Presence Of Slip Velocity Research Articles

Study on a tangent hyperbolic thermal fluid flow over a porous stretching sheet with a magnetic field and the effect of suction/injection

This work examines a steady and incompressible flow of 2-dimensional MHD tangent hyperbolic fluid over a linearly stretchable surface with an injection/suction effect. It also investigates the impact of thermal radiation, heat source/sink, a porous medium and variable thermal conductivity. The slippery boundary conditions are employed to consider the presence of velocity slip near the surface. The Lie symmetric analysis with a novel homotopy approach is used to study the influence of non-dimensional characteristics, including the Weissenberg number, the Hartmann number, the power-law index, the Prandtl number, the porosity parameter and the heat absorption/generation parameter, on the fluid flow and temperature. Moreover, the numerical data include an examination of the influence of various parameters on both the surface drag force and the heat transmission rate, presented through graphs and tables. Ultimately, the acquired outcomes have been numerically verified with the pre-existing results. Finally, the heat transmission rate escalates with the augmentation of the Prandtl number and the variable thermal conductivity parameter.

Scrutinization of Unsteady Magnetohydrodynamics Williamson Nanofluid Flow and Heat Transfer Past a Permeable Shrinking Sheet

This study contributes to the thermal characteristics and flow behaviour of magnetohydrodynamics (MHD) unsteady flow of Williamson nanofluid over a permeable stretching/shrinking sheet in the presence of velocity slip at the boundary. The PDEs with the corresponding constraints are transformed into a set of non-linear ODEs using similarity transformations and are then solved numerically using fourth order Runge-Kutta integration scheme along with shooting technique. The results show that for the flow past a shrinking sheet, dual solutions exist for a certain range of physical parameters. The analysis shows that velocity profile is an increasing function of magnetic parameter M (0.0 ≤ M ≤ 0.3), velocity slip parameter δ (0.0 ≤ δ ≤ 0.25) and suction parameter s (2.0 ≤ s ≤ 2.2) while decreasing function of Williamson parameter β (0.0 ≤ β ≤ 0.8) and unsteadiness parameter A (−3.5 ≤ A ≤ 0.0) for the first solution branch. The temperature profile augments due to the increase of M and δ for the first solution branch. Computational outcomes of the skin friction coefficient, the Nusselt number, the Sherwood number are tabulated with suitable interpretations. The temporal stability analysis reveals that among the two solutions, first solution is stable and physically realizable. Our method of finding dual solutions and analyzing stability analysis is of practical importance to those interested in fluid dynamics as it provides one with a way to determine whether a steady state solution is physically meaningful or not.

MHD Mixed Convection of Hybrid Ferrofluid Flow over an Exponentially Stretching/Shrinking Surface with Heat Source/Sink and Velocity Slip

This paper investigates the mixed convection flow related to Fe3O4-CoFe2O4/water hybrid ferrofluids on stagnation point over an exponentially stretching/shrinking surface with the influence of magnetohydrodynamic (MHD), velocity slip, and heat source/sink. The proposed system of differential equations is reduced using the similarity transformation procedure that is numerically solvable using MATLAB. Dual solutions are obtained for various governing parameters, in which the first solution is found to be in a stable state via the stability analysis. The CoFe2O4 nanoparticles volume fraction increases the heat transfer rate and the skin friction coefficient while delaying the separation of the boundary layer at the bifurcation point. Adding CoFe2O4 nanoparticles in hybrid ferrofluids gives a better heat transfer rate than that obtained with ferrofluids. The presence of a magnetic field enhances the fluid flow velocity. The increased strengths of the heat sink and stretching parameters give better results on the heat transfer, while the results are reversed for the heat source and shrinking parameters. The presence of velocity slip does influence the skin friction and the fluid flow.

Semi-analytical and numerical explorations on entropy optimization of EMHD in Casson hybrid nanofluid with radiation slip and convective boundary conditions

TheTheoretical study of 3D electro magnetohydrodynamic boundary layer steady flow of a Casson fluid across a rotating disk in the presence of velocity slip, porous medium and thermal radiation is indeed the subject of this article. Engine oil with (Copper–Zirconium dioxide) hybrid nanoparticles takes up the fluid in the containment. The nonlinear differential systems are transformed into ordinary differential systems using a suitable self-similarity variable, which are obtained using the Runge–Kutta scheme. When compared to the numerical method, the HPM yields a more precise and dependable conclusion than the Runge–Kutta method. With new parameters, Casson fluid velocity, temperature, entropy production rate, bejan number, skin friction factor and rate of heat transfer are explored and the findings are graphically shown for two different fluid cases that is Newtonian and non-Newtonian. The entropy generation increases for greater values of the electric field parameter, Brinkman number and temperature ratio parameters. Hybrid nanoparticles play a significant role in Power transmission lines, the Automobile industry, fuel cell membranes, and joint implants.

