Secondary Velocity Research Articles

Hall Effect on ECF Flow along a Rotating Infinite Porous Plate in the Presence of Transverse Magnetic Field

Unsteady extracellular fluid (ECF) flow along with a rotating infinite vertical porous plate in the presence of a transverse magnetic field has been studied numerically. The dimensional governing equations have been non-dimensionalized by useful dimensionless variables. The explicit finite difference method has been used to solve dimensionless equations. The numerical results have been calculated by studio developer FORTRAN 6.6a and MATLAB 2018a. For perfect conducting case, Magnetic Diffusivity Parameter 5 ≤ Pm ≤ 15 has been taken in induction equation. For good accuracy, stability and convergence analysis have been analyzed. Mesh Sensitivity test, steady-state solution test, and code validation test have been performed. For time step τ = 1, the numerical results have been found for the primary velocity, secondary velocity, angular velocity, primary induced magnetic field, secondary induced magnetic field, temperature as well as shear stresses along x and z direction, couple stress along z direction, current densities along x and z direction and the Nusselt number. Finally, the effects of various parameters have been separately discussed and illustrated graphically.

Investigation of the Effects of Some Physical Parameters and Hall Current on MHD Fluid Flow with Heat Flux over a Porous Medium

In this paper, an investigation of the effects of some physical parameters and Hall current on magneto hydrodynamics (MHD) fluid flow with heat flux over a porous medium was carefully examined, taking into consideration Hall effects where the temperature and concentration are assumed to be oscillating with time. Furthermore, perturbation method is used in solving the governing equations. The profiles of velocity, temperature and concentration are presented graphically, going into the problem the primary and secondary velocity are presented and compute for some physical parameters such as mass Grashof number (Gc), Schmidt number Sc, Prandtl number (Pr) viscoelastic parameter (K1) and hall current parameter (m). Results indicated that primary velocity increases with increase in values of Gc on one hand and on the other hand it decreases with increase in the values of Pr, K1 and m. Secondary velocity demonstrated opposite trend.

Numerical simulation of jet formation underwater by focusing annular liner

Basing on the application background of anti-submarine torpedo using shaped charge technology, a new structure of shaped charge liner named focusing annular liner was designed. The Autodyn-2D software was used to simulate the jet formation of this liner underwater. The result shows that: Through two times of convergence, the focusing annular liner can form one jet, this jet is thicker than normal jet. And during Secondary convergence, jet velocity and collision pressure are greatly increased.

Structural optimization of vortex finder for a centrifugal air classifier

To further improve the centrifugal air classifier performance, effects of the fully-inserted vortex finders with slots are investigated. Experimental results show that the classifier with the non-uniform slotted vortex finder has the higher particle selectivity, smaller cut size and narrower product particle size distribution than the classifier with the uniform slotted vortex finder and the base partly-inserted vortex finder. The classifier obtains the particle classifying sharpness of 1.72 when the primary and secondary gas velocities are 12 m/s and 2.4 m/s. The experimental curves present a same distorted S-shape with the fish-hook dip at about 4 μm. Simulation results indicate that the non-uniform slotted vortex finder could accelerate the swirling flow with the gas tangential velocity averagely increased by 3 m/s. The static pressure varies from −350 Pa to 1700 Pa. Meanwhile, the slotted vortex finder can reduce the influence of the short circuit flow on coarse particles. The DPM model can well predict the cut size with a maximum error of 4.9%, but not the fish-hook effect. The obtained results can provide a guideline for the vortex finder design of the centrifugal air classifier.

Chemically reactive MHD micropolar nanofluid flow with velocity slips and variable heat source/sink

