Secondary Velocity Research Articles

RETRACTED: Analysis of rotating-symmetric frame and MHD for peristaltic multiphase flow: An exact solution

The rotational mechanism forms the basis of various cosmic and geophysical transports. In medical science, rotational blood flows have been related to healthy cardiac function. This study consists of a mathematical model representing magnetohydrodynamic effects on the two-phase pumping flow of a Ree–Eyring–Powell stress model in a rotating frame. The model is controlled by switching the system into a wave frame of reference for better analysis of the wave phenomenon. Moreover, a lubrication theory is applied to the resulting set of relations in order to get a more comprehensive form of the reduced mathematical model. In the end, an exact solution is found to discuss the substantial contents of the study. The data on velocity and stream function are presented diagrammatically to examine the theoretical behavior of various quantities under the variation of considerable physical factors. It is concluded from the graphs that axial and secondary velocities are decreasing against rotation, magnetic field, and fluid’s factor, but the same rise in the case of wall stiffness and particle concentration. In both industrial and biomedical applications, this type of flow measurement gives tomographic information on the multiphase flow process, which entails acquiring signal changes at the edges of objects like fluid pipes or blood vessels to determine how the objects are distributed within. This work is extendable by considering nanoparticles of various types to enhance the thermal conductivity of the flow.

Magnetohydrodynamic flow and Hall current effects on a boundary layer flow and heat transfer over a three-dimensional stretching surface

The current investigation is being carried out to investigate the impacts of magnetohydrodynamic flow and hall current effects on boundary layer flow across a three-dimensional stretching surface. The governing equations are framed with reasonable assumptions, and appropriate similarity transformations are applied to convert a set of partial differential equations into ordinary differential equations. To solve the reduced equations, the Runge Kutta Fehlberg 4th 5th order technique is utilised. The results reveal that primary and secondary velocity improves with the velocity parameter and Eckert number decrease for the magnetic parameter. The improvement in the Grashof number will improve the primary velocity but a reverse trend is seen in the case of secondary velocity. The thermal profile improves with the magnetic parameter, the velocity parameter, and the Eckert number, but it degrades with the Grashof number. The rate of heat transmission increases with the magnetic parameter and the Eckert number, whereas it decreases with the remaining factors.

Neural network method for quadratic radiation and quadratic convection unsteady flow of Sutterby nanofluid past a rotating sphere

In this study, the heat relocation properties of quadratic thermal radiation and quadratic convective unsteady stagnation point flow of electro-magnetic Sutterby nanofluid past a spinning sphere under zero mass flux and convective heating conditions are investigated. The governing equations are developed and expressed as partial differential equations, which are afterwards transformed into ordinary differential equations by applying similarity conversion. In the investigation, the JAX library in Python is employed with the numerical approach to artificial neural networks. It is investigated to what extent physical characteristics affect primary and secondary velocity, temperature, and concentration fields. The results demonstrate that due to increasing unsteadiness, Sutterby fluid, and magnetic field parameters, the flow of Sutterby nanofluid in the flow zone accelerates in the primary (x-direction) and slows down in the rotational (z-direction). The outcome also shows that an increase in the quadratic radiation parameter, the magnetic field constraint, and the electric field constraint induce increases in the temperature distribution of the Sutterby nanofluid. The study also shows that the concentration of nanoparticles decreases with increasing Lewis numbers and unsteadiness parameter values. Additionally, a graph illustrating the mean square error is investigated and provided.

Slip Condition Effects on Unsteady MHD Fluid Flow with Radiative Heatflux over a Porous Medium

The objective of this paper is to study unsteady magneto hydrodynamic (MHD) free flow of viscoelastic fluid (Walter’s B) past an infinite vertical plate through porous medium. The temperature is assumed to be oscillating with time. The solution obtained shows different profiles of effects of slip conditions on primary and secondary velocity. Also, the effects of various parameters on temperature, concentration, primary and secondary velocity profiles were presented graphically. The result indicated the secondary velocity is enhanced with increase in slip parameter. Primary velocity demonstrated opposite trend.