Hybrid nanofluid stagnation point flow past a slip shrinking Riga plate

Magnetic nanofluids cover many of uses since their characteristics are externally controllable, and their physical properties may vary with the nanoparticle volume fraction and magnetic field strength. Hybrid nanofluid also has been commercialized as the advancement of traditional nanofluid. The preliminary research on hybrid magnetic nanofluids inspired the present study to discover the stagnation-point flow of hybrid magnetite-cobalt ferrite/water nanofluid towards a shrinking Riga plate with the presence of velocity slip. The complex governing model of the flow is simplified by implementing the similarity transformation. A well-established numerical package, namely bvp4c in MATLAB, is used for numerical calculation as well as stability analysis. Two solutions are found due to the opposing flow from the shrinking Riga plate. From the stability analysis, the first solution which fulfills the boundary condition is the physically stable solution. The rising values of electromagnetohydrodynamic (EMHD) parameter and cobalt ferrite concentration augment the skin friction coefficient. Specifically, the critical point is lessened by 3% when the EMHD parameter is augmented from 0.3 to 0.5 and 0.5 to 0.7, which concludes that a suitably higher EMHD parameter could prevent the separation of the boundary layer. The heat transfer progress is actively performed with the enhancement of EMHD and velocity slip parameters which conclusively shows the suitability of these parameters in developing the cooling heat transfer fluid.

Stability Solution of Unsteady Stagnation-Point Flow and Heat Transfer over a Stretching/Shrinking Sheet in Nanofluid with Slip Velocity Effect

Computational of unsteady flow with slip condition is essential since physically the heat transfer process is time-dependent and there may exist slip between fluid and surface. Therefore, this study aims to investigate the unsteady stagnation-point flow and heat transfer over a stretching/shrinking sheet immersed in nanofluid in the presence of slip velocity. By applying boundary layer theory and Tiwari-Das model, the governing equations are developed and transformed into a system of ordinary differential equations using similarity transformation, which are then solved numerically using bvp4c solver in MATLAB. The influence of slip velocity, stretching/shrinking parameters, nanoparticle volume fraction and unsteadiness parameter on the local skin friction coefficient, local Nusselt number, as well as velocity and temperature profiles are analysed. There are three types of nanoparticles considered, namely Copper (Cu), Alumina (Al203), Titania (TiO2) and water (H20) is the base fluid. It is found that dual solutions occur for certain parameters and the stability analysis is performed. The analysis shows that the first solutions are found to be stable than the second solution. The local skin friction coefficient and local Nusselt number are increasing with slip velocity, nanoparticle volume fraction for shrinking case; however, the opposite trend is observed for stretching case. By raising 20% of nanoparticle volume fraction for the shrinking sheet ( the friction at the surface increases 24% and 15.5% for heat transfer rate for the first solution. Moreover, for 10% of nanoparticle volume fraction for the shrinking sheet (and the first solution, varying slip parameters from 0 to 0.2, give rise to approximately 21% of the friction at the surface and 68% of the heat transfer rate.

Unsteady Slip Flow and Heat Transfer Analysis of Oldroyd-B Fluid Over the Stretching Wedge

The unsteady flow of the upper-convected Oldroyd-B fluid over the heated wedge in the presence of velocity slip was discussed. The process of heat transfer and the effect of the thermal retardation time on heat transfer were simulated with the relaxation-retardation heat flux model. The buoyancy, the thermal radiation and the convective heat transfer boundary condition were considered to further elucidate the flow and heat transfer characteristics. The homotopy analysis method was used to obtain the approximate analytical solutions to ordinary differential equations. It is found that the magnification of the slip parameter can promote the flow of fluid, and the fluid temperature rises with the thermal radiation parameter. In addition, the temperature field shows opposite trends in the thermal relaxation time and the thermal retardation time.