The two-dimensional electrically conducting magnetohydrodynamic flow of micropolar nanofluid over an extending surface with chemical reaction and secondary slips conditions is deliberated in this article. The flow of nanofluid is treated with heat source/sink and nonlinear thermal radiation impacts. The system of equations is solved analytically and numerically. Both analytical and numerical approaches are compared with the help of figures and tables. In order to improve the validity of the solutions and the method convergence, a descriptive demonstration of residual errors for various factors is presented. Also the convergence of an analytical approach is shown. The impacts of relevance parameters on velocity, micro-rotation, thermal, and concentration fields for first- and second-order velocity slips are accessible through figures. The velocity field heightens with the rise in micropolar, micro-rotation, and primary order velocity parameters, while other parameters have reducing impact on the velocity field. The micro-rotation field reduces with micro-rotation, secondary order velocity slip, and micropolar parameters but escalates with the primary order velocity slip parameter. The thermal field heightens with escalating non-uniform heat sink/source, Biot number, temperature ratio factor, and thermal radiation factor. The concentration field escalates with the increasing Biot number, while reduces with heightening chemical reaction and Schmidt number. The assessment of skin factor, thermal transfer, and mass transfer are calculated through tables.

Mechanisms of particle preferential concentration induced by secondary motions in a dilute turbulent square duct flow

Particle-laden turbulent square duct flows at Reτ = 300 (based on the duct half-width and the mean friction velocity) are investigated using direct numerical simulation with one-way coupled Lagrangian particle tracking. Four particle-to-fluid density ratios are considered with the corresponding shear Stokes number St+ = 0.31, 25, 125, and 260. Particle motion is governed by drag, lift, added-mass, and pressure gradient forces. The main purpose of this work is to examine the effect of the turbulence-driven secondary flows on particle preferential accumulation and their dependence on the Stokes number. Results obtained indicate that the cross-stream secondary motions encourage inertial particles to accumulate preferentially in the duct corners, where the maximum of the cross-sectional particle concentration occurs. The extent of accumulation here is strongly dependent on the Stokes number, with the greatest accumulation found at St+ = 25. Interestingly, the maximum of the intensity of the secondary particle velocity along the corner bisector is also achieved at St+ = 25, whereas in the region adjacent to the wall, it is found to decrease with a particle Stokes number. Additionally, it is observed that the higher inertia particles are more easily trapped in the stagnation zone of secondary flows with low turbulence intensity in the corner region. In the near-wall region, the heavier particles (St+ ≥ 25) are prone to reside and form elongated clusters along the low-speed streamwise velocity streaks, with this trend less pronounced with the increasing Stokes number. Along the wall, away from the corner where the secondary motion is attenuated, particle accumulation is dominated by the near-wall coherent vortices. This phenomenon is further discussed using a region-based correlation analysis between the particle spatial distribution and local flow topology. An in-depth particle dynamic analysis determines that the average cross-sectional drag force resulting from the secondary flow is mainly responsible for the particle motion throughout the duct cross section, which tends to push particles away from the walls in the near-wall region but shows the exact opposite trend in the bulk flow region. Moreover, the pressure gradient force also plays an important role for low-inertia particles. As the Stokes number is increased, the lift force becomes progressively dominant in the viscous sublayer, acting to pull particles toward the corners and walls of the duct.

Mathematical Modeling of Convective Heat and Mass Transfer of a Rotating Nano-Fluid Bounded by Stretching and Stationary Walls in a Vertical Conduit

The influence of thermal emission and unvarying magnetic field of convective heat and mass transfer of a rotating nano-liquid in an upright conduit constrained by a stretching and motionless wall is studied. The temperature, concentration profile, primary and secondary velocities have been computed through similarity transformation and fourth-order Runge-Kutta shooting technique. The objective of this article is to measure the impact of emission constraint, Brownian movement constraint and Eckert number, thermophoresis constraint, Prandtl number, space, and temperature-dependent heat source constraint on velocity. The results are presented in tables and graphs. Further, various constraint impacts on the skin friction coefficient, heat and mass transfer rates are also explored. This work is pertinent to biotechnological and engineering uses, like mass and heat transfer enhancement of microfluids and design of bioconjugates.

Effect of the Hall currents and thermal radiation on the flow of a nanofluid through a vertical rotating channel

The present article is intended to focus on the combined influence of Hall currents and thermal radiation on the magnetohydrodynamic flow of a nanofluid through a vertical rotating channel. The nanofluid is prepared by choosing the copper nanoparticles and water as a base fluid. The impact of mixed convection is also considered. The solution to the formulated problem is computed through a mathematical software Matlab. The physical interpretation of the problem is performed by preparing the graphical results. Consequences manifest that a decline in both primary and secondary velocity is produced via a rise in the strength of Lorentz forces. However, the disparate impact of the Hall parameter on primary and secondary velocity is noticed. Increasing the angular velocity of the vertical channel raises both velocity profiles. The tangent phase of the rate of heat transfer at the left vertical wall significantly decays for increment in the radiation parameter; however, it is directly related to the Prandtl number and the frequency parameter. Further, the temperature is intensified for a rise in the Prandtl number and the frequency parameter, and it decays for an increase in radiation parameters.

