Increase In Skin Friction Research Articles

Investigation of convective heat transfer enhancement for nanofluid flow over flat plate

In this paper, the laminar flow over flat plate of three different nanofluids is investigated. The fluid is considered as water with three different kind of solid particles Al2O3, TiO2, and Fe3O4 of different volume fractions (1, 2, 3, and 4%). The values of viscosity, heat capacity, density, and thermal conductivity depending on volume fraction for the three nanofluids are evaluated. Numerical simulation has been conducted for analysis the impact of the nanoparticles on the heat transfer properties, on the temperature and velocity profiles, on the wall shear stress and on the skin friction coefficient. The results show that as the value of volume fraction increases the values of the wall shear stress, skin friction, and heat transfer increase, but the velocity decreases. A comparison between the three nanofluids presents the difference in the thermal enhancement, velocity profiles, and thermal boundary layer. With the volume fraction for all three nanofluids polynomial connections has been obtained to describe for the relation of the wall shear stress, skin friction coefficient and average heat transfer coefficient.

Numerical Solution of Nonlinear Diff. Equations for Heat Transfer in Micropolar Fluids over a Stretching Domain

A numerical study based on finite difference approximation is attempted to analyze the bulk flow, micro spin flow and heat transfer phenomenon for micropolar fluids dynamics through Darcy porous medium. The fluid flow mechanism is considered over a moving permeable sheet. The heat transfer is associated with two different sets of boundary conditions, the isothermal wall and isoflux boundary. On the basis of porosity of medium, similarity functions are utilized to avail a set of ordinary differential equations. The non-linear coupled ODE’s have been solved with a very stable and reliable numerical scheme that involves Simpson’s Rule and Successive over Relaxation method. The accuracy of the results is improved by making iterations on three different grid sizes and higher order accuracy in the results is achieved by Richardson extrapolation. This study provides realistic and differentiated results with due considerations of micropolar fluid theory. The micropolar material parameters demonstrated reduction in the bulk fluid speed, thermal distribution and skin friction coefficient but increase in local heat transfer rate and couple stress. The spin behavior of microstructures is also exhibited through microrotation vector N ( η ) .

Lie Group Analysis of Unsteady Flow of Kerosene/Cobalt Ferrofluid Past A Radiated Stretching Surface with Navier Slip and Convective Heating

In this work, we identified the characteristics of unsteady magnetohydrodynamic (MHD) flow of ferrofluid past a radiated stretching surface. Cobalt–kerosene ferrofluid is considered and the impacts of Navier slip and convective heating are additionally considered. The mathematical model which describes the problem was built from some partial differential equations and then converted to self-similar equations with the assistance of the Lie group method; after that, the mathematical model was solved numerically with the aid of Runge–Kutta–Fehlberg method. Graphical representations were used to exemplify the impact of influential parameters on dimensionless velocity and temperature profiles; the obtained results for the skin friction coefficient and Nusselt number were also examined graphically. It was demonstrated that the magnetic field, Navier slip, and solid volume fraction of ferroparticles tended to reduce the dimensionless velocity, while the radiation parameter and Biot number had no effects on the dimensionless velocity. Moreover, the magnetic field and solid volume fraction increase skin friction whereas Navier slip reduces the skin friction. Furthermore, the Navier slip and magnetic field reduce the Nusselt number, whereas solid volume fraction of ferroparticles, convective heating, and radiation parameters help in increasing the Nusselt number.

Study of shock train/flame interaction and skin-friction reduction by hydrogen combustion in compressible boundary layer

A numerical study is carried out to investigate the shock train/flame interaction and skin friction with boundary layer combustion in compressible boundary layer. The Transition k−kl−w model is employed as the turbulence model and the finite-rate model is selected as the combustion model. The results showed that the skin friction could be reduced by 50% through boundary layer combustion while the pure-mixing case can only bring about a 10% drag reduction. The ignition of hydrogen in the boundary layer leads to a rapid reduction in skin friction. When a shock wave intersects with the flame surface, in addition to the reflection, it is also refracted, which will cause the change of both skin friction and heat transfer to the wall. Studies on the effects of air/fuel temperature ratio reveal that both the skin friction and heat transfer increase with air/fuel temperature ratio. When the concentration of H2O increases in airflow, the skin friction is enhanced as the mixing and combustion between oxygen and hydrogen is suppressed with H2O addition. The results of changing the air/fuel pressure ratios show that at high airflow pressure, the distance between the flame and the wall is reduced, leading to increase of heat transfer to the wall.

