Search Results (159)

This paper investigates the flow of a second-grade hybrid nanofluid through a Darcy–Forchheimer porous medium under Cattaneo–Christov heat and mass flux models. The hybrid nanofluid, composed of alumina and copper nanoparticles in water, enhances thermal and mass transport, while the second-grade model captures viscoelastic effects, and the Darcy–Forchheimer medium accounts for both linear and nonlinear drag. Using similarity transformations and the spectral quasilinearisation method, the nonlinear governing equations are solved numerically and validated against benchmark results. The results show that hybrid nanoparticles significantly boost heat and mass transfer, while Cattaneo–Christov fluxes delay thermal and concentration responses, reducing the near-wall temperature and concentration. The distributions of velocity, temperature, concentration, and microorganism density are markedly affected by porosity, the Forchheimer number, the bio-convection Peclet number, and relaxation times. The results illustrate that hybrid nanoparticles significantly increase heat and mass transfer, whereas thermal and concentration relaxation factors delay energy and species diffusion, thickening the associated boundary layers. Viscoelasticity, porous medium resistance, Forchheimer drag, and bio-convection all have an influence on flow velocity and transfer rates, highlighting the subtle link between these mechanisms. These breakthroughs may be beneficial in establishing and enhancing bioreactors, microbial fuel cells, geothermal systems, and other applications that need hybrid nanofluids and non-Fourier/non-Fickian transport. Full article

Managing hydraulic behaviour and water quality in semi-arid, transboundary rivers such as the Talas River in Kazakhstan requires reliable numerical tools for predicting free-surface flow through porous hydraulic structures. This study develops and verifies a two-dimensional computational fluid dynamics (CFD) framework for simulating free-surface water flow through porous media and demonstrates its applicability to a real river reach of the Talas in the Zhambyl region. The model combines the Volume of Fluid (VOF) method with the Darcy–Forchheimer formulation to represent porous resistance, while turbulence is described by the RNG k–$\epsilon$ model, and pressure–velocity coupling is handled by the PISO algorithm. Model verification is conducted against a classic dam-break experiment involving a rectangular porous barrier across a laboratory channel. The simulations successfully reproduce the main experimental observations, including rapid drawdown after gate opening, formation and attenuation of the free-surface wave, localized depression above the porous insert, and the subsequent approach to a quasi-steady state. Time histories of water levels at control points and the spatial progression of the wet front show close agreement with measurements. Using the validated setup, a site-specific two-dimensional domain for the Talas River is constructed to analyse the hydraulic influence of a porous bar. The model quantifies velocity redistribution and energy dissipation across the porous patch and provides physically consistent flow fields suitable for engineering assessments under various discharge conditions. Full article

Heat pipe (HP) performance depends on several interacting physical phenomena, such as phase change and liquid transport within the wick. The latter is strongly affected by the permeability of the porous material, whose accurate evaluation is essential for a reliable prediction of the heat transfer capability. This work investigates the permeability of an additively manufactured aluminum wick by comparing two experimental and two numerical methods, using acetone and ethanol as working fluids. In the first experimental approach, the analytical capillary rise curve was fitted to data obtained through infrared thermography and by monitoring the fluid level decrease in an input reservoir. In the second, the mass flow rate through the samples was directly measured under an imposed pressure difference. Numerical simulations were performed using the Finite Volume Method in OpenFOAM and the Lattice Boltzmann Method in Palabos on computational domains reconstructed from microtomographic scans of a real wick. The permeability values, determined through the Darcy–Forchheimer formulation, were then used to estimate the maximum heat transport capability based on the capillary limit model for representative HP geometries. The results show that all four methods provide consistent permeability estimates, with deviations below $30\%$ in the porosity range relevant to real HPs. Full article