Exploration of the effects of Coriolis force and thermal radiation on water-based hybrid nanofluid flow over an exponentially stretching plate

Hybrid nanofluids’ enhanced thermophysical properties make them applicable in a plethora of mechanical and engineering applications requiring augmented heat transfer. The present study focuses on a three-dimensional Copper-Aluminium Oxide left( Cutext{- }Al_{2}O_{3}right)-water based hybrid nanofluid flow within the boundary layer with heat transfer over a rotating exponentially stretching plate, subjected to an inclined magnetic field. The sheet rotates at an angular velocity Omega and the angle of inclination of the magnetic field is gamma. Employing a set of appropriate similarity transformation reduces the governing PDEs to ODEs. The resulting ODEs are solved with the finite difference code with Shooting Technique. Primary velocity increases at large rotation but the secondary velocity reduces as the rotation increases. In addition, the magnetic field is found to oppose the flow and thereby causing a reduction in both the primary and secondary velocities. Increasing the volume fraction reduces the skin friction coefficient and enhances the heat transfer rate.

Rotation, electromagnetic field, and variable thermal conductivity effects on free convection flow past an eternity vertical porous plate

AbstractThe present research may facilitate the reduction of the number of conversion steps required to include the low output voltages in an electrokinetic biomass process. Variable thermal conductivity and electroosmosis flow have already established great potential in the thermo‐elastic models of various manufacturing industries and have been widely used in energy technologies. As a result, the current framework investigates the characteristics of natural convection flow with the influence of variable thermal conductivity and electroosmosis over an eternity vertical porous plate. Coriolis forces and Hall current effects are considered in the momentum equations, and also thermal radiation and variable thermal conductivity are taken as energy equations. A linear chemical reaction parameter is used in the concentration equation. The equation of Poisson–Boltzmann is exploited to depict the electric potential characteristics within the accelerated plate medium. The pdepe command in Matlab software is used to figure out the numerical solutions to equations about momentum, energy, and concentration. The expressions of fluid transverse velocity, fluid axial velocity, fluid temperature, and concentration profiles are presented as numerical results and also derived vital relevant stream parameters diagrammatically, whereas the numerical values of primary skin friction, secondary skin friction, and Nusselt number are presented in tabular form for various values of pertinent flow parameters. The temperature rises as the strength of the thermal conductivity variable parameter increases. Also, as the values of the Taylor number and the thermal conductivity variable parameter go up, the primary velocity goes down. Similarly, secondary velocity increases in the opposite direction as the Taylor number and thermal conductivity variable parameter increase.

Reynolds stress modeling of supercritical narrow channel flows using OpenFOAM: Secondary currents and turbulent flow characteristics

In this study, the full Launder, Reece and Rodi pressure-strain model, and nonlinear boundary damping functions were incorporated in OpenFOAM® to simulate the turbulence-driven secondary currents in supercritical narrow channel flows, such as in sediment bypass tunnels. Five simulations were performed under uniform flow conditions covering Froude numbers from 1.69 to 2.56 and aspect ratios (channel width to flow depth) ar from 0.9 to 1.91 to investigate the formation of secondary currents and their impacts on longitudinal velocity, turbulence characteristics, and bed shear stress distribution. The numerical results of the maximum longitudinal velocity and the average shear velocity show marginal deviations, of less than 2.6%, from two-dimensional experimental results acquired under decelerating flow conditions. However, some differences are observed for the secondary currents and for the vertical turbulence intensity and Reynolds shear stress in the outer flow region, especially for cases with higher flow nonuniformity (that can influence the surface perturbation) whose influence is missing in the numerical model. No intermediate vortex is observed for ar = 1.91. However, it develops for lower ar and detaches from the free surface vortex when ar ≤ 1.05. Such vortex bulges the longitudinal velocity contour lines inward and the zone of higher longitudinal velocity narrows and deepens with a decrease in ar. The decrement reduces the magnitude of the normalized maximum secondary velocity. It also affects the bottom vortex which alters the bed shear stress distribution.

