Effects Of Partial Slip Research Articles

Effects of magnetic field and partial