even more important topic of concern when designing a pumping installation. The objective of the present study is to introduce a user-friendly Excel workbook that enables the design of pumping systems with centrifugal pumps. It was initially conceived for use in Hydraulic Machines Master’s lectures, but its use might be examined from a wider perspective. The workbook includes 22 worksheets, all linked to each other, addressing different aspects of the design. Special attention is given to the calculation of the major and minor head losses, to the cavitation phenomenon, to the use of dimensionless coefficients to determine the rotation speed to obtain a specific operating point, and to the calculation of the system curve. Today, energy efficiency represents an important goal in every pumping facility; therefore, one of the objectives of this tool is to enable the user to quantify both the shaft power and the efficiency of different operating points, thus allowing a sustained definition of the best solution. Full article

Micro-scale lubrication flow of a gas between eccentric circular cylinders with an arbitrary temperature difference is studied on the basis of the Navier–Stokes set of equations and the velocity slip and temperature jump boundary conditions. The dimensionless curvature, which is defined as the mean clearance divided by the radius of the inner cylinder, is small, the Knudsen number and the Reynolds number based on the mean clearance are small, and the temperature ratio is arbitrary. The Reynolds-type lubrication equation is derived analytically. For a verification of the equation, an assessment is conducted against the solution of the direct numerical analysis of the Bhatnagar–Gross–Krook–Welander (BGKW) model of the Boltzmann equation in the author’s previous work [Doi, T. Phys. Fluids 2024, 36, 042016]. The solution of the lubrication equation agrees with that of the Boltzmann equation satisfactorily well over the slip flow regime, not only in the eccentric force and the torque but also in the local distribution of the temperature, flow velocity, and the normal stress. A superiority of the lubrication equation over the lubrication model proposed in the author’s previous work is also discussed. Full article