MHD convective rotating flow of viscoelastic fluid past an infinite vertical oscillating porous plate with Hall effects

AbstractIt is considered the unsteady and incompressible magnetohydrodynamic rotating free convection flow of viscoelastic fluid with simultaneous heat and mass transfer near an infinite vertical oscillating porous plate under the influence of uniform transverse magnetic field and taking Hall current into account. The governing equations of the flow field are then solved by a regular perturbation method for a small elastic parameter. The expressions for the velocity, temperature, and concentration have been derived analytically and also its behavior is computationally discussed with reference to different flow parameters with the help of graphs. The skin friction on the boundary, the heat flux in terms of the Nusselt number, and the rate of mass transfer in terms of the Sherwood number are also obtained and their behavior discussed. The resultant velocity enhances with increasing Hall parameter and rotation parameter. The reversal behavior is observed with increasing viscoelastic parameters. The resultant velocity enhances and experiences retardation in the flow field with increasing radiation parameters, whereas the secondary velocity component increases with increasing rotation parameters. The temperature diminishes as the Prandtl number and/or the frequency of oscillations. The concentration reduces at all points of the flow field with the increase in the Schmidt number.

Numerical investigation of heat transfer & hall effects on MHD nanofluid flow past over an oscillating plate with radiation

The effects of convective heat generation and the oscillatory motion of a plate in the presence of MHD, Alumina nanofluid flow, thermal radiation, and Hall current are considered. The plate oscillates harmonically in its axes with uniform temperature. The dimensional equations have to be changed into non-dimensional equations with a set of dimensionless parameters. The Laplace transformation technique is utilized to get an exact solution. The possessions of velocity and temperature are analyzed with several parameters like Prandtl number (Pr), Grashof number (Gr), Hall parameter (m), magnetic parameter (M), radiation (R), solid volume fraction(ᵠ), phase angle(ω).The influence of primary and secondary velocity is discussed by the graph. It is observed that the increment of Hall parameter (m) diminishes the primary velocity, an increment of Grashof number leads to an increase in both velocities, and increasing solid volume fraction raises the temperature. The Nusselt number and skin friction coefficient values have expressed in the table. It is apparent that an increment of radiation increased the value of the Nusselt number and also an increment of phase angle value diminished the skin friction coefficient value.

Three-dimensional rotating flow of Cu–Al2O3/kerosene oil hybrid nanofluid in presence of activation energy and thermal radiation

The present exploration talks to a steady and incompressible chemically reacting hybrid-nanofluid rotating flow toward a stretchable sheet in presence of activation energy and magnetic field. We have chosen kerosene oil as base fluid and two nanoparticles specifically Al2O3 and Cu for hybrid-nanofluid and Al2O3 for regular nanofluid. Relative studies of imprint factors between hybrid nanofluid and customary nanofluid have been implemented for our present article. The leading system of PDEs subject to their compatible boundary conditions are renovated into a system of ODEs and then resolved by the Runge–Kutta–Fehlberg quadrature method with shooting practice. The stimulus of ignite flow parameters on the flow precise is carried off accurately through figures, bar diagrams and tables. Our analysis conveys that the primary velocity profiles for both hybrid and regular nanofluid diminish with intensifying values of Hartmann number and rotational parameter, however secondary velocity profile enhances with augmentation of the rotational parameter. Temperature profiles of both category fluids lead to increase with growing values of radiation parameter and Hartmann number, whereas opposite phenomena observe for concentration profiles with improving values of chemical reaction parameter. Again, rate of heat transfer diminishes sharply for leading Hartmann number.

Featuring the Hall effect and variable thermal conductivity on magnetized hybrid nanoliquid flow for three distinct shapes of nanoparticles: A comparative study

