Skin Friction Components Research Articles

Cross-Diffusion and Higher-Order Chemical Reaction Effects on Hydromagnetic Copper–Water Nanofluid Flow Over a Rotating Cone in a Porous Medium

Spin coating of engineering components with advanced functional nanomaterials which respond to magnetic fields is growing. Motivated by exploring the fluid dynamics of such processes, a mathematical model is developed for chemically reactive Cu–H2O magnetohydrodynamic (MHD) nanofluid swirl coating flow on a revolving vertical electrically insulated cone adjacent to a porous medium under a radial static magnetic field. Heat and mass transfer is included and Dufour and Soret cross-diffusion effects are also incorporated in the model. Thermal and solutal buoyancy forces are additionally included. To simulate chemical reaction of the diffusing species encountered in manufacturing processes, a higher-order chemical reaction formulation is also featured. Via suitable scaling transformations, the governing nonlinear coupled partial differential conservation equations and associated boundary conditions are reformulated as a nonlinear ordinary differential boundary value problem. MATLAB-based shooting quadrature with a Runge–Kutta method is deployed to solve the emerging system. Concentration, temperature and velocity variations for various nondimensional flow parameters have been visualized and analyzed. In addition, key wall characteristics, i.e., radial and circumferential skin friction, Nusselt number and Sherwood number, have also been computed. Validation with earlier studies is also included. The simulations indicate that when compared to a lower-order chemical reaction, a higher-order chemical reaction allows a greater rate of heat and mass transfer at the cone surface. Increasing Dufour (diffuso-thermal) and Soret numbers generally reduces radial and circumferential skin friction and also Nusselt number, whereas it elevates the Sherwood number. Both skin friction components are also suppressed with increasing Richardson number. Strong deceleration in the tangential and circumferential velocity components is induced with greater magnetic field.

Vortex force map for incompressible multi-body flows with application to wing–flap configurations

The vortex force map method for incompressible viscous flows with multiple bodies is derived in this work. The method breaks the fluid force into inertial, vortex-pressure, viscous-pressure and skin-friction components, and it could be used to analyse the fluid dynamic forces on individual bodies in a multi-body assembly. For the first time, we provide a graphical representation of the vortex-pressure force – the vortex force map – for individual bodies in a multi-body assembly. We have shown that the vortex force map in a multi-body set-up differs from single-bodied counterparts from modifications to their hypothetical potential through a nonlinear cross-coupling, and that the inertial and viscous-pressure contributions contain influences from other bodies explicitly. We then demonstrate the multi-body vortex force decomposition method with a wing–flap starting flow problem using computational fluid dynamics data, identifying the positive and negative force-generating critical regions or directions. It is found that the dominant force is the vortex-pressure force, and the force variation against time is closely related to the evolution of the vortex structures. Furthermore, we showed that the existence of another body significantly alters the force contribution roles of vortices in the flow.

Three-Dimensional Fluctuating Flow of a Second-Grade Fluid along an Infinite Horizontal Plate with Periodic Suction

Laminar flow control plays a vital role in reducing drag resulting enhancement in the vehicle power by a significant amount. Theoretical and experimental studies have proven that the transition from laminar to turbulent flow (causing the drag coefficient to enhance) may be delayed/prevented by the suction of the fluid from the boundary layer to the wall. The purpose of this work is to study the effects of periodic suction on the unsteady 3-dimensional fluctuating flow of a second grade incompressible fluid flowing laminarly over a horizontal porous infinite plate. The plate is subjected to a sinusoidal transverse suction velocity while the free stream velocity oscillates in time about a constant mean. The flow turns out to be 3-dimensional because of transverse direction of the periodic suction velocity. By the series expansion method, analytic expressions for transient velocity, skin friction components, and pressure are attained. Impact of nondimensional parameters evolving in the mathematical model of the problem on these physical quantities are visualized graphically and discussed analytically. The velocity component u is found to be rising with a growth in suction parameter α. The pressure is noted to be growing with a growth in Reynolds number R e . Further, due to suction at the plate and transient free stream velocity, the pressure increases near the plate and then reaches to a steady value far-off the plate. The skin friction along the main flow is noticed to be decreasing with the rise in α for 0.5 ≤ R e ≤ 1.4 , however, an exponential rise is observed for R e > 1.4. The skin friction along the cross flow is noted to be enhancing for the rising values of suction parameter and elastic parameter. The present results have excellent agreement with previous published results in the limiting sense. This study is beneficial in designing and manufacturing laminar flow control system to enhance the vehicle power requirement.