In gas reservoirs, high gas velocity causes significant inertial effects, leading to a nonlinear relationship between pressure gradient and velocity, especially near wellbores or fractures. In such cases, Darcy’s law is inadequate, and the Forchheimer equation is commonly used to model nonlinear flow behavior. Although the Forchheimer equation improves simulation accuracy for high-velocity flow in porous media, incorporating it into conventional numerical simulations greatly increases computational time, as nonlinear flow equations must be solved over the entire reservoir. This difficulty is exacerbated in heterogeneous fractured reservoirs, where complex fracture–matrix interactions and localized high-velocity flow complicate solving nonlinear equations. To address this, this work proposes a fast numerical simulation method based on diffusive time of flight (DTOF). By using DTOF as a spatial coordinate, the original three-dimensional flow equations incorporating the Forchheimer equation are reduced to a one-dimensional form, enhancing computational efficiency. DTOF represents the diffusive time for a pressure disturbance from a well to reach a specific reservoir location and can be efficiently computed by solving the Eikonal equation via the fast marching method (FMM). Once the DTOF field is obtained, the three-dimensional problem is transformed into a one-dimensional problem. This dimensionality reduction enables fast and reliable modeling of nonlinear high-velocity gas transport in complex reservoirs. The proposed method’s results show good agreement with those from COMSOL Multiphysics, confirming its accuracy in capturing nonlinear gas flow behavior. Full article

An ambit of enhancing heat transfer throughout thermal convection in a cavity is explored numerically in this study, contemplating the heat dispersal from a segmental heat source circumscribed in a square-vented porous cavity with a moving lid. The cavity can be used as a heat sink for electronic cooling, material processing, and convective drying. Aluminum $10$ PPI metal foam saturated by aluminum oxide–water nanofluid is occupied in this lid-driven vented cavity system. The bottom cavity wall is fully and partially heated by a heat source of specific length $L_H$, and the left wall and inlet fluid are kept at the same cold temperature, while the right wall and top-driven wall are thermally insulated. Thermal dispersion and local thermal non-equilibrium effects are included in an energy equation, and continuity and Darcy–Brinkmann–Forchheimer momentum equations are implemented and resolved by utilizing the finite volume method with the aid of a vorticity–stream function approach operation. The inspirations behind pertinent parameters, including the Reynolds number ($Re=10–50$), Grashof number ($Gr={10}^3–{10}^6$), inlet and outlet ports’ aspect ratio ($D/H=0.1–0.4$), outlet port location ratio ($S/H=0.25–0.75$), and discrete partial heating ratio ($L_H/L=0.25–1$) are scrutinized. The baseline circumstance corresponds to full-length heating $L_H/L=1$ and the outlet port location ratio $S/H=0.25$. The results reveal that the fluid and heat flow domains are addressed mostly via these specification alterations. For $Gr={10}^3$, increasing $Re$ from $10$ to $40$ does not alter streamlines or the isotherm field, but when $Re=50$ it is detected that streamlines increase monotonically. Streamlines are not altered when $L_H/L$ and $S/H$ are amplified but strengthened more when the opening vent aspect ratio is increased. A greater temperature difference occurs as $L_H/L$ is raised from $0.25–0.75$ and isotherms are intensified, and the thermal boundary layer becomes more distinct when $S/H$ is augmented. The average Nusselt number rises as $Re$, $Gr$, $L_H/L$, and $D/H$ are increased by about $30\%$, $3.5\%$, $23\%$, and $19.4\%$, respectively, and it decreases with $S/H$ amplifying is increased by around $5.5\%$. Full article

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

Nanotechnology has become a transformative field in modern science and engineering, offering innovative approaches to enhance conventional thermal and fluid systems. Heat and mass transfer phenomena, particularly fluid motion across various geometries, play a crucial role in industrial and engineering processes. The inclusion of nanoparticles in base fluids significantly improves thermal conductivity and enables advanced phase-change technologies. The current work examines Powell–Eyring nanofluid’s heat transmission properties on a stretched Riga plate, considering the effects of magnetic fields, porosity, Darcy–Forchheimer flow, thermal radiation, and activation energy. Using the proper similarity transformations, the pertinent governing boundary-layer equations are converted into a set of ordinary differential equations (ODEs), which are then solved using the boundary value problem fourth-order collocation (BVP4C) technique in the MATLAB program. Tables and graphs are used to display the outcomes. Due to their significance in the industrial domain, the Nusselt number and skin friction are also evaluated. The velocity of the nanofluid is shown to decline with a boost in the Hartmann number, porosity, and Darcy–Forchheimer parameter values. Moreover, its energy curves are increased by boosting the values of thermal radiation and the Biot number. A stronger Hartmann number M decelerates the flow (thickening the momentum boundary layer), whereas increasing the Riga forcing parameter Q can locally enhance the near-wall velocity due to wall-parallel Lorentz forcing. Visual comparisons and numerical simulations are used to validate the results, confirming the durability and reliability of the suggested approach. By using a systematic design technique that includes training, testing, and validation, the fluid dynamics problem is solved. The model’s performance and generalization across many circumstances are assessed. In this work, an artificial neural network (ANN) architecture comprising two hidden layers is employed. The model is trained with the Levenberg–Marquardt scheme on reliable numerical datasets, enabling enhanced prediction capability and computational efficiency. The ANN demonstrates exceptional accuracy, with regression coefficients $R\approx 1.0$ and the best validation mean squared errors of $8.52\times {10}^{-10}$, $7.91\times {10}^{-9}$, and $1.59\times {10}^{-8}$ for the Powell–Eyring, heat radiation, and thermophoresis models, respectively. The ANN-predicted velocity, temperature, and concentration profiles show good agreement with numerical findings, with only minor differences in insignificant areas, establishing the ANN as a credible surrogate for quick parametric assessment and refinement in magnetohydrodynamic (MHD) nanofluid heat transfer systems. Full article