Thermophoresis effect on peristaltic flow of viscous nanofluid in rotating frame

In this paper simultaneous effects of Coriolis forces, Brownian motion and thermophoresis on the peristaltic motion of Newtonian fluid are incorporated. The governing nonlinear flow equations with appropriate conditions are converted into non-dimensional form, afterward, they were solved numerically by the Keller box procedure. Also, another numerical method is used to solve these transformed equations and by tabular data, we made a comparison of the numerical values of velocities, temperature and concentration profiles. A parametric investigation was conducted and the influence of various parameters on primary and secondary velocities is conducted for both slip and no-slip flow cases. The obtained results are compared with the existing literature as a particular case and found with an excellent agreement. Furthermore graphical results for temperature and nanoparticle concentration profiles are reported for both rotating and non-rotating frames. It is worth mentioning that the effects of Nt and Nb are the dominant in rotating frame as compared to the non-rotating frame of reference and the magnitude of temperature distribution is small for slip flow.

Local Flow and Heat Transfer of Supercritical CO2 in Semicircular Zigzag Channels of Printed Circuit Heat Exchanger during Cooling

Understanding and predictions of the local thermal-hydraulic performance of supercritical CO2 in channels of printed circuit heat exchanger geometries are of great importance to the design and optimization of the pre-cooler and recuperators in supercritical CO2 cycle. The local flow and heat transfer of supercritical CO2 in horizontal semicircular zigzag channel during cooling near the critical or pseudo-critical point have been numerically investigated in this paper. The effects of thermophysical property variations, mass flux, and the channel geometrical parameters on the flow and heat transfer are discussed. It is found that the extrude angle in the zigzag channel impedes the bulk flow and generates secondary flow, which induces asymmetric flow and temperature distribution, and enhances fluid mixing and mitigates the temperature stratification. A dimensionless secondary flow velocity is adopted to evaluate the influence of secondary flow on the heat transfer, which is more enhanced for cases with relatively large mass flux and in channels with relatively large inclined angle and small pitch length, however, the pressure drop increases meanwhile. Finally, pitch-averaged local flow and heat transfer correlations have been developed based on the numerical results and mechanism analysis accounting for the thermophysical property variations and the channel geometrical parameters.

Theoretical analysis of two-layer fluids with continuity of stresses at interface and slip at the walls of an inclined channel

The rotating flow of two fluids having an interface separating the viscous fluid and magnetite-water ferrofluid is studied. The fluids are non-miscible and streaming in an inclined channel. The walls of the channel are smooth enough to examine the slip effects on the flow. The channel is subjected to the transverse magnetic field and thermal radiations. To achieve the flow equations governing the flow phenomena a fully developed flow is taken into consideration. The resultant ordinary differential equations (ODEs) are converted into non-dimensional forms which are coupled and non-linear. Approximate series solutions for flow fields are obtained separately by the aid of the Perturbation technique and then matched at the interface region via relevant matching conditions. The results are drawn graphically to comprehend the effects of various essential parameters on temperature and flow fields. A decreasing response in the primary velocity profile is observed with a rise in rotation parameter, ferroparticles volume fraction and Hartmann number while it increases with a rise in slip parameters. The secondary velocity shows an oscillating behavior for rotation parameter whilst magnetic flux and slip parameters increase the secondary profiles. The primary and secondary velocities will decrease throughout the channel if the fluid in the lower layer is more viscous relative to the upper one. It can also be noticed that the radiation decreases the influence of natural convection by decreasing the temperature difference and temperature profile increases with a rise in thermal conductivity (TC).