AbstractThe purpose of this work is to capture the circumstances of variable thermal conductivity and the Hall effect on the three‐dimensional rotating flow of hybrid nanofluid towards a bidirectional stretching sheet. The hybrid nanofluid is made by suspending nanometer‐sized copper (Cu) and alumina (Al2O3) nanoparticles in the base liquid water (H2O). The sheet is immersed in a Darcy porous medium. The flow is induced by both stretching of the sheet and thermal buoyancy force due to free convection. Further, nonlinear thermal radiation, frictional and Joule heating are prevalent in the temperature field. The surface boundary also imposes two constraints, namely velocity slip and convective heating. Another aspect of this analysis is to examine the impact of different shapes of copper and alumina nanoparticles on temperature distribution. For that, three variants, namely, spherical, blade, and lamina of nanoparticles shape, are considered. The resulting nonlinear differential equations are tackled by using Runge–Kutta–Fehlberg and secant methods‐based shooting technique. A detailed discussion on the physical impacts of various relevant parameters over velocity, temperature, local skin friction coefficients and Nusselt number is carried out with the help of graphs. Primary and secondary velocities of the hybrid nanofluid are accelerated for growing values of Hall current parameter, whereas the reverse trend is noticed w.r.t. velocity slip and suction parameters. Moreover, the hybrid nanofluid temperature profile has a direct relation with viscous dissipation and thermal radiation parameters. This research may have important applications in high‐ and low‐temperature operations, paints, space technologies, medications, cosmetics, conductive coatings, and so forth.

Impact of convection on three dimensional Casson rotatory fluid over an extending sheet: A numerical approach

Natural convection occurs in fluid environments. Usually, it is facilitated by the buoyancy effect. It is significantly less efficient than forced convection, due to the lack of fluid motion. As a result, it is completely dependent on the buoyancy effect's strength and the fluid's viscosity. The current work investigates the convective flow of a three-dimensional Casson fluid across a rotating linear expanding sheet. The nonlinear governing equations of the steady flow were presented and reconstructed using appropriate similarity transformations. To solve the resultant equations, the three-stage collocation approach namely Lobatto IIIA was applied using MATLAB. Graphs were used to illustrate the physical properties of the required data. It was observed that while the primary velocity profile decreases as the Casson, convective, and rotational parameters increase, the secondary velocity profile exhibits the opposite behaviour. The effect of rotation, Casson parameter, and others on drag coefficient, heat transfer coefficient, and mass transfer coefficient was evaluated, interpreted, and found to be reasonably consistent with earlier research.

Simulation of liquid jet atomization and droplet breakup via a Volume-of-Fluid Lagrangian–Eulerian strategy

The hybrid Volume-of-Fluid and Lagrangian–Eulerian (VoFLE) strategy is an attractive approach for reducing the computational cost of spray simulations while retaining a reasonable amount of fidelity. It is based on the concept of transitioning small liquid bodies or droplets to a Lagrangian–Eulerian (LE) representation, alleviating the burden of maintaining high resolution for small droplets. This hybrid VoFLE methodology is extended in the present work by incorporating a hydrodynamic breakup model based on maximum entropy formalism (MEF). This approach is particularly suitable for realistic spray conditions, such as high-pressure fuel injectors, where adequate numerical resolution of the smallest droplets is extremely difficult. The first step in the present VoFLE treatment is the identification of unresolved liquid structures targeted for LE transition. This step is followed by the application of the MEF breakup model for those structures that are hydrodynamically unstable, resulting in the assignment of secondary drop sizes and velocities. The model is evaluated statistically and tested against experimental data from the Engine Combustion Network and the breakup of a water jet. Relatively favorable results are encountered in these tests.

Hall Current and Soret Effects on Unsteady MHD Rotating Flow of Second-Grade Fluid through Porous Media under the Influences of Thermal Radiation and Chemical Reactions

The unsteady MHD free convection heat and mass transfer flow of a viscous, incompressible, and electrically conducting fluid passing through a vertical plate embedded in a porous medium in the presence of chemical reactions and thermal radiation is investigated. The effects of the Hall current, rotation and Soret are studied. Using the perturbation approach, one can obtain an accurate analytical solution to the governing equations for the fluid velocity, fluid temperature, and species concentration, provided that the initial and boundary conditions are acceptable. It is possible to obtain expressions for the shear stress, rate of heat transfer, and rate of mass transfer for both plates with the ramping temperature and isothermal conditions. On the one hand, the numerical values of the primary and secondary fluid velocities, fluid temperature, and species concentration are presented graphically. On the other hand, the numerical values of the shear stress and rate of mass transfer for the plate are presented in tabular form for various values of the relevant flow parameters. These values are given for a range of pertinent flow parameters. It was determined that an increase in the Hall and Soret parameters over the whole fluid area leads to a corresponding increase in the resulting velocity. The resultant velocity continually climbs to a high level due to the contributions of the thermal and solute buoyancy forces. Lowering the heat source parameter reduces the temperature distribution, resulting in a lower overall temperature. When there is a rise in the chemical reaction parameter over the whole fluid area, there is a corresponding decrease in the concentration. The concentration buoyancy force, Hall current, and Prandtl number reduce the skin friction. On the other hand, the permeability of the porous medium, rotation, chemical reaction, the Soret number, thermal buoyancy force, and mass diffusion all have the opposite effects on the skin friction.