Slip hydrodynamics of combined electroosmotic and pressure driven flows of power law fluids through narrow confinements

Electroosmotic flows (EOF) in microfluidic devices can be greatly enhanced over superhydrophobic surfaces because the high shear rates within the electrical double layer can drive large slip velocities at the interface. Using the power law fluid model, we derive a novel formulation for the Helmholtz–Smoluchowski (HS) velocity and use it to examine the effect of slip on the hydrodynamics of a coupled pressure driven and EOF. Semi analytical relations for the velocity gradient are obtained for cases of a favourable pressure gradient but exact solutions of the velocity can be found only for certain power law indices. Cases of adverse pressure gradient and fractional power law indices are investigated using numerically using the Galerkin Finite Element Method. The validity of the semi analytical relations verified by comparison with the numerical method. The presence of velocity slip at the wall leads to an enhancement of the HS velocity that is most pronounced in shear thinning fluids. Adverse pressure gradients are observed to generate an inflection in the velocity profile and even a two-way flow for certain flow parameters. The strength of the adverse pressure gradient needed to setup a reverse flow at the channel centre reduces as the slip length is increased. The location of the point of inflection is found to depend on the channel height, pressure gradient, electric field, slip length, Debye length and non-Newtonian behaviour.

Numerical study of activation energy and thermal radiation effects on Oldroyd‐B nanofluid flow using the Cattaneo–Christov double diffusion model over a convectively heated stretching sheet

AbstractThis paper investigates a theoretical model of a mixed convective Oldroyd‐B nanofluid with thermal radiation and activation energy effects. A thorough analysis is done by employing the nonhomogeneous Buongiorno model in the presence of velocity slip and suction. The surface is porous in nature, and nanoparticle mass flux is maintained passively at the surface. The thermal and concentration equations are modeled with the Cattaneo–Christov theory of heat and mass flux, respectively. Proper transformations are utilized for the conversion of transport equations and boundary conditions. The similarity solution is obtained through a numerical approach by utilizing the Runge–Kutta–Fehlberg method and shooting technique. The vital outcomes of this study and the influence of controlling parameters on the flow field, temperature, and concentration profiles are discussed graphically and in a tabular manner. Furthermore, a detailed discussion is provided to explain the results physically. The velocity of the nanofluid increases when the porosity parameter is increased, and temperature decreases with increasing thermal relaxation parameter. The outcomes elucidate that the suction parameter, thermal radiation parameter, and thermal relaxation parameter are positively correlated with the heat transfer coefficient. The result of passive control of nanoparticles at the surface is that the Brownian motion parameter has no influence on the temperature of the Oldroyd‐B nanofluid flow and rate of heat transfer at the surface.

Simultaneous effects of bioconvection and velocity slip in three-dimensional flow of Eyring-Powell nanofluid with Arrhenius activation energy and binary chemical reaction

Recent investigations relate the enhancement of extrusion processes and transportation of heat systems via solar radiation and utilization of nanoparticles. The prime aim of the current exploration is to analyze the rheology of three-dimensional magnetized Eyring-Powell nanofluid in the presence of velocity slip, thermal radiation and Arrhenius activation energy. The suggested flow model attains both nanoparticles and gyrotactic microorganisms. The dimensionless system for flow problem is introduced with utilization of convenient transformation. The self similar solution of converted equations is integrated numerically with the help of well-known shooting technique via MATLAB software. The aspects of pertinent parameters like combine parameter Ha, slip parameter α, stretching parameter β, Biot number Bi, Lewis number Le, Peclet number Pe, bio-convection Lewis number Lb are graphically influenced for velocities, temperature, nanoparticles concentration and density of motile microorganism. The nanoparticles significance for each physical quantity is comprehensively pointed out. Study revealed that an interaction of buoyancy forces resists the fluid particles movement near the surface effectively. It is further observed that slip factor enhanced the both heat and mass transportation phenomenon. An increment in local Nusselt and Sherwood numbers is resulted with variation of mixed convection parameter and Prandtl number. The reported results are valuable for the energy transportation enhancement and applications of bio-nanofuels cells.

Three-Dimensional Hybrid Nanofluid Flow and Heat Transfer past a Permeable Stretching/Shrinking Sheet with Velocity Slip and Convective Condition

The present work deals with the three-dimensional hybrid Cu-Al2O3/water nanofluid flow towards a stretching/shrinking sheet with the presence of velocity slip and convective conditions. A permeable sheet is considered to maintain the shrinking flow through an adequate wall mass suction. The nonlinear governing boundary layer coupled with energy equations are transformed into the ordinary differential equations using similarity transformation. Numerical computations are performed with the aid of boundary value problem solver (bvp4c) in the Matlab software and the results are presented in the tables and graphs. The boundary layer separation occurs in the shrinking flow region. An upsurge of slip and copper nanoparticle volume fraction parameters can increase the range of first and second solutions whereas Biot parameter give zero impact on delaying the boundary layer separation. However, an increase of Biot and slip parameters can boost the heat transfer rate while opposite result is obtained with the augmentation of the copper solid volume fraction. The stability of both solutions are examined, and it is validated that the first (upper branch) solution is more stable than second solution.