Practical applications such as solar power energy systems, electronic cooling, and the convective drying of vented enclosures require continuous developments to enhance fluid and heat flow. Numerous studies have investigated the enhancement of heat transfer in L-formed vented cavities by inserting heat-generating components, filling the cavity with nanofluids, providing an inner rotating cylinder and a phase-change packed system, etc. Contemporary work has examined the thermal performance of L-shaped porous vented enclosures, which can be augmented by using metal foam, using nanofluids as a saturated fluid, and increasing the wall surface area by corrugating the cavity’s heating wall. These features are not discussed in published articles, and their exploration can be considered a novelty point in this work. In this study, a vented cavity was occupied by a copper metal foam with $PPI=10$ and saturated with a copper–water nanofluid. The cavity walls were well insulated except for the left wall, which was kept at a hot isothermal temperature and was either non-corrugated or corrugated with rectangular waves. The Darcy–Brinkman–Forchheimer model and local thermal non-equilibrium models were adopted in momentum and energy-governing equations and solved numerically by utilizing commercial software. The influences of various effective parameters, including the Reynolds number ($20\le Re\le 1000$), the nanoparticle volume fraction ($0\%\le \phi \le 20\%$), the inflow and outflow vent aspect ratios ($0.1\le D/H\le 0.4$), the rectangular wave corrugation number ($N=5$ and $N=10$), and the corrugation dimension ratio ($CR=1$ and $CR=0.5$) were determined. The results indicate that the flow field and heat transfer were affected mainly by variations in $Re$, $D/H$, and $\phi$ for a non-corrugated left wall; they were additionally influenced by $N$ and $CR$ when the wall was corrugated. The fluid- and solid-phase temperatures of the metal foam increased with an increase in $Re$ and $D/H$. The fluid-phase Nusselt number near the hot left sidewall increased with an increase in $\phi$ by $\left(25–60\right)\%$, while the solid-phase Nusselt number decreased by $\left(10–30\right)\%$, and these numbers rose by around $3.5$ times when the Reynolds number increased from $20$ to $1000$. For the corrugated hot wall, the Nusselt numbers of the two metal foam phases increased with an increase in $Re$ and decreased with an increase in $D/H$, $CR$, or $N$ by $10\%$, $19\%$, and $37\%$. The original aspect of this study is its use of a thermal, non-equilibrium, nanofluid-saturated metal foam in a corrugated L-shaped vented cavity. We aimed to investigate the thermal performance of this system in order to reinforce the viability of applying this material in thermal engineering systems. Full article

Fish protection and guidance are critical factors in the design and operation of water intakes at hydropower plants. In this study, the hydraulic performance of the angled Oppermann fine screen has been investigated in a hybrid model with and without a guidance wall. The experiments were conducted under two different angles of 30° and 45°, and a bar spacing of 10 mm at a large-scale flume with a width of 2 m. Just up- and downstream of the screen, three-dimensional velocities were measured with Acoustic Doppler Velocimetry (ADV). In the computational fluid dynamics (CFD) model, the Large Eddy Simulation (LES) coupled with the Darcy–Forchheimer law, in which screens were modeled as homogeneous porous media, was employed. The experimental results revealed that velocities less than 0.5 m/s just upstream of the Oppermann fine screen and tangential velocity gradients over the entire cross-section of the screen were found to be 0.04–0.338 m/s/m and 0.04–0.856 m/s/m for α = 30° and α = 45°, respectively, creating favorable hydraulic conditions for effective downstream fish guidance. The CFD model was validated against the experimental data within an acceptable error range, both for the velocity and the turbulent kinetic energy. Numerical simulations showed that implementing a curved guidance wall creates a symmetrical and homogeneous downstream flow field without the formation of recirculation zones behind the angled screen. Full article

