Stagnation Point Research Articles

ANALYTICAL SOLUTION FOR POTENTIAL FLOW AROUND A ROTATING SPHERE AND COMPARISON WITH CFD

A three-dimensional analytical solution was derived for an incompressible steady potential at an initially uniform velocity flow around a sphere, which translates forward, backward, rotates longitudinally or transversally. The concept of relative velocity was used to analyze the flow around the transitionally moving sphere. To analyze the flow around the longitudinally rotating sphere, A formula of the circumferential velocity of the fluid is found at the equatorial plane of the sphere and then generalized to the whole sphere as an approximation. The superposition principle of velocities was used to analyze the flow around the transversely rotating sphere, the stagnation points were detected and analyzed, the pressure distribution at the equator was calculated and compared with the experimental and CFD results, and the lift coefficient was calculated and compared with the experimental results and a good agreement for C_p and C_L was found at low spin factors, In contrast, at high spin factors the results begin to diverge due to the viscous effects and eddy formation.

Parametric optimisation for heat transfer through nanofluid impinging upon a Riga plate: the Taguchi method

The article presents a comprehensive analysis of the flow and heat transfer characteristics of the stagnation point flow of Casson nanofluid towards a Riga plate. The mathematical modelling of the problem is carried out by using Buongiorno's two-phase model for convective heat transport within nanofluids. The solution methodology includes the process of transforming the system of Partial Differential Equations (PDEs) into a set of Ordinary Differential Equations (ODEs) which then solved using a semi-analytical Optimal Homotopy Analysis Method (OHAM). The influence of various flow parameters on the skin friction coefficient ( C f x ) and Nusselt number is presented and analysed graphically. Furthermore, a parametric study for the optimisation of skin friction coefficient and Nusselt number ( N u x ) is performed using the Taguchi analysis along with ANOVA and the multivariate regression analysis. The parametric optimisation reveals that for skin friction coefficient, EMHD parameter is most significant term, whereas Prandtl number is found to be the parameter with the highest influence on the Nusselt number. The findings of the study may have bearings in engineering and industrial applications such as the thermal design of industrial equipment dealing with molten plastics and polymeric liquids.

Numerical study on local scour characteristics around submarine pipelines in the Yellow River Delta silty sandy soil under waves and currents

AbstractDue to their high reliability and cost‐efficiency, submarine pipelines are widely used in offshore oil and gas resource engineering. Due to the interaction of waves, currents, seabed, and pipeline structures, the soil around submarine pipelines is prone to local scour, severely affecting their operational safety. With the Yellow River Delta as the research area and based on the renormalized group (RNG) k‐ε turbulence model and Stokes fifth‐order wave theory, this study solves the Navier–Stokes (N–S) equation using the finite difference method. The volume of fluid (VOF) method is used to describe the fluid‐free surface, and a three‐dimensional numerical model of currents and waves–submarine pipeline–silty sandy seabed is established. The rationality of the numerical model is verified using a self‐built waveflow flume. On this basis, in this study, the local scour development and characteristics of submarine pipelines in the Yellow River Delta silty sandy seabed in the prototype environment are explored and the influence of the presence of pipelines on hydrodynamic features such as surrounding flow field, shear stress, and turbulence intensity is analyzed. The results indicate that (1) local scour around submarine pipelines can be divided into three stages: rapid scour, slow scour, and stable scour. The maximum scour depth occurs directly below the pipeline, and the shape of the scour pits is asymmetric. (2) As the water depth decreases and the pipeline suspension height increases, the scour becomes more intense. (3) When currents go through a pipeline, a clear stagnation point is formed in front of the pipeline, and the flow velocity is positively correlated with the depth of scour. This study can provide a valuable reference for the protection of submarine pipelines in this area.