Mathematical analysis of casson fluid flow with energy and mass transfer under the influence of activation energy from a non-coaxially spinning disc

A Casson fluid is the most suitable rheological model for blood and other non-Newtonian fluids. Casson fluids hold yield-stress and have great significance in biomechanics and polymer industries. In this analysis, a numerical simulation of non-coaxial rotation of a Casson fluid over a circular disc was estimated. The influence of thermal radiation, second-order chemical reactions, buoyancy, and heat source on a Casson fluid above a rotating frame was studied. The time evolution of secondary and primary velocities, solute particles, and energy contours were also examined. A magnetic flux of varying intensity was applied to the fluid flow. A nonlinear sequence of partial differential equations was used to describe the phenomenon. The modeled equations were reduced to a non-dimensional set of ordinary differential equations (ODEs) using similarity replacement. The obtained sets of ODEs were further simulated using the parametric continuation method (PCM). The impact of physical constraints on energy, concentration, and velocity profiles are presented through figures and tables. It should be noted that the effect of the Casson fluid coefficient, the Grashof number, and the magnetic field reduces the fluid’s primary velocity contour. The mass transfer field decreases with the action of constructive chemical reactions, but is augmented by the effects of destructive chemical reactions. The accelerating trend in Schmidt number lowers the mass profile, while it is enhanced by increasing values of activation energy and Soret number.

On multiphase wavy movements of non-Newtonian Jeffery fluid in a rotating channel with MHD and compliant walls: exact solutions

This paper discusses the peristaltic flow of magnetized Jeffrey fluid in a two-phase (liquid and dust) scenario inside a rotating planar channel executing compliant walls through the constraints of lubrication theory. The rotation of the channel considers the orthogonal direction axis. The present investigation is made to examine the impact of the magnetic field on the flow rates of the primary and secondary velocity components due to rotational effects. The fluid is electrically conducted by an inclined magnetic field and the rotating channel is assumed to perform the peristaltic wave stream along the vertical surfaces possessing various amplitudes and velocity profiles for dual phases. Exact solutions have been composed for fluid and particulate phases on Mathematica using the built-in tool DSolve. We examined that the velocity profile for the fluid phase gets smaller values than that of the particulate phase under the same parameters by plotting the graph. It is concluded from the obtained readings that the rotational effects and the magnetic field an inverse impact on the flow speed. This study will be applied to the attributes of rotating pumping devices used in medical equipment.

Flow of hybrid CNTs past a rotating sphere subjected to thermal radiation and thermophoretic particle deposition

Thermal radiation and thermophoretic particle deposition have important applications in research and engineering. These two principles are employed in practical applications such as electrical fuel, projectiles, thermal transportation, renewable energy, nuclear power plants, gas turbines, and aerospace engineering. In light of the aforementioned applications, the current study investigates the stagnation point hybrid CNTs movement around a rotating sphere in the existence of thermal radiation and thermophoretic particle deposition. Using appropriate similarity factors, nonlinear governing equations are converted into ordinary differential equations. The Runge Kutta Fehlberg 45 (RKF-45) order and a shooting approach are used to find the numerical results of the simplified equations and boundary conditions. The numerical findings are presented graphically. It is explored how different limitations impact their individual profiles. According to the research, primary velocity increases with acceleration parameter but decreases with secondary velocity. As the radiation parameter value increases, so does the thermal distribution. Concentration decreases as both the Schmidt number and the thermophoretic parameter decrease. The heat dispersion rate heightens as the percentage of volume fraction of solid and the radiation parameter increase. Mano CNTs have a higher primary velocity than hybrid CNTs.