Entropy generation and mixed convection of CuO–water near an oblique stagnation point: modified Chebyshev wavelets approach

In this article, an analysis of CuO–water nanofluid over a moving wall with oblique stagnation point has been studied under the influence of a heat source. CuO nanoparticles having shapes of platelet, brick and spheres were used in this study. The aim of this study is to explore the impact of the shapes of nanoparticles on the flow properties near an oblique stagnation point flow. The flow system was governed by a set of nonlinear partial differential equations (PDEs). These PDEs were converted to nonlinear ordinary differential equations, which were further solved numerically using a modified Chebyshev wavelet method. The effects of parameters appeared in analysis on skin friction, local Nusselt number, velocity, temperature and entropy are plotted graphically. Streamlines are also plotted to analyze patterns of flow for different levels of stretching and different angles of strike. Tabular results are generated to specify numerical values of free parameter A, components of skin friction, local Nusselt number and stagnation point. It is found that platelets shaped nanoparticles show more efficient results for inertial and thermal boundary layer. Entropy of system is influenced by stretching, angle of intact and mixed convection parameter.

Hydrodynamic behaviour of velocity of applied magnetic field on unsteady MHD Couette flow of dusty fluid in an annulus

This research work inspects mass transport phenomenon of Saffman’s dusty fluid model for transient magnetohydrodynamics fluid flow of a binary mixture passing through an annular duct. Particularly, effort has been devoted to theoretically explore the role of velocity of applied magnetic field. Here, our treatment of the governing momentum equations accountable for the flow is done using the classical Laplace transform technique and Riemann-Sum Approximation. The effects of the physical parameters such as time, relaxation time parameter, radii ratio, Hartmann number, variable mass parameter and velocity of applied magnetic field on the fluid phase velocity, dust phase velocity and skin friction have been illustrated pictorially. It is concluded that contrary to the known classical effect of boosting Hartmann number on velocity, both components of flow (fluid and dust phase) and skin friction are seen to be heightened with an overwhelming presence of velocity of applied magnetic field. For large time, it is anticipated that higher profiles for velocity and skin friction are seen with fluid phase and an accelerated moving wall.

The influence of the flow separation bubble and transition location on the profile drag of three 4-digit NACA aerofoil profiles

Modeling of the flow over aerofoil profiles at low Reynolds numbers is difficult due to the complex physics associated with the laminar flow separation mechanism. Two major problems arise in the estimation of profile drag: (1) the drag force at low Reynolds numbers is extremely small to be measured in a wind tunnel by force balance techniques, (2) the profile drag is usually calculated by pressure integration, hence the skin friction component of drag is excluded. In the present work, three different 4-digit NACA aerofoils are investigated. Measurements are conducted in an open-ended subsonic wind tunnel, while numerical work is performed by time Reynolds-averaged Navier Stokes (RANS) coupled with the laminar-kinetic-energy ( K-kl-w) turbulence model. The influence of the flow separation bubbles and transition locations on the profile drag is discussed and addressed. This paper gives important insights into importance of measurements at low Reynolds numbers for better aerodynamic loads predictions.