Heat and Mass Transfer on Magnetohydrodynamic Convective Flow of Second Grade Fluid Through a Vertical Porous Channel with Non-Uniform Wall Temperature

We analyze the impact of suction/injection on MHD convective oscillatory flow of second grade fluid through a Porous Medium in a vertical channel with non-uniform wall temperature. The liquid is occupied with a transverse Magnetic field and the velocity slip at the left plate is taken into consideration. The precise solutions of the dimensionless equations are obtained and the effects of the flow parameters on velocity, temperature and concentration profiles, skin friction and rates of heat and mass transfer are discussed. It is fascinating to take note of that skin friction increases on together channel plates as permeability increases.

Cu-Al2O3/water hybrid nanofluid flow over a permeable moving surface in presence of hydromagnetic and suction effects

In this new era of technology in fluid field, hybrid nanofluid has become a fruitful interest topic among researchers due to it thermal properties and potential which gives better result compared to nanofluid in enhancing the heat transfer rate. The intention here is to present the significant effects of suction and magnetic field over a moving plate containing hybrid nanofluid with base fluid is water, Alumina Oxide (Al2O3) and Copper (Cu) as the nanoparticles. A mathematical modelling consists of partial differential equation for the fluid flow are constructed and transformed to a set of ordinary differential equations hence solved numerically using bvp4c in MATLAB. Effects of magnetohydrodynamics (MHD), M, suction, S and relevant thermophysical properties on velocity, temperature, skin friction,Cf and local Nusselt,Nux number are thoroughly examined and presented graphically. It is noted that duality exists in certain range when λc<-1and unique solution at λ>-1. The range on duality of solution are widen as the values of M and S increase. Due to that, a stability analysis is implied to determine which duality of solution is stable and realizable. As M and ϕ2increase, the skin friction increases. For rate of heat transfer, as M increase, the heat transfer rate increase while for arising of ϕ2, the heat transfer decrease. Furthermore, it is noted that the hybrid nanofluid possess better result compared to nanofluid.

Analysis of MHD Carreau fluid flow over a stretching permeable sheet with variable viscosity and thermal conductivity

An Analysis has been carried out to study the magnetohydrodynamic boundary layer flow of Carreau fluid with variable thermal conductivity and viscosity over stretching/shrinking sheet. The thermal conductivity and viscosity is considered to be vary linearly with temperature. By applying suitable similarity transformations, the constitutive equation of Carreau fluid along with energy and transport equations transformed to set of ordinary differential equations. The obtained problem is solved analytically by Homotopy Analysis Method (HAM). As increasing magnetic force, skin friction and heat transfer rate are decreased in the stretching case, while opposite effects are seem in the shrinking case. Similarly, increase in the Lewis number leads to a reduction in the concentration profile. furthermore, increasing the power index and the Weissenberg number leads to an increase in skin friction and a heat transfer rate in the case of stretching, while both are reduced in case of shrinking For validity purpose the problem is also solved numerically using BVP4C (Matlab routine). Analysis of results show that analytical and numerical solutions are in excellent agreement. Furthermore, the impacts of different fluid parameters such as the Weissenberg number We2, Magnetic parameter M2, Suction parameter s, Prandtl number Pr, Lewis number Le, Stretching/ Shrinking parameter B and the heat flux constants on the velocity, temperature and concentration profiles are investigated graphically.

Non-linear natural convection and mass transfer flow near a vertical moving porous plate with chemical reaction and Soret effect

PurposeThe purpose of this paper is to conduct a theoretical study on steady fully developed non-linear natural convection and mass transfer flow past an infinite vertical moving porous plate with chemical reaction and thermal diffusion effect. Closed-form expressions for dimensionless velocity, concentration, Sherwood number and skin-friction are obtained by solving the present mathematical model.Design/methodology/approachThe fully developed steady non-linear natural convection and mass transfer flow near a vertical moving porous plate with chemical reaction and thermal diffusion effect is investigated. The non-linear density variation and Soret effect were taken into consideration. The dimensionless velocity, temperature and concentration profiles were obtained in terms of exponential functions, and were used to compute the governing parameters, skin-friction and Sherwood number.FindingsThe effect of coefficient of the non-linear density variation with the temperature (NDT) and concentration (NDC) parameter, chemical reaction parameter, thermal diffusion parameter are discussed with the aid of line graphs and tables. The analysis of the result shows that the velocity as well as skin-friction having higher values in the case of non-linear variation of density with temperature and concentration in comparison to linear variation of density with temperature and concentration. It is observed that the velocity and skin-friction increase with an increase in the Soret parameter.Originality/valueThe aim of this paper is to extend the work of Muthucumaraswamy (2002) by incorporating the thermal diffusion (Soret) effect and non-linear density variation with temperature (NDT) and concentration (NDC), on which, to the best knowledge of the authors, no studies have been carried out.