Scrutinization of Slip Due to Lateral Velocity on the Dynamics of Engine Oil Conveying Cupric and Alumina Nanoparticles Subject to Coriolis Force

This study is an attempt to investigate the three-dimensional flow of engine oil-based nanofluid under the impact of rotation and partial slip phenomenon over a stretchable surface. Partial slip condition is incorporated into the system at boundaries and the arising quotient of angular speed to stretching constant is regarded as rotation impression on freely moving three-dimensional flow of copper oxide-engine oil and aluminum oxide-engine oil nanofluid. The designed problem has been tackled numerically with the boundary value problem technique, this numerical mechanism requires one to transform the flow governing highly nonlinear PDEs into first-order differential equations along with associated boundary conditions. This procedure is carried out by employing a suitable similarity transformation. The investigation determines the impact of slip and rotation on primary and secondary velocity profiles, shear stress rates, and heat transfer coefficient. Minimum skin friction and Maximum Nusselt number has been observed for CuO − Engine Oil nanofluid under partial slip parameter as compared to Al 2 O 3 − Engine Oil nanofluid. Reduced skin coefficients were achieved for both nanofluids. Moreover, the outcomes of the study have been related with already available literature and were found in good agreement.

Time-resolved PIV measurements inside and downstream of a 180° bend

The flow in a 180° bend with a radius of curvature 1.5 time the pipe diameter (Rc/D of 1.5) was studied for a Reynolds number of 34,800 to characterize the development of the mean velocity and Reynolds stresses and the unsteady motions that may affect the heat or mass transfer in the latter part of the bend. Two-component, time-resolved measurements were performed on the axial symmetry plane and on cross sectional planes in the bend and up to 1D downstream of the bend using refractive index matched Particle Image Velocimetry. The unsteady flow structures were examined using the Snapshot Proper Orthogonal Decomposition (POD) technique. Frequency spectra of the POD coefficients, transients of the coefficients and low-order reconstructions were used to characterize the time scales and dynamics of the motions. The results showed that the initial development of the flow was similar to that in a 90° bend but the development of the mean secondary flow, and the low-speed region associated with this feature, appeared delayed relative to the 90° bend in the middle section of the 180° bend. The results in the second half of the 180° bend showed that the mean longitudinal velocity near the inner wall was larger than that near the outer wall in the latter part of the bend. Changes in the unsteady interaction of the flow with the outer wall in the middle of the 180° bend also appeared to cause significant unsteadiness in the flow near the inner wall in the latter part of the bend. The mean secondary flow towards the end of the 180° bend was significantly diminished relative to the flow in the middle of the bend and largely suppressed by 1D downstream of the bend. Reconstructions of the instantaneous secondary flow showed occurrences of large secondary velocities along the sidewalls up to 170°, but these were substantively reduced even at 0.25D into the downstream bend.

The outcome of Newtonian heating on Couette flow of viscoelastic dusty fluid along with the heat transfer in a rotating frame: second law analysis

The outcome of Newtonian heating on the viscoelastic fluid plays a vital role in daily life applications such as conjugate heat transfer around fins, heat exchanger, solar radiation, petroleum industry, etc. Also, rotation of viscoelastic fluid has various importance in product-making industries and engineering. Viscoelastic dusty fluids and Newtonian heating are applicable in nuclear reactors, gas cooling systems, control temperature of the system and centrifugal separators, etc. Therefore, based on this motivation, the present study presents the Newtonian heating effect on the dusty viscoelastic fluid. Additionally, a free convective heat transfer is taken for Couette flow in a rotating frame along with a uniform applied magnetic field. The dust particles possess complex velocities due to rotation and therefore it is the combination of the primary and secondary velocities. For the specified flow, the entropy generation and Bejan number are also computed. Poincare-Light Hill technique has been used for the solution of the system of partial differential equations. The velocity profile for dust particles and fluid are discussed in this article. The influence of different parameters on the Nusselt number, temperature profile, velocity of fluid and dust particle is discussed thoroughly.