The placement of hydraulic elements in existing pool-type fishways to make them more suitable for Cyprinid fish is an issue of increasing interest in fishway research. Hydrodynamic characteristics and fish behavior at the representative pool of the fishway with bottom orifices and notches were assessed at the Dagdelen hydropower plant in the Ceyhan River Basin, Türkiye. Three-dimensional velocity measurements were taken in the pool of the fishway using an Acoustic Doppler velocimeter. The measurements were taken with and without a brush block at two different vertical distances from the bottom, which were below and above the level of bristles tips. A computational fluid dynamics (CFD) analysis was conducted for the studied fishway. The numerical model utilized Large Eddy Simulation (LES) combined with the Darcy–Forchheimer law, wherein brush blocks were represented as homogenous porous media. Our results revealed that the relative submergence of bristles in the brush block plays a very important role in velocity and Reynolds shear stress (RSS) distributions. After the placement of the submerged brush block, flow velocity and the lateral RSS component were reduced, and a resting area was created behind the brush block below the bristles’ tips. Fish movements in the pool were recorded by underwater cameras under real-time operation conditions. The heatmap analysis, which is a 2-dimensional fish spatial presence visualization technique for a specific time period, showed that Capoeta damascina avoided the areas with high turbulent fluctuations during the tests, and 61.5% of the fish presence intensity was found to be in the low Reynolds shear regions in the pool. This provides a clear case for the real-world ecological benefits of retrofitting existing pool-weir fishways with such flexible hydraulic elements. Full article

Based on admirable porous media performance and the popularity of additive manufacturing technology, gradient porous media are progressively being applied in increasing fields. In this study, convection heat transfer within a square vented cavity, partially occupied by two copper metal foam layers of $10$ and $20$ PPI saturated with nanofluid, was assessed numerically. The left wall was heated uniformly and non-uniformly by applying multi-frequency spatial heating following a sinusoidal function. Governing equations, including continuity, the Darcy–Brinkmann–Forchheimer model, and local thermal non-equilibrium energy equations, were adopted and solved by employing the finite volume method. The influences of relevant parameters, including nanoparticle concentrations $\left(0\%\le \phi \le 10\%\right)$, Reynolds number ($1\le Re\le 100$), inlet and outlet port aspect ratios $\left(0.1\le D/H\le 0.4\right)$, three outlet vent opening locations ($\left(S_o=0\right)$ left, ($S_o=\left(H/2-D/2\right)$) middle, and ($S_o=\left(H-D\right)$) right), sinusoidal offset temperature (${\theta }_o=0.5$, $1$), frequency ($f=1, 3, 5$), and amplitude ($A=0-1$), were examined. The results demonstrate that flow and heat transfer fields are impacted mainly by these parameters. Streamlines are more intensified at the upper-left corner when the outlet opening vent is shifted towards the right-corner upper wall. Fluid- and solid-phase Nusselt number increases $Re$, $D/H$, ${\theta }_o$, $A$, and $f$ are raised, specifically when $A\ge 0.3$. The Nusselt number remains constant when the frequency is raised from $3$ to $5$, definitely when $D/H\ge 0.25$. In uniform and non-uniform heating cases, the Nusselt number of both phases remains constant as the outlet port is shifted right for $Re\le 10$ and slightly for higher $Re$ as the outlet vent location is translated from left to right. Full article