Hall and ion‐slip effects on MHD free convection flow of rotating Jeffrey fluid over an infinite vertical porous surface

AbstractAn attempt has been made to explore Hall and ion‐slip effects on an unsteady magnetohydrodynamic rotating flow of an electrically conducting, viscous, incompressible, and optically thick radiating Jeffrey fluid past an impulsively vertical moving porous plate. Analytical solutions of the governing equations are obtained by Laplace transform technique. The analytical expressions for skin friction, Nusselt number, and Sherwood number are also evaluated. The velocity, temperature, and concentration distributions are displayed graphically in detail. From engineering point of view, the changes in skin friction, Nusselt number, and Sherwood number are observed with the computational results presented in a tabular manner. It is observed that the effects of rotation and Hall current tend to accelerate secondary velocity and decelerate primary velocity throughout the boundary layer region. Thermal and concentration buoyancy forces tend to accelerate both velocity components. Thermal radiation and thermal diffusion tend to enhance fluid temperature throughout the boundary layer region. Rotation and Jeffrey fluid parameters tend to enhance both stress components.

Modeling and analysis of peristalsis of hybrid nanofluid with entropy generation

This investigation intends to explore the peristaltic transport of rotating fluid in a channel. The channel is considered symmetric with flexible walls, and porous medium fills the saturated space. In this analysis, hybrid nanofluid consisting of titanium oxides and copper particles is taken. Water is used as the base fluid. MHD and Hall effects are employed in this problem. Formulation of energy equation is based on radiation and non-uniform heat source or sink parameter. Convection conditions are utilized for the boundary. Thermodynamics second relation is employed for entropy generation. Maxwell–Garnetts model of thermal conductivity is employed. Numerical analysis is carried out using NDSolve of Mathematica. The effect of nanoparticle volume fraction, Taylor number, Hartman number, porosity and Hall parameters is analyzed for axial and secondary velocities, temperature, entropy generation and heat transfer rate. This study divulges that an enhancement in rotation parameter caused an increase in secondary velocity. Moreover, as volume fraction of nanoparticles enhances from 0.01 to 0.04, decay is noticed in fluid’s axial and secondary velocities. In this case, entropy also decreases. This study further disclosed that heat transfer rate gradually increases as we exceed the volume fraction of nanoparticles from 0.02 to 0.08. More pores also lead to an enhancement in fluid velocity, temperature and entropy.

Dissipative Power-law fluid flow using spectral quasi linearization method over an exponentially stretchable surface with Hall current and power-law slip velocity

The present article aims to reports laminar, incompressible, electrically conducting two-dimensional non-Newtonian (power-law) liquid flow via exponentially stretching sheet with power-law slip velocity conditions. Transverse magnetic field, Hall current, viscous dissipation and radiative flux effects are incorporated in the formulation. Rosseland's diffusion model is defined for the radiation heat transfer. The non-linear partial derivation formulations satisfying the flow are transformed to the non-linear derivative equations by employing the local similarity quantities and then solved analytically through spectral quasi-linearization method (SQLM). The resultant solution is computed for different parameters in tables and graphical representation for clear understanding of the thermo-physical terms. Extensive visualization of primary and secondary velocities, temperature distributions for various emerging parameters presented for n = 0.7 (pseudo-plastic fluid) and n = 1,3 (dilatant fluid). The results are verified for limiting cases by comparing with various investigations and found excellent accuracy for Newtonian case. It is interesting to note that secondary flow rate is more dominant for both the cases of pseudo plastic and dilatant fluids for Hall parameter and Eckert number. Increasing Hall current leads suppress the fluid temperature but as Eckert number grows it leads grow the fluid temperature. Further, it is observed that as Hall parameter increases local Nusselt number strongly elevates.