Stefan Blowing and Slip Effects on Unsteady Nanofluid Transport Past a Shrinking Sheet: Multiple Solutions

AbstractThe aim of a present article is to investigate the laminar unsteady two‐dimensional boundary layer flow of a nanofluid with Stefan blowing and slip effect. First, governing boundary layer equations are converted in the ordinary form of the differential equations (ODEs) from partial differential equations using appropriate coordinate transformations. The obtained ODEs are then solved by applying a shooting method with the Runge‐Kutta fourth order method by implementation of the Maple software. The influences of different controlling dimensionless parameters over the dimensionless velocity, temperature, concentration, friction factor, local heat as well as mass transfer have been discussed and represented by plots. It is found that there exist dual solutions for the different applied nanofluid parameters along with the blowing parameter. The results reveal that by increasing the values of the Brownian motion (Nb), thermophoresis (Nt) and blowing parameters (fw), the skin friction increases (decreases) in the first (second) solution.

An extension of the second moment closure model for turbulent flows over macro rough walls

An advanced second moment closure for rough wall turbulence is proposed. In contrast to previously proposed models relying on an empirical correlation based on equivalent sand grain roughness, the proposed model mathematically derives roughness effects by applying spatial and Reynolds averaging to the governing equations. The additional terms in the momentum equations are the drag force and inhomogeneous roughness density terms. The drag force term is modeled with respect to the plane porosity and plane hydraulic diameter. The two-component limit pressure-strain model is applied to the additional pressure-strain term, which is related to the external force terms. An evaluation of turbulence over surfaces with randomly distributed semi-spheres confirms that the developed model reasonably reproduces the effects of roughness on mean velocity, Reynolds stress, and energy dissipation. Turbulence over rough surfaces of marine paint is also simulated to assess the predictive performance for higher Reynolds number turbulent flows over real rough surfaces. The developed model successfully reproduces the dependence of the Reynolds number on roughness effects. Moreover, qualitative agreement of the skin friction increase with the experimental data is confirmed.

Effect of adverse pressure gradient on supersonic compressible boundary layer combustion

Influences of adverse pressure gradient (APG) on supersonic turbulent boundary layers are numerically studied using Reynolds-averaged Navier–Stokes (RANS) equations. The RANS methodology is validated by comparing the numerical results with the existing experimental data. Although the flame is restricted in the boundary layer, the heat flux is reduced rather than increased for the suppressed turbulence momentum transportation ability. Moreover, APG contributes more to the heat flux than combustion heat release does. Compared with no-injection case, a large skin friction reduction can be obtained by boundary layer combustion, and further reduction can be achieved in APG state. Additionally, the effects of combustion in APG on the velocity laws of the wall show that White's velocity law is close to the numerical results in the outer region of boundary layer, and Nichols's velocity law is appropriate in the whole boundary layer unless the APG is too strong. Turbulence intensity influences are analyzed in the end. Results show that the additional reduction of skin friction due to induced combustion cannot offset the skin friction increase caused by high turbulence intensity.

Thermal convection of MHD Blasius and Sakiadis flow with thermal convective conditions and variable properties

A theoretical study on the effect of magnetohydrodynamic field on the classical Blasius and Sakiadis flows of heat transfer characteristics with variable conditions and variable properties are studied in this paper. Hydromagnetic flows and heat transfer in porous media have been considered extensively in recent years due to their occurrence in several engineering processes such as compact heat exchangers, metallurgy, casting, filtration of liquid metals, cooling of nuclear reactors and fusion control. The governing partial differential equations are converted into ordinary differential equations using the suitable similarity transformations. The transformed boundary layer equations like momentum and energy equations are solved numerically by using Runge–Kutta method. The effect of governing physical parameters over the velocity and temperature distributions is demonstrated graphically. Moreover, the local friction factor coefficient and rate of heat transfer in terms of Nusselt number are computed and discussed through tables. We validated the present solutions with already existing studies under limited cases. It is found that the thermal buoyancy parameter enhances the velocity depreciates the temperature field for both the Sakiadis and Blasius flow cases. The influence of Biot number increases skin friction coefficient and local Nusselt number for both Sakiadis and Blasius flow cases.The rate of heat transfer for temperature ratio parameter is high in Blasius flow case when compared with Sakiadis flow case.