Modified Chebyshev wavelets approach for mixed convection flow due to oblique stagnation point along a vertically moving surface with zero mass flux of nanoparticles

In this article mixed convection flow of nanofluid near a vertical wall is studied for cases of active and passive control. Flow is governed by nonlinear Partial Differential Equations (PDEs), which are transformed into nonlinear ODEs by using similarity transformations. Nonlinear system of equations is solved via two different techniques which are: Modified Chebyshev wavelets scheme and Finite different method. The impact of emerging parameters including free parameter "A" on velocity, temperature and concentration profiles is plotted. Some values of the physical parameters against the active and passive controls for streamlines are calculated. Tables for values of A, components of skin friction, heat flux and mass flux against different parameters are also given. Streamlines are also plotted to predict the flow patterns at various locations inside flow. In this study we found that velocity of flow has same behavior in both active and passive controls, however, temperature and concentration profiles are more sensitive to the passive control.

Numerical and perturbative analysis on non-axisymmetric Homann stagnation-point flow of Maxwell fluid

In this paper, we examined the numerical and perturbative analysis of non-Newtonian fluid towards non-axisymmetric Homann stagnation-point flow. The Maxwell fluid model is applied to investigate the behavior of viscoelastic fluid for this particular geometry. The influence of Maxwell parameter {beta }_{1} and ratio gamma on different profiles are addressed in this analysis. The governed partial differential equations are reduced to ordinary differential equations with the help of similarity transformations. The numerical and perturbative outcomes of the resulting system of differential equations are obtained by applying the shooting technique. The solution is achieved for diverse values of relaxation time parameter {beta }_{1} and ratio gamma. The wall shear stress is compared to their large-gamma asymptotic behaviors and displacement thicknesses are also presented. The numerical data for velocity profiles are obtained in terms of plots. It is predicted through analysis that a gradual increase in relaxation time raises wall skin friction components. On the other hand, velocity decreases which constitutes to reduce the reverse flow. Meanwhile, displacement thicknesses in x and y direction decreases. However, three-dimensional displacement thickness increases due to more viscoelastic material like Maxwell fluid than viscous fluid.

MHD Three-Dimensional Free Convective Flow with Periodic Permeability and Heat Transfer of a Second-Grade Fluid

The present study delivers the mathematical model and theoretical analysis of a three-dimensional flow in a free convection for an electrically conducting incompressible second-grade fluid through a very high porous medium circumscribed by an infinite vertical porous plate subject to a constant suction. A uniform magnetic field along the normal to the surface of plate is applied. Periodic permeability for the medium is assumed, while velocity of free stream is taken to be uniform. Analytic expressions are presented for velocity and temperature fields, pressure, and skin friction components by perturbation technique. The impacts on these physical quantities by the physical parameters existing in the model are discussed and envisioned graphically. It is interesting to note that elastic and permeability parameters are able to control the skin friction along the main flow direction, magnetic field to reduce the pressure, and Reynolds number to control the thermal boundary layer thickness. It is also noted that temperature distribution does not depend upon permeability parameter.

Effects of Hall current on MHD natural convection in between two vertical flat walls with induced magnetic field and heat source/sink

ABSTRACT The effects of Hall current and heat source/sink are considered on MHD natural convective flow of an electrically conducting viscous fluid in between two vertical flat walls with an induced magnetic field. The exact analytical solutions for converted flow equations from governing equations after using suitable non-dimensional variables are obtained. The effects of Hall current, heat source/sink, and magnetic field on the velocity components, induced magnetic field in flow dynamics, and the induced current density are presented through some figures and tables. The impact of the Hall current is massive on both components of velocity and those increases with Hall current. Whereas, both the components of the induced magnetic field and induced current density decrease due to Hall current. Whereas due to heat source(sink), the primary velocity enhances(reduces) and the effect is opposite for the secondary velocity. For increasing heat source parameter both primary and secondary induced magnetic field and induced current density increase, while temperature-dependent heat sink shows contrary effects. In two flat vertical walls, the variations in the skin-friction components, i.e. surface drag force components for the presence of magnetic field are opposite to each other. In addition, mass flow rate components enhance for Hall current and reduce for a stronger magnetic field. With increasing heat source parameter, the primary skin-friction component rises and secondary skin-friction component decreases at the left wall with higher temperature, while at the right wall with lower temperature both skin-friction components have increasing nature, and reverse impacts are observed for the heat sink. Due to the presence of heat source, primary (secondary) mass flow rate component enhances (reduces) and opposite effects have found for the heat sink.