Magnetic Rotating Flow of a Hybrid Nano-Materials Ag-MoS2 and Go-MoS2 in C2H6O2-H2O Hybrid Base Fluid over an Extending Surface Involving Activation Energy: FE Simulation

Numeric simulations are performed for a comparative study of magnetohydrodynamic (MHD) rotational flow of hybrid nanofluids (MoS2-Ag/ethyleneglycol-water (50–50%) and MoS2-Go/ethyleneglycol-water (50–50%)) over a horizontally elongated plane sheet. The principal objective is concerned with the enhancement of thermal transportation. The three-dimensional formulation governing the conservation of mass, momentum, energy, and concentration is transmuted into two-dimensional partial differentiation by employing similarity transforms. The resulting set of equations (PDEs) is then solved by variational finite element procedure coded in Matlab script. An intensive computational run is carried out for suitable ranges of the particular quantities of influence. The primary velocity component decreases monotonically and the magnitude of secondary velocity component diminishes significantly when magnetic parameter, rotational parameter, and unsteadiness parameter are incremented. Both the primary and secondary velocities are smaller in values for the hybrid phase Ag-MoS2 than that of hybrid phase Go-MoS2 but the nanoparticle concentration and temperature are higher for hybrid phase Ag-MoS2. The increased values of parameters for thermophoresis, Brownian motion, shape factor, and volume fraction of ϕ2 made significant improvement in the temperature of the two phases of nano liquids. Results are also computed for the coefficients of skin friction(x, y-directions), Nusselt number, and Sherwood number. The present findings manifest reasonable comparison to their existing counterparts. Some of the practical engineering applications of the present analysis may be found in high-temperature nanomaterial processing technology, crystal growing, extrusion processes, manufacturing and rolling of polymer sheets, academic research, lubrication processes, and polymer industry.

Flow processes and sedimentation in a straight submarine channel on the Qiongdongnan margin, northwestern South China Sea

ABSTRACT Straight channels are ubiquitous in deep-water settings, yet flow dynamics and sedimentation in them are far from being well understood. Stratigraphy and flow dynamics of a middle to late Miocene straight channel in Qiongdongnan Basin were quantified, in terms of angle of channel-complex-growth trajectories (Tc), stratigraphic mobility number (M), Froude number (Fr), layer-averaged flow velocity (U), flow thickness (h), and water entrainment coefficient (Ew). The documented channels are composed of three channel complexes (CC1 to CC3) all of which are all characterized by symmetrical channel cross sections without levees and by organized vertical channel-stacking patterns (represented by high mean value of Tc = 37.4° and low mean value of M = 0.038). Turbidity currents in them were estimated to have U of 1.6 to 2.0 m/s (averaging 1.8 m/s), h of 63 to 89 m (averaging 78), Fr of 0.849 to 0.999 (averaging 0.912), and Ew of 0.0003 to 0.0005. They were, in most case, subcritical over most of the channel length, and had a low degree of water entrainment and low flow height scaled to the channel depth (i.e., 0.786 to 0.81 of the channel depth), most likely inhibiting the gradual loss of sediment to form levees. With reference to modeling results of secondary flow velocity vectors of numerical straight channels with the same sinuosity, two parallel gullies seen on both sides of the interpreted channel beds are interpreted to be induced by high-velocity downward backflows produced by the negative buoyancy. Such symmetrical secondary flow structures most likely promoted symmetrical intrachannel deposition (i.e., less deposition along both channel margins but more deposition near the channel center), and thus forced individual channel complexes to progressively aggrade in a synchronous manner, forming straight-channel complexes with symmetrical channel cross sections and organized vertical channel-stacking patterns.

Spectroscopic Detection of the Pre-White Dwarf Companion of Regulus

Abstract Mass transfer in an interacting binary will often strip the mass donor of its entire envelope and spin up the mass gainer to near critical rotation. The nearby B-type star Regulus represents a binary in the post-mass transfer stage: it is a rapid rotator with a very faint companion in a 40 days orbit. Here we present the results of a search for the spectral features of the stripped-down star in an extensive set of spectra with high signal-to-noise ratio and high resolution obtained with the CFHT/ESPaDOnS and TBL/NARVAL spectrographs. We first determine revised orbital elements in order to set accurate estimates of the orbital Doppler shifts at the times of observation. We then calculate cross-correlation functions of the observed and model spectra, and we search for evidence of the companion signal in the residuals after removal of the strong primary component. We detect a weak peak in the co-added residuals that has the properties expected for a faint pre-white dwarf. We use the dependence of the peak height and width on assumed secondary velocity semiamplitude to derive the semiamplitude, which yields masses of M 1/M ⊙ = 3.7 ± 1.4 and M 2/M ⊙ = 0.31 ± 0.10 (assuming orbital inclination equals the spin inclination of Regulus). We estimate the temperature of the pre-white dwarf T eff = (20 ± 4) kK through tests with differing temperature model spectra, and we find the radius R 2/R ⊙ = 0.061 ± 0.011 from the component temperatures and the flux ratio associated with the amplitude of the signal in the cross-correlation residuals.