Non-linear radiation and chemical reaction effects on slip flow of Williamson nanofluid due to a static/moving wedge: a revised model

In the present study, heat and mass transfer characteristics of unsteady, two-dimensional stagnation-point flow of Williamson nanofluid along a static/moving wedge in the presence of velocity slip and chemical reaction effects are investigated. The Rosseland approximation is adopted for thermal radiation effects and Buongiorno model is used for incorporating the effects of Brownian diffusion and thermophoresis. The wall of wedge is heated by the convection current from hotter fluid and revised model is also considered in this study. The governing boundary-layer equations are altered into a coupled non-linear ordinary differential equations using suitable transformations and then tackled numerically employing Runge–Kutta–Fehberg method with shooting technique. The effects of intricate physical parameters on the dimensionless velocity, temperature, nanoparticle concentration profiles as well as skin friction coefficient and local Nusselt number are explored graphically and discussed in detail. Verification of present code is achieved via benchmarking with previously published results, and generally, very excellent agreement is revealed. Our study reveals that the intensifying values of temperature ratio parameter enhances the nanofluid temperature and thermal boundary-layer thickness. The rate of heat transfer is seen to be higher with the growth of Prandtl number and Biot number. Moreover, the nanoparticle concentration is decreased as the Brownian motion and Schmidt number increasing.

Peristalsis of nanofluid through curved channel with Hall and Ohmic heating effects

Nanofluids have attracted many scientists due to their remarkable thermophysical properties. Small percentage of nanoparticles when added to conventional fluid significantly enhances the heat transfer features. Sustainability and efficiency of nanomaterials have key role in the advancement of nanotechnology. This article analyzes the Hall, Ohmic heating and velocity slip effects on the peristalsis of nanofluid. Convective boundary conditions and heat generation/absorption are considered to facilitate the heat transfer characteristics. Governing equations for the peristaltic flow through a curved channel are derived in curvilinear coordinates. The equations are numerically solved under the assumption of long wavelength and small Reynold number. It has been observed that nanofluid enhances the heat transfer rate and reduces the fluid temperature. Hartman number and Hall parameter show reverse behavior in fluid motion and heat transfer characteristics. In the presence of velocity slip, the pressure gradient rapidly decreases and dominant effect is seen in narrow portion of channel.

Role of Brownian Motion and Thermophoresis Effects on Hydromagnetic Flow of Nanofluid Over a Nonlinearly Stretching Sheet with Slip Effects and Solar Radiation

Hydromagnetic flow of water based nanofluids over a nonlinearly stretching sheet in the presence of velocity slip, temperature jump, magnetic field, nonlinear thermal radiation, thermophoresis and Brownian motion has been studied. The article focuses on Cu water nanofluid and Ag water nanofluid. The similarity transformation technique is adopted to reduce the governing nonlinear partial differential equations into nonlinear ordinary differential equations and then they are solved numerically utilizing the Nachistem – Swigert shooting method along with the fourth order Runge Kutta integration technique. The influence of physical parameters on the flow, temperature and nanoparticle volume fraction are presented through graphs. Also the values of the skin friction coefficient at the wall and nondimensional rate of heat transfer are given in a tabular form. A comparative study with previous published results is also made.

Stability analysis for model-based study of nanofluid flow over an exponentially shrinking permeable sheet in presence of slip

This article aims to present the nanofluid flow over an exponentially porous shrinking sheet in the presence of velocity slip and thermal slip. Single-phase fluid model for nanofluid has been used. In this investigation, the effects of silver (Ag) nanoparticle in two different types of base fluids (water and kerosene oil) are investigated. Using similarity transformations, the governing boundary-layer equations and the boundary conditions are reduced to the system of coupled nonlinear ordinary differential equations and then solved numerically with the help of shooting method. Dual solutions exist for some particular range of values of the governing parameters. A stability analysis has been performed to find out the stable solution. A comparison is made between the boundary-layer flow of Ag–water and Ag–kerosene. Impacts of various parameters on velocity, temperature profiles, skin friction coefficient, and Nusselt number are computed and presented in graphs and tables. The fluid velocity and temperature both increase with the increasing nanoparticle volume fraction.