The development of shale bedding and fractures exacerbates the invasion of drilling fluid, leading to significant reservoir damage. This article elucidates the strength degradation behavior of shale with bedding orientations of 0° and 90° under drilling fluid immersion, as determined through triaxial compression experiments. An improved Hooke–Brown anisotropic strength criterion has been established to quantitatively characterize the degradation effects. Additionally, a dynamic mechanism of pore pressure accumulation was simulated. The research findings indicate the following: (1) As the intrusion pressure increases from 6 MPa to 8 MPa, the penetration depth significantly increases. In the horizontal bedding direction (0°), cracks dominate the flow mode, resulting in a sudden drop in strength; (2) An increase in bedding density or opening exacerbates the degree of invasion and strength degradation in the horizontal bedding direction, with a degradation rate exceeding 40%. In contrast, the vertical bedding direction is influenced by permeability anisotropy and crack blockage, leading to limited seepage and minimal degradation. By optimizing the dosage of emulsifiers and other treatment agents through orthogonal experiments, a low-viscosity, high-shear-strength plugging oil-based drilling fluid system was developed, effectively reducing the invasion depth of the drilling fluid by over 30%. The primary innovations of this article include the establishment of a quantitative model for Reynolds number degradation for the first time, which elucidates the mechanism of accelerated crack propagation during turbulent transition (when the Reynolds number exceeds the critical value of 10). Additionally, a novel method for synergistic control between sealing and rheology is introduced, significantly decreasing the degradation rate of horizontal bedding. Furthermore, the development of the Darcy–Forchheimer partitioning algorithm addresses the issue of prediction bias exceeding 15% in high-Reynolds-number regions (Re > 30). The research findings provide a crucial theoretical foundation and data support for the optimized design of drilling fluids. Full article

Control of buoyancy-assisted convective flow and the associated thermal behavior of nanofluids in finite-sized conduits has become a great challenge for the design of many types of thermal equipment, particularly for heat exchangers. This investigation discusses the numerical simulation of the buoyancy-driven convection (BDC) of a nanofluid (NF) in a differently heated cylindrical annular domain with an interior cylinder attached with a thin baffle. The annular region is filled with non-Darcy porous material saturated-nanofluid and both NF and the porous structure are in local thermal equilibrium (LTE). Higher thermal conditions are imposed along the interior cylinder as well as the baffle, while the exterior cylinder is maintained with lower or cold thermal conditions. The Darcy–Brinkman–Forchheimer model, which accounts for inertial, viscous, and non-linear drag forces was adopted to model the momentum equations. An implicit finite difference methodology by considering time-splitting methods for transient equations and relaxation-based techniques is chosen for the steady-state model equations. The impacts of various pertinent parameters, such as the Rayleigh and Darcy numbers, baffle dimensions, like length and position, on flow, thermal distributions, as well as thermal dissipation rates are systematically estimated through accurate numerical predictions. It was found that the baffle dimensions are very crucial parameters to effectively control the flow and associated thermal dissipation rates in the domain. In addition, machine learning techniques were adopted for the chosen analysis and an appropriate model developed to predict the outcome accurately among the different models considered. Full article

The non-Darcy seepage characteristics of broken rock mass is important for analyzing the seepage and stability of rock and soil mass. At present, the research on non-Darcy seepage models considering hydraulic conditions and medium void structures has considerable room for improvement. In this study, non-Darcy seepage tests were conducted on broken rock mass under the influence of different hydraulic pressures, sample gradations, and porosities. The influence of sample gradation and porosity on the linear and nonlinear term coefficients of Forchheimer’s law, the critical criterion of non-Darcy seepage, and the seepage flow regime was clarified. The influence of hydraulic gradient on the value of traditional hydraulic conductivity was revealed. A non-Darcy equivalent hydraulic conductivity, which changed with pressure gradient, was defined, then Forchheimer’s law and Darcy’s law were modified. Results showed that the relationship between pressure gradient and flow rate highly obeyed Forchheimer’s law. The minimum value of Forchheimer number was 9.4 times the critical value. Owing to the influence of inertial force and variable seepage channels, the linear and nonlinear term coefficients of Forchheimer’s law decreased while the Forchheimer number increased with the increase of pressure gradient, sample gradation, and porosity. With high hydraulic gradient, the non-Darcy equivalent hydraulic conductivity decreased nonlinearly, causing Darcy’s law to overestimate the seepage flow in this study by 2.47–13.40 times. Finally, Forchheimer’s law and Darcy’s law were modified to consider the influence of hydraulic gradient, sample gradation, and porosity. The modified Darcy’s law does not require the determination of the seepage flow regime and can accommodate the mutual transformation and coexistence between Darcy and non-Darcy seepage. Full article