Natural convection boundary layer flow of nanofluids around different stations of the sphere and into the plume above the sphere

AbstractThe main intent of the present study is to investigate the natural convection boundary layer flow of nanofluids around different stations of the sphere and eruption of the fluid from the boundary layer in to the plume above the sphere. It is pertinent to point out that in this study heated sphere is treated as point source. The system of transport boundary layer equations is based on the effects of Brownian motion and thermophoresis. The system of dimensioned boundary layer equations is transformed into nondimensional form. Later, the nondimensional form of the mathematical model is solved numerically by using implicit finite difference method. The solution of the problem depends on a controlling parameters Prandtl number Pr, Lewis number , thermophoresis parameter , and Brownian motion parameter . Particularly, it is observed that for Lewis number , Prandtl number Pr, Brownian motion parameter , and thermophoresis parameter the velocity profile is maximum at station and minimum at station . On the other hand temperature distribution is uniform at each station around the sphere and slightly reduced for . It is also observed that nanoparticles concentration is maximum at station and minimum at station We also established the result that with the increase of skin friction is reduced while the heat and mass flux are increased in the plume region‐III.

Natural bioconvection flow of a nanofluid containing gyrotactic microorganisms about a truncated cone

Abstract A mathematical model is presented to investigate the natural convection boundary-layer flow of a water-based nanofluid containing gyrotactic microorganisms over a truncated cone with convective boundary condition at the surface. The governing partial differential equations are converted into ordinary differential equations by using suitable transformations. These equations are solved numerically using RKF7 with shooting method. Several comparisons with previously published works are reported and the results are found to be in excellent agreement. The numerical results are obtained and discussed for nanoparticle concentration, density of motile microorganisms profiles as well as the local skin-friction coefficient local Nusselt number, the local Sherwood number, the local density number of the motile microorganisms. It is found that density number of motile microorganisms, Sherwood number, Nusselt number and skin friction increase along the surface.

Radiation and heat source effects on MHD flow over a permeable stretching sheet through porous stratum with chemical reaction

Purpose The purpose of this paper is to investigate the steady 2D buoyancy effects on MHD flow over a permeable stretching sheet through porous medium in the presence of suction/injection. Design/methodology/approach Similarity transformations are employed to transform the governing partial differential equations into ordinary differential equations. The transformed equations are then solved numerically by a shooting technique. Findings The working fluid is examined for several sundry parameters graphically and in tabular form. It is observed that with an increase in magnetic field and permeability of porous parameter, velocity profile decreases while temperature and concentration enhances. Stretching sheet parameter reduces velocity, temperature and concentration, whereas it increases skin friction factor, Nusselt number and Sherwood number. Originality/value Till now no numerical studies are reported on the effects of heat source and thermal radiation on MHD flow over a permeable stretching sheet embedded in porous medium in the presence of chemical reaction.

Critical Protuberance Height for Transition of Leading Edge Boundary Layers

Leading edge contamination on aircraft wings can occur through the accumulation of insect residues, ice, or dirt or through existing surface defects. Such protuberances can increase skin friction drag by causing an earlier transition of the boundary layer from laminar to turbulent flow. To determine the likelihood of this effect, a simple and approximate model was developed for determining the critical height for boundary-layer transition on the airfoil leading edge. The model assumes an outer potential flow based on an effective leading edge radius coupled with an inner flow based on semi-empirical laminar boundary profiles. The effective leading edge radius was based on leading edge pressure distribution as related to flow over a cylinder and tends to the geometric leading edge radius for the limits of no camber and zero angle of attack. The model was compared with available experimental transition results, which showed that the predictions are reasonable but approximate. The potential susceptibility of various airfoils to transition was next considered using sample insect residues heights. The results indicate that laminar flow airfoils for large commercial aircraft would be significantly susceptible to transition due to insect contamination, whereas high-altitude low-speed UAVs would generally not have such susceptibility.