Homotopy Simulation of Dissipative Micropolar Flow and Heat Transfer from a Two-Dimensional Body with Heat Sink Effect

Non-Newtonian flow from a wedge constitutes a fundamental problem in chemical<br /> engineering systems and is relevant to processing of polymers, coating systems, etc. Motivated by such applications, the homotopy analysis method (HAM) was employed to<br /> obtain semi-analytical solutions for thermal convection boundary layer flow of incompressible micropolar fluid from a two-dimensional body (wedge). Viscous dissipation<br /> and heat sink effects were included. The non-dimensional boundary value problem<br /> emerges as a system of nonlinear coupled ordinary differential equations, by virtue of<br /> suitable coordinate transformations. The so-called Falkner-Skan flow cases are elaborated. Validation of the HAM solutions was achieved with earlier simpler models, as well as with a Nakamura finite difference method for the general model. The micropolar model employed simulates certain polymeric solutions quite accurately, and features rotary motions of micro-elements. Primary and secondary shear stress, wall couple stress, Nusselt number, microrotation velocity, and temperature were computed for the effect of<br /> vortex viscosity parameter (micropolar rheological), Eckert number (viscous dissipation),<br /> Falkner-Skan (pressure gradient) parameter, micro-inertia density, and heat sink parameter. The special cases of Blasius and stagnation flow were also addressed. It was observed from the study that the temperature and thermal boundary layer thickness are both suppressed with increasing wedge parameter and wall heat sink effect, which is beneficial to temperature regulation in polymer coating dynamics. Further, strong reverse spin was generated in the microrotation with increasing vortex viscosity, which resulted in<br /> increase in angular momentum boundary layer thickness. Also, both primary and secondary skin friction components were reduced with increasing wedge parameter. Nusselt number was also enhanced substantially with greater wedge parameter.

Surface temperature and free-stream velocity oscillation effects on mixed convention slip flow from surface of a horizontal circular cylinder

The present phenomena address the slip velocity effects on mixed convection flow of electrically conducting fluid with surface temperature and free stream velocity oscillation over a non-conducting horizontal cylinder. To remove the difficulties in illustrating the coupled PDE, the primitive variable formulation for finite dif?ference technique is proposed to transform dimensionless equations into primitive form. The numerical simulations of coupled non-dimensional equations are exam?ined in terms of fluid slip velocity, temperature, and magnetic velocity which are used to calculate the oscillating components of skin friction, heat transfer, and cur?rent density for various emerging parameters magnetic force parameter, ?, mixed convection parameter, ?, magnetic Prandtl number, ?, Prandtl number, and slip factor, SL. It is observed that the effect of slip flow on the non-conducting cylinder is reduced the fluid motion. A minimum oscillating behavior is noted in skin friction at each position but maximum amplitude of oscillation in heat transfer is observed at each position ? = ?/4 and 2?/3. It is further noticed that a fluid velocity increas?es sharply with the impact of slip factor on the fluid-flow mechanism. Moreover, due to frictional forces with lower magnitude between viscous layers, the rise in Prandtl number leads to decrease in skin fiction and heat transfer which is physi?cally in good agreement.