Dual numerical solutions of Casson SA–hybrid nanofluid toward a stagnation point flow over stretching/shrinking cylinder

Abstract A computational study of Casson sodium alginate–hybrid nanofluid of stagnation point flow through a shrinking/stretching cylinder with radius effect was carried out. Since the hybrid nanofluid is considered more contemporary type of nanofluid, it is currently being employed to enhance the efficiency of heat transmission rates. The aim of this study is to scrutinize the effect of particular parameters, such as the shrinking parameter, the Reynold number, the Casson fluid parameter, the solid copper volume fraction, and the Prandtl number, on the temperature and velocity profiles. Furthermore, the research looked into the variation of skin friction coefficient as well as the Nusselt number according to the Casson fluid parameters, and the copper solid volume fraction against shrinking parameter was investigated as part of this study. By including the appropriate similarity variables in the alteration, the nonlinear partial differential equation has been transformed into a set of ordinary differential equations (ODEs). In the end, the MATLAB bvp4c solver program is used to rectify ODEs. The findings revealed the existence of two solutions for shrinking surface with varying copper volume fractions and Casson fluid parameter values. Furthermore, the temperature profile rate was reduced in both solutions as the strength of the Reynold number, Casson fluid parameter, and copper volume fraction increased. Finally, non-unique solutions were obtained in the range of λ ≥ λ ci \lambda \ge {\lambda }_{{\rm{ci}}} .

Model-based comparative analysis of MHD stagnation point flow of hybrid nanofluid over a stretching sheet with suction and viscous dissipation

The effects of steady MHD stagnation point flow with viscous dissipation over a permeable stretching surface are examined. The fluid water is infused with Al 2 O 3 − Cu hybrid nanofluid particles. Magnetohydrodynamics (MHDs), suction with viscous dissipation reveals a mechanism for the transmission of heat and flow. Many different thermal conductivity models, such as the Hamilton–Crosser, Yamada–Ota, and Xue models are utilized to learn more about the thermophysical properties of hybrid nanoparticles. By using the boundary layer approximation, the partial differential equations may be transformed into ordinary differential equations (ODEs), which are linked and highly nonlinear. This is accomplished by employing a separate set of equations. Mathematica is used to find the numerical solution by applying the Runge-Kutta (RK-IV) technique to the coupled system in question. Visualization of the resulting numerical data shows the velocity, temperature, and skin friction. There have also been discoveries about the local heat transfer rate. Afterwards, the data is presented in tables and discussed. Suction S is studied together with magnetism M , Eckert number Ec , and the nanoparticle volume fraction toward stretching to better understand the performance of flow, heat transfer within these systems. According to the findings of this investigation, the stretching sheet offers a novel approach. When compared to the Hamilton–Crosser and Xue models of hybrid nanofluid, the Yamada–Ota model of the hybrid nanofluid achieves higher heat transfer rates than the other two models combined for mass suction. Also, the tri-models demonstrate growing tendencies to growing the volume fraction rate of Al 2 O 3 − Cu / H 2 O hybrid nanoparticles. Furthermore, the hybrid nanoparticles performance is superior to that of conventional nanofluids.

Flow and irreversible mechanism of pure and hybridized non-Newtonian nanofluids through elastic surfaces with melting effects

Abstract The significance of nanofluid research in nanotechnology, pharmaceutical, drug delivery, food preparation, and chemotherapy employing single- and two-phase nanofluid models has drawn the attention of researchers. The Tiwari–Das model does not capture the diffusion and random movement of nanoparticles (NPs) when they are injected into complex functional fluids. In order to fix the peculiar behavior of NPs, more complex models like the Buongiorno model are coupled with the single-phase model. To examine the heat-mass transfer attributes of nanofluids, a single- and two-phase mixture model is coupled for the first time. The effect of hybrid NPs on the hemodynamic properties of the blood flow through a stretched surface with interface slip in the neighborhood of the stagnation point is examined. Due to their significance in medicinal uses and nominal toxicity, blood is loaded with zinc–iron ( ZnO − F e 2 O 3 ) {\rm{ZnO}}\left-{\rm{F}}{{\rm{e}}}_{2}{{\rm{O}}}_{3}) NPs. However, blood is speculated to have the hematocrit viscosity of the Powell–Eyring fluid. The single-phase model predicts an improvement in heat transport due to an increased volumetric friction of NPs, while the two-phase models provide closer estimates of heat-mass transfer due to Brownian and thermophoretic phenomena. Entropy evaluation predicts the details of irreversibility. The mathematical structures are effectively solved with a Runge–Kutta fourth-order algorithm along with a shooting mechanism. The Eyring–Powell parameters decrease the drag coefficient and mass/thermal transport rate. A higher estimation of the slip, material, and magnetic parameters decreases the flow behavior. The Bejan number increases with the diffusion parameter and decreases as the magnetic and Brinkman numbers increase. The effect of iron oxide ( F e 2 O 3 ) \left({\rm{F}}{{\rm{e}}}_{2}{{\rm{O}}}_{3}) is observed to be dominant.