Unsteady magneto-hydrodynamic transport of rotating Maxwell nanofluid flow on a stretching sheet with Cattaneo–Christov double diffusion and activation energy

A description of magnetohydrodynamic effects on the transient rotational flow of Maxwell nanofluids is considered. The temperature and concentration distributions are associated with Cattaneo- Christove double diffusion, Brownian motion and thermophoresis. The diffusion of chemically reactive specie is investigated with Arrhenius activation energy. The governing equations in the three-dimensional form are transmuted into dimensionless two-dimensional form with the implementation of suitable scaling transformations. The variational finite element procedure is harnessed and coded in Matlab script to obtain the numerical solution of the coupled non-linear partial differential problem. The varying patterns of velocities, skin friction coefficients, Nusselt number, Sherwood number, fluid temperature and concentration functions are computed to reveal the physical nature of this study. It is observed that higher inputs of the parameters for magnetic force, Deborah number, rotational fluid, and cause to slow the primary as well as secondary velocities but they raise the temperature like thermophoresis and Brownian motion does. However, the thermal relaxation parameter reduces the nanofluid temperature. The local heat transfer rate reduces against Nt, rotational, and Nb parameters, and it is higher for Prandtl number. The current FEM (finite element method) solutions have been approved widely with the recently published results, showing an excellent correlation. The examination has significant applications in the food industry and relevance to energy systems, biomedical, and modern technologies of aerospace systems.

Hall current, viscous and Joule heating effects on steady radiative 2-D magneto-power-law polymer dynamics from an exponentially stretching sheet with power-law slip velocity: A numerical study

A mathematical model is developed for 2-D laminar, incompressible, electrically conducting non-Newtonian (Power-law) fluid boundary layer flow along an exponentially stretching sheet with power-law slip velocity conditions in the presence of Hall currents, transverse magnetic field and radiative flux. The secondary flow has been induced with appliance of Hall current. The distinguish features of Joule heating and viscous dissipation are included in the model since they are known to arise in thermal magnetic polymeric processing. Rosseland’s diffusion model is employed for radiation heat transfer. The non-linear partial differential equations describing the flow (mass, primary momentum, secondary momentum and energy conservation) are transformed into non-linear ordinary differential equations by employing local similarity transformations. The non-dimensional nonlinear formulated set of equations is numerically evaluated with famous shooting algorithm by using MATLAB software. The validation of simulated numerical results has been completed with generalized differential quadrature (GDQ). Extensive visualization of primary and secondary velocities and temperature distributions for the effects of the emerging parameters is presented for both pseudo-plastic fluids (n = 0.8) and dilatant fluids (n = 1.2). The study is relevant to the manufacturing transport phenomena in electro-conductive polymers (ECPs).

Finite Element Study of Magnetohydrodynamics (MHD) and Activation Energy in Darcy–Forchheimer Rotating Flow of Casson Carreau Nanofluid

Here, a study for MHD (magnetohydrodynamic) impacts on the rotating flow of Casson Carreau nanofluids is considered. The temperature distribution is associated with thermophoresis, Brownian motion, and heat source. The diffusion of chemically reactive specie is investigated with Arrhenius activation energy. The governing equations in the 3D form are changed into dimensionless two-dimensional form with the implementation of suitable scaling transformations. The Variational finite element procedure is harnessed and coded in Matlab script to obtain the numerical solution of the coupled non-linear partial differential problem. The variation patterns of Sherwood number, Nusselt number, skin friction coefficients, velocities, concentration, and temperature functions are computed to reveal the physical nature of this examination. It is seen that higher contributions of the magnetic force, Casson fluid, and rotational fluid parameters cause a raise in the temperature like thermophoresis and Brownian motion does but also causes a slowing down in the primary as well as secondary velocities. The FEM solutions show an excellent correlation with published results. The current study has significant applications in the biomedical, modern technologies of aerospace systems, and relevance to energy systems.