Surface temperature and free-stream velocity oscillation effects on mixed convention slip flow from surface of a horizontal circular cylinder

The present phenomena address the slip velocity effects on mixed convection flow of electrically conducting fluid with surface temperature and free stream velocity oscillation over a non-conducting horizontal cylinder. To remove the difficulties in illustrating the coupled PDE, the primitive variable formulation for finite dif?ference technique is proposed to transform dimensionless equations into primitive form. The numerical simulations of coupled non-dimensional equations are exam?ined in terms of fluid slip velocity, temperature, and magnetic velocity which are used to calculate the oscillating components of skin friction, heat transfer, and cur?rent density for various emerging parameters magnetic force parameter, ?, mixed convection parameter, ?, magnetic Prandtl number, ?, Prandtl number, and slip factor, SL. It is observed that the effect of slip flow on the non-conducting cylinder is reduced the fluid motion. A minimum oscillating behavior is noted in skin friction at each position but maximum amplitude of oscillation in heat transfer is observed at each position ? = ?/4 and 2?/3. It is further noticed that a fluid velocity increas?es sharply with the impact of slip factor on the fluid-flow mechanism. Moreover, due to frictional forces with lower magnitude between viscous layers, the rise in Prandtl number leads to decrease in skin fiction and heat transfer which is physi?cally in good agreement.

Periodic mixed convection flow along the surface of a thermally and electrically conducting cone

The main aim of the present work is to highlight the significances of periodic mixed convection flow and heat transfer characteristics along the surface of magnetized cone by exerting magnetic field exact at the surface of the cone. The numerical simulations of coupled non-dimensional equations are computed in terms of velocity field, temperature and magnetic field concentration and then used to examine the periodic components of skin friction, ?w, heat transfer, qw, and current density, jw, for various governing parameters. A nice periodic behavior of heat transfer qw is concluded for each value of mixed convection parameter, ?, but maximum periodicity is sketched at ? = 50. It is also computed that the lower value of magnetic Prandtl number ? = 0.1 gets poor amplitude in current density but highest amplitude is sketched for higher ? = 0.5. The behavior of heat and fluid-flow in the pres?ence of aligned magnetic field is associated with the phase angle and amplitude of oscillation. It is also noted that due to the increase in magnetic force parameter, ?, there are wave like disturbances generate within the fluid layers. These disturbances are basically hydromagnetic waves which becomes more prominent as the strength of magnetic force parameter is increased.

Periodic mixed convection flow along the surface of a thermally and electrically conducting cone

The main aim of the present work is to highlight the significances of periodic mixed convection flow and heat transfer characteristics along the surface of magnetized cone by exerting magnetic field exact at the surface of the cone. The numerical simulations of coupled non-dimensional equations are computed in terms of velocity field, temperature and magnetic field concentration and then used to examine the periodic components of skin friction, ?w, heat transfer, qw, and current density, jw, for various governing parameters. A nice periodic behavior of heat transfer qw is concluded for each value of mixed convection parameter, ?, but maximum periodicity is sketched at ? = 50. It is also computed that the lower value of magnetic Prandtl number ? = 0.1 gets poor amplitude in current density but highest amplitude is sketched for higher ? = 0.5. The behavior of heat and fluid-flow in the pres?ence of aligned magnetic field is associated with the phase angle and amplitude of oscillation. It is also noted that due to the increase in magnetic force parameter, ?, there are wave like disturbances generate within the fluid layers. These disturbances are basically hydromagnetic waves which becomes more prominent as the strength of magnetic force parameter is increased.

Three-dimensional free convective flow of a second-grade fluid through a porous medium with periodic permeability and heat transfer

In this study, we model and theoretically analyze a free convective three-dimensional flow of an incompressible second-grade fluid through a highly porous medium bounded by an infinite vertical porous plate subjected to a constant suction. We assume the permeability of the medium to be periodic and the free stream velocity to be uniform. The assumption of either constant or time-dependent permeability of a porous medium leads to two-dimensional flows; however, the flow becomes three-dimensional due to variable permeability of the porous medium. We obtain analytic solutions for velocity field, pressure, skin friction components, temperature distribution, and discuss and graphically visualize effects of physical parameters emerging in the mathematical model of the physical phenomenon on these physical quantities. We note that the main flow velocity component decreases due to enhancement in non-Newtonian parameter; however, the pressure rises due to thickening of the fluid.