Numerical investigation of time-dependent axisymmetric stagnation point flow and heat transfer of $$A{l}_{2}{O}_{3}-{H}_{2}O$$ and $$Cu-{H}_{2}O$$ nanofluid over a stretching sheet with variable physical features

Numerical investigation of time-dependent axisymmetric stagnation point flow and heat transfer of $$A{l}_{2}{O}_{3}-{H}_{2}O$$ and $$Cu-{H}_{2}O$$ nanofluid over a stretching sheet with variable physical features

Intelligent computing infrastructure for nodal/saddle stagnation point slip flow of an aqueous convectional magnesium oxide–gold hybrid nanofluid with viscous dissipation

ABSTRACT Using the power of numerical computation through Levenberg Marquardt backpropagation ( LMB ), the fluidic issue in the present study has features of heat transfer by convection in the hybrid nanofluid suspension of magnesium oxide and gold nanoparticles. The influence of slip effects on boundary layer flow with viscous dissipation at the nodal/saddle stagnation point is examined using a mathematical model. The current study considers water to be the base fluid, MgO and Au as nanoparticles, and the circular cylinder to be the medium’s surface. Non-linear partial differential equations are converted into ordinary differential equations via similarity transformations. The dataset for Levenberg Marquardt backpropagation is generated in Mathematica software using an explicit RK-4 approach by varying different parameters such as the slip parameter ( λ ), convective parameter ( Bi ), Eckert number ( E c ∗ ) and volume fraction ( ϕ 2 ), Bi with Ec. Validation, training, and testing are utilized for network modeling through the Levenberg-Marquardt backpropagation approach for various scenarios of the fluidic model. The result shows that the base fluid’s thermal behavior is quickly increased by the MgO − Au /water hybrid nanofluid. The reliability of the findings is evaluated using autocorrelation, regression, mean square error, absolute error, and error histogram analyses.

Entropy generation for stagnation point dissipative hybrid nanofluid flow on a Riga plate with the influence of nonlinear convection using neural network approach

Entropy generation for stagnation point dissipative hybrid nanofluid flow on a Riga plate with the influence of nonlinear convection using neural network approach

Nonsimilar mixed convection analysis of ternary hybrid nanofluid flow near stagnation point over vertical Riga plate

PurposeThis work aims to concentrate on the mixed convection of the stagnation point flow of ternary hybrid nanofluids towards vertical Riga plate. Aluminum trioxide (Al2O3), silicon dioxide (SiO2) and titanium dioxide (TiO2) are regarded as nanoparticles, with water serving as the base fluid. The mathematical model incorporates momentum boundary layer and energy equations. The Grinberg term for the viscous dissipation and the wall parallel Lorentz force coming from the Riga plate are taken into consideration in the context of the energy equation.Design/methodology/approachThrough the use of appropriate nonsimilar transformations, the governing system is transformed into nonlinear nondimensional partial differential equations (PDEs). The numerical method bvp4c (built-in package for MATLAB) is used in this study to simulate governing equations using the local non-similarity (LNS) approach up to the second truncation level.FindingsNumerous graphs and numerical tables expound on the physical properties of the nanofluid temperature and velocity profiles. The local Nusselt correlations and the drag coefficient for pertinent parameters have been computed in tabular form. Additionally, the temperature profile drops while the velocity profile increases when the mixed convection parameter is included to oppose the flow.Originality/valueThe fundamental goal of this work is to comprehend how ternary nanofluids move towards a vertical Riga plate in a mixed convective domain with stagnation point flow.