Effects of slip on Cu–water or Fe $$_{3}$$ 3 O $$_{4}$$ 4 –water nanofluid flow over an exponentially stretched sheet

This study aims to report the boundary layer flow of nanofluid over an exponentially stretched sheet in the presence of velocity slip as well as thermal slip. Utilising similarity transformations, the governing momentum and temperature equations are converted into ordinary differential equations and then solved numerically by shooting technique. An interesting behaviour of the solution for the converted self-similar equations is noted: dual solutions are obtained for some particular range of values of the governing parameters for the flow past an extended sheet. A comparison is made between the boundary layer flow of Cu–water and Fe $$_{3}$$ O $$_{4}$$ –water nanofluids. Both fluid velocity and temperature increase due to the enhancement in the velocity slip parameter. With the rising values of solid volume fraction, velocity diminishes but temperature increases.

A useful case study to develop lattice Boltzmann method performance: Gravity effects on slip velocity and temperature profiles of an air flow inside a microchannel under a constant heat flux boundary condition

Mixed convection heat transfer of air in a 2-D microchannel is investigated numerically by using lattice Boltzmann method. The effects of buoyancy forces on slip velocity and temperature profiles are presented while the microchannel side walls are under a constant heat flux boundary condition. Three states are considered as no gravity, Gr = 100 and Gr = 500. At each state, the value of Knudsen number is chosen as Kn = 0.005, Kn = 0.01 and Kn = 0.02 respectively; while Reynolds number and Prandtl number are kept fixed at Re = 1 and Pr = 0.7. Density-momentum and internal energy distribution functions are used in order to simulate the hydrodynamic and thermal domains in LBM approach. Develop the ability of LBM to simulate the constant heat flux boundary condition along the microchannel walls in the presence of slip velocity and buoyancy forces is proved for the first time at present work. The new and interesting results are achieved such as generating a rotational cell through the fluid flow due to buoyancy forces which leads to see the negative slip velocity at these areas.

Unsteady Stagnation-Point Flow and Heat Transfer Over a Permeable Exponential Stretching/Shrinking Sheet in Nanofluid with Slip Velocity Effect: A Stability Analysis

A model of unsteady stagnation-point flow and heat transfer over a permeable exponential stretching/shrinking sheet with the presence of velocity slip is considered in this paper. The nanofluid model proposed by Tiwari and Das is applied where water with Prandtl number 6.2 has been chosen as the base fluid, while three different nanoparticles are taken into consideration, namely Copper, Alumina, and Titania. The ordinary differential equations are solved using boundary value problem with fourth order accuracy (bvp4c) program in Matlab to find the numerical solutions of the skin friction and heat transfer coefficients for different parameters such as stretching/shrinking, velocity slip, nanoparticle volume fraction, suction/injection, and also different nanoparticles, for which the obtained results (dual solutions) are presented graphically. The velocity and temperature profiles are presented to show that the far field boundary conditions are asymptotically fulfilled, and validate the findings of dual solutions as displayed in the variations of the skin friction and heat transfer coefficients. The last part is to perform the stability analysis to determine a stable and physically-realizable solution.

Unsteady stagnation-point flow and heat transfer over an exponential stretching sheet in Copper-water nanofluid with slip velocity effect

This paper is performed in order to study the behavior of unsteady stagnation-point flow and the heat transfer in nanofluid with the presence of velocity slip over an exponential stretching sheet. The nanofluid model namely Tiwari-Das model is considered where the influence of volume of nanoparticle in the base fluid is also part of the focus in this study. Copper is the nanoparticle and water is chosen as the base fluid. The transformation of governing equation in partial differential equations form to the system of ordinary differential equations is carried out using suitable similarity variables. The system is solved using bvp4c program in Matlab software where the numerical results for dual solutions are presented graphically for the skin friction coefficient, the local Nusselt number and the velocity as well as the temperature profiles are obtained for different parameters namely, velocity slip, nanoparticle volume fraction, suction/ injection and unsteadiness parameters.

Blood Flow in a Radially Non Symmetric Stenosed Artery Under Slip Effect Through Porous Medium

A mathematical model is developed to analyze the non-Newtonian flow of blood in an axially symmetric but radially non symmetric stenosed artery through porous medium in the presence of slip velocity. Blood is modeled as Casson fluid to characterize the non-Newtonian behaviour. Flow characteristics like axial velocity, flow rate and impedance are expressed analytically. These expressions show remarkable variations in flow of blood through constricted artery. The effects of porosity, slip velocity and stenosis shape on the various flow characteristics have been examined and shown graphically. These results are in good agreement with the experimental findings existing in the literature and can aid medical practitioner to treat cardiovascular diseases.