Effectiveness of Magnetic Dipole and Framing the Performance of $$\hbox {Fe}_{3}\hbox {O}_{4}$$ Fe 3 O 4 in Rotating Transport Influenced by Viscous Dissipation

The present study is a theoretical study of three-dimensional rotating ferrofluid flow on stretching sheet. Flow is influenced by a magnetic dipole in presence of viscous dissipation. Formulation of Navier stoke equations with ferromagnetic particle’s interaction is carried out. By applying dimensional analysis coupled differential equations are reduced to an ordinary system of equations. Finite difference approach is applied to solve the obtained system of equations. Effects of viscous dissipation and the magnetic dipole on flow and temperature of fluid are illustrated graphically and in tabular form. It is proved that temperature and skin friction is a decreasing function of Eckert number. Ferromagnetic hydrodynamic interaction parameter results in reducing both of velocities (axial and transverse), heat flux, and increasing skin friction.

Al2O3–Water nanofluid heat transfer and entropy generation in a ribbed channel with wavy wall in the presence of magnetic field

In this article, a parametric study is conducted to evaluate heat transfer enhancement in a ribbed channel containing Al2O3–Water nanofluid with wavy wall. The physical domain is under the influence of the magnetic field that creates a negative force against the working fluid to move. Nanofluid with higher temperature enters the cool ribbed duct and heat is exchanged along the walls of channel. The effects of the dominant parameters including number of the blocks, solid volume fractions of nanofluid, Hartmann number, Reynolds number, and different states of amplitude sine waves are numerically tested on the local and average Nusselt number, skin friction, and total entropy generation. Excellent agreement between present study and previous literature is observed. It is found that, an augmentation in magnetic field will result in higher values of both local and average Nusselt number accompanying with bigger values of skin friction and entropy generation. Computations illustrate that, increasing the solid volume fraction of the Al2O3 nanoparticles will raise the Nusselt number and total entropy generation rate but its effect on the skin friction is negligible. Also, numerical results imply that increasing amplitude sine waves of the geometry has incremental effect on the Nusselt number and skin friction but its effect on the total entropy generation rate is not so clear. Moreover, by adding number of the used blocks in the presence of magnetic field, the local Nusselt number experiences more jumps but it does not increase the average Nusselt number, necessarily. In addition, using more blocks increases skin friction but it has a reverse effect on the total entropy generation rate.

Fractal Riblets

Koch-like riblets that iteratively protrude toward the outside (the fluid region) or cave in at the wall are examined. The near-wall microscopic fluid problem is addressed by solving for the Stokes flow with a boundary element method, yielding slip lengths for all the surface shapes considered. Such lengths are then used in Navier boundary conditions of the macroscopic, turbulent problem, which is solved by direct numerical simulations. The results of the direct simulations demonstrate that inward-contracting riblets enjoy an additional drag reduction when compared to the base, triangular configuration, whereas outward-protruding riblets experience a skin-friction increase. The results are in excellent agreement with a theoretical model.

Fe3O4–(CH2OH)2 nanofluid analysis in a porous medium under MHD radiative boundary layer and dusty fluid

In this paper, magnetohydrodynamic (MHD) boundary layer flow and heat transfer of an incompressible Iron (II,III) oxide (Fe3O4)-ethylene glycol ((CH2OH)2) nanoparticle on micropolar fluid with homogeneously suspended dust particles over a stretching sheet in the presence of thermal radiation and Joule heating are investigated. After transforming the partial differential equations (PDEs) governing the problem into the ordinary differential equations (ODEs), Runge–Kutta Fehlberg fourth fifth order numerical method is applied. The main criterion of this paper is to study the effects of different parameters and dimensionless numbers on velocity and temperature distribution in two phases of fluid and dust for two prescribed surface temperature (PST) and prescribed heat flux (PHF) cases. Velocity reduction in both fluid and dust phases is due to the Lorentz force against flow by increasing Hartman number, enhancement of temperature and thickness of thermal boundary layer are due to the increase of radiation parameter and Eckert number for both PST and PHF cases are the most important results. Also, in the final section of this paper, the effect of changes in the value of different parameters on skin friction coefficient and local Nusselt number in (PST and PHF PHF) have been discussed. These results indicated increasing the Hartman parameter (Ha) would cause an increase skin friction coefficient, also increasing the Eckert number would cause an increase local Nusselt number in PST case and reverse effect in PHF case.