Multicompartmental coacervate-based protocell by spontaneous droplet evaporation

Hierarchical compartmentalization, a hallmark of both primitive and modern cells, enables the concentration and isolation of biomolecules, and facilitates spatial organization of biochemical reactions. Coacervate-based compartments can sequester and recruit a large variety of molecules, making it an attractive protocell model. In this work, we report the spontaneous formation of core-shell cell-sized coacervate-based compartments driven by spontaneous evaporation of a sessile droplet on a thin-oil-coated substrate. Our analysis reveals that such far-from-equilibrium architectures arise from multiple, coupled segregative and associative liquid-liquid phase separation, and are stabilized by stagnation points within the evaporating droplet. The formation of stagnation points results from convective capillary flows induced by the maximum evaporation rate at the liquid-liquid-air contact line. This work provides valuable insights into the spontaneous formation and maintenance of hierarchical compartments under non-equilibrium conditions, offering a glimpse into the real-life scenario.

Time-dependent stagnation point flow of nano Casson fluid with Joule heating over an elongated surface subjected to viscous heating and exponential space-based heat source/sink: Boungiorno model

The unsteady two-directional flow of a non-Newtonian magneto-Casson nanoliquid flow over an elongated flat surface with the porous matrix is investigated. The flow is subjected to space-based exponential heat generation/absorption (ESHS), thermophoresis, Brownian motion of nanoparticles, and transverse magnetic field. Within the base fluid, the diffusion of chemically reactive nanoparticles is assumed to be highly significant; hence considered. The governing equations of the flow model admit self-similar equations and are numerically solved by employing the Runge-Kutta-based shooting technique (RKSM). The significance of key parameters on the temperature, velocity, friction factor at the surface, heat transfer rate, and mass transfer rate distributions is analyzed. The use of high-Prandtl number base fluid and nanoparticles of high thermal conductivity could be of practical use to increase the heat transfer rate and avoid nanoparticle accumulation. The occurrence of nanoparticles in the operating liquids reduces the shearing stress at the plate surface to avoid backflow.

Dynamic behaviors of a bubble near a rectangular wall with a bulge

In this paper, the cavitation bubble dynamics near a rectangular wall with a bulge are theoretically investigated. High-speed photography is employed to provide experimental verification of the theoretical results. Through a series of conformal transformations and the image method, the analytical description of how this complex wall configuration affects the bubble is shown to be equivalent to the superposition of eight virtual bubbles. The physical meaning of the eight virtual bubbles can be divided into four groups, corresponding to the influence of the left wall, the bottom wall, the angle formed by the two flat walls, and the bulge. The influence of the bulge on the liquid velocity distribution, as well as the intensity and direction of the Kelvin impulse exerted on the bubble, is explored for cases in which the bubble is located at symmetric and asymmetric positions. The main findings are given as follows: During the bubble collapse, a high-velocity area of the liquid exists to the side of the bubble farthest from the bulge, and three stagnation points with three low-velocity areas appear on the bulge surface. The bulge mainly influences the impulse intensity when the bubble is located near the symmetric position. The existence of the bulge causes the impulse angle to attain a minimum as the distance between the bubble and the bulge increases. For a larger bulge radius, the changes in the impulse angle become more complicated as the bubble position angle increases.