Magnetohydrodynamic Three-Dimensional Couette Flow of a Second-Grade Fluid with Sinusoidal Injection/Suction

A mathematical model for magnetohydrodynamic (MHD) three-dimensional Couette flow of an incompressible second-grade fluid is developed and analyzed theoretically. The application of normal sinusoidal injection at the lower fixed plate and its equivalent deduction by suction through the uniformlymoving upper plate leads to three-dimensional flow.Approximate solutions for components of velocity, pressure and skin friction are obtained. The effects of flow parameters such as Hartmann number, Reynolds number, suction/injection parameter, non-Newtonian parameter on velocity components, skin friction factors along main flow direction and transverse direction, and pressure through parallel porous plates are discussed graphically. It is noted that Hartmann number provides a mechanism to stable the skin friction component along the main flow direction.

Numerical study of heat transfer and viscous flow in a dual rotating extendable disk system with a non‐Fourier heat flux model

AbstractNonlinear, steady‐state, viscous flow, and heat transfer between two stretchable rotating disks spinning at dissimilar velocities are studied with a non‐Fourier heat flux model. A nondeformable porous medium is intercalated between the disks and the Darcy model is used to simulate matrix impedance. The conservation equations are formulated in a cylindrical coordinate system and via the von Karman transformations are rendered into a system of coupled, nonlinear ordinary differential equations. The emerging boundary value problem is controlled by number of dimensionless parameters, that is, Prandtl number, upper disk stretching, lower disk stretching, permeability, non‐Fourier thermal relaxation, and relative rotation rate parameters. A perturbation solution is developed and the impact of selected parameters on radial and tangential velocity components, temperature, pressure, lower disk radial, and tangential skin friction components and surface heat transfer rate are visualized graphically. Validation of solutions with the homotopy analysis method is included. Extensive interpretation of the results is presented which are relevant to rotating disk bioreactors in chemical engineering.

Three-dimensional Couette flow of a Jeffrey fluid along periodic injection/suction

Three-dimensional Couette flow of an incompressible Jeffrey fluid is formulated and discussed analytically and graphically. The suction is applied over uniformly moving upper plate and its equivalent deduction by injection at the lower stationary plate. Because of this type of suction/injection, this flow turns into three-dimensional. An analytical method is applied to get main flow velocity, secondary flows velocities and pressure components. Also skin friction components along the main and secondary flow directions have been calculated. The effects of different physical parameters, for example, the Deborah number, suction/injection parameter, the ratio of relaxation time to the retardation time and Reynolds number have been discussed graphically. It is witnessed that the Deborah number plays vital role to control the main flow velocity.

Analysis of Free Convective Jeffery’s Fluid with Periodic Permeability and Cattaneo-Christov Heat Transfer

Abstract In this study a free convective three-dimensional flow of an incompressible Jeffery’s fluid through a highly porous medium bounded by an infinite vertical porous plate subjected to a constant suction is modeled and analyzed theoretically. The permeability of the medium is assumed to be periodic while free stream velocity is assumed to be uniform. The assumption of either constant or time dependent permeability of a porous medium leads to two-dimensional flows, however, the flow becomes three-dimensional due to variable permeability of the porous medium. Cattaneo-Christov approach is used for the transfer of heat in fluid flow. Analytic solutions for velocity field, pressure, skin friction components and temperature distribution are obtained. The effects of physical parameters emerging in the mathematical model of the physical phenomenon on these physical quantities are discussed and visualized graphically. It is noted that main flow velocity component decreases due to enhancement in non-Newtonian parameter, however, pressure rises due to thickening of the fluid.