A Study of Nanofluid Flow with Free Bio-Convection in 3D Nearby Stagnation Point by Hermite Wavelet Technique

A new wavelet-numerical method for solving a system of partial differential equations describing an incompressible bio-convection nanofluid flow in a three-dimensional region close to the stagnation point is the primary focus of this article. Hermite wavelets form the basis of the algorithm. An assortment of similitude factors is utilized to improve on the overseeing conditions addressing the protection of all out mass, force, nuclear power, nanoparticles, and microorganisms to a bunch of completely connected nonlinear common differential conditions. The most important physical quantities that have a practical impact on the spread of motile bacteria are presented and analyzed in this paper. During bio-convection, the Prandtl, Lewis, Peclet, Schmidt, and Rayleigh numbers can alter the distribution of moving molecules. The dispersion of microorganisms can be emphatically affected by the kinds of nanoparticles and by the varieties in the temperature as well as volumetric part of the nanoparticles between the wall and the encompassing liquid. With excellent agreement for coupled nonlinear differential equations in engineering applications, our result demonstrates how powerful and simple the HWM is for solving these coupled nonlinear ordinary differential equations.

Jetting bubbles observed by x-ray holography at a free-electron laser: internal structure and the effect of non-axisymmetric boundary conditions

In this work, we study the jetting dynamics of individual cavitation bubbles using x-ray holographic imaging and high-speed optical shadowgraphy. The bubbles are induced by a focused infrared laser pulse in water near the surface of a flat, circular glass plate, and later probed with ultrashort x-ray pulses produced by an x-ray free-electron laser (XFEL). The holographic imaging can reveal essential information of the bubble interior that would otherwise not be accessible in the optical regime due to obscuration or diffraction. The influence of asymmetric boundary conditions on the jet’s characteristics is analysed for cases where the axial symmetry is perturbed and curved liquid filaments can form inside the cavity. The x-ray images demonstrate that when oblique jets impact the rigid boundary, they produce a non-axisymmetric splash which grows from a moving stagnation point. Additionally, the images reveal the formation of complex gas/liquid structures inside the jetting bubbles that are invisible to standard optical microscopy. The experimental results are analysed with the assistance of full three-dimensional numerical simulations of the Navier–Stokes equations in their compressible formulation, which allow a deeper understanding of the distinctive features observed in the x-ray holographic images. In particular, the effects of varying the dimensionless stand-off distances measured from the initial bubble location to the surface of the solid plate and also to its nearest edge are addressed using both experiments and simulations. A relation between the jet tilting angle and the dimensionless bubble position asymmetry is derived. The present study provides new insights into bubble jetting and demonstrates the potential of x-ray holography for future investigations in this field.

On the dynamics of the turbulent flow past a three-element wing

A comprehensive analysis of the unsteady flow dynamics past the 30P30N three-element high lift wing is performed by means of large eddy simulations at different angles of attack (α = 5°, 9°, and 23°) and at a Reynolds number of Rec=750 000 (based on the nested chord). Results are compared with experimental and numerical investigations, showing a quantitatively good agreement and, thus, proving the reliability and accuracy of the present simulations. Within the slat and main coves, large recirculation bubbles are bounded by shear layers, where the onset of turbulence is triggered by Kelvin–Helmholtz instabilities. In the energy spectrum of the velocity fluctuations, the footprint of these instabilities is detected as a broadband peak; its frequency being moved toward lower values as the angle of attack increases. Kelvin–Helmholtz vortices roll-up and break down into small scales that eventually impinge into the slat and main coves lower surfaces. The slat impingement shows to be more prominent, and hence, larger velocity and pressure fluctuations are observed. The impingement strength diminishes with the angle of attack in both coves, while higher fluctuations are originated on the slat and main respective suction sides, leading to larger boundary layers. This is associated with the displacement of the stagnation point with the angle of attack. Another salient feature observed is the laminar-to-turbulent flow transition in the main and flap leading edges although the average location of this transition seems to not be affected by the angle of attack. Tollmien–Schlichting instabilities precede this transition, with the disturbances amplified by the inviscid mode at low angles of attack, while at α=23°, the local Reynolds number on the main suction side is incremented and the viscous mode becomes important. The analysis shows that the turbulent wake formed at the trailing edge of all elements dominates the dynamics downstream. This is especially true at the higher angle of attack, where a large region of velocity deficit above the flap is observed, thus indicating the onset of stall conditions.

Numerical Analysis on Stagnation Point Flow of Micropolar Nanofluid with Thermal Radiations over an Exponentially Stretching Surface

Several industrial developments such as polymer extrusion in metal spinning and continuous metal casting include energy transmission and flow over a stretchy surface. In this paper, the stagnation point flow of micropolar nanofluid over a slanted surface is presenting also considering the influence of thermal radiations. Buongiorno’s nanoliquid model is deployed to recover the thermophoretic effects. By using similarity transformations, the governing boundary layer equations are transformed into ordinary differential equations. The Keller-box approach is used to solve transformed equations numerically. The numerical outcomes are presented in tabular and graphical form. A comparison of the outcomes attained with previously published results is done after providing the entire formulation of the Keller-Box approach for the flow problem under consideration. It has been found that the reduced sherwood number grows for increasing values of radiation parameter while, reduced Nusselt number and skin friction coefficient decreases. Furthermore, the skin-friction coefficient increases as the inclination factor increases, but Nusselt and Sherwood's numbers decline.

Impact of inclined magnetic field on non-orthogonal stagnation point flow of CNT-water through stretching surface in a porous medium

The magnetohydrodynamic (MHD) nanofluid flow at non-orthogonal stagnation point, with suspended carbon nanotubes in water on a stretched sheet in a permeable media with non-lin-ear thermal radiation is studied. This work aims to explore the inclined magnetic field impacts on normal velocity, tangential velocity and temperature for both types of carbon nanotubes (CNTs). The governing flow equations which are continuity equation, momentum equation and energy equation are reformed into ordinary differential form with the proper boundary conditions using appropriate transformations. The computational solution of the nonlinear ODEs is obtained using the Bvp4c method. The graphs are presented to show the influence of certain physical factors which ranged as magnetic parameter (0.5 ≤ M ≤ 2.5), inclination angle of the magnetic field (п/2 ≤ ζ ≤ п/4), permeability parameter (0 ≤ Ω ≤ 2), volume fraction of nanoparticle (0.03 ≤ Φ ≤ 0.07), stretching ration parameter (0.3 ≤ γ2 ≤ 0.7), Radiation param-eter (0.5 ≤ Nr ≤ 0.9), the heating parameter (0.5 ≤ θw ≤ 1.5) and Prandtl number (5 ≤ Pr ≤ 10). The normal and tangential velocity drops with the augmentation of (M), (ζ) and (Ω), while the temperature rise with enhance of (Nr) and (θw). This study’s findings may be used to manage the heat transmission and fluid velocity rate to achieve the required final product quality in numerous manufacturing processes such as electronic cooling, solar heating, biomedical and nuclear system cooling. Validation against previous research available in the literature in spe-cific situations shows excellent agreement.

Stagnation Point Nanofluid Flow in a Variable Darcy Space Subject to Thermal Convection Using Artificial Neural Network Technique

Stagnation Point Nanofluid Flow in a Variable Darcy Space Subject to Thermal Convection Using Artificial Neural Network Technique

Exploring the marvels of heat transfer: MHD convection at a stagnation point in non-Newtonian fluid with yield stress and chemical reactions

This study uses a non-Newtonian fluid with yield stress to investigate the complex dynamics of heat transmission in a stagnation-point MHD (Magnetohydrodynamic) convection system. The Casson fluid flow is used to model the fluid’s behaviour, and for analytical tractability, the governing partial differential equations (PDEs) are converted into ordinary differential equations (ODEs). The RK-Fehlberg method is used to obtain the numerical solution. The study’s main outcomes include the effects of magnetic field strength on the temperature, flow fields and the complex correlations that are shown between the Casson fluid parameters and heat transfer properties. Furthermore, the study highlights the mutually reinforcing impacts of thermal radiations and chemical processes on the heat transfer process. The study offers important insights for applications in a variety of domains, from materials science to environmental engineering, and advances our understanding of the linked impacts of magnetic fields, non-Newtonian behaviour, and chemical reactions on heat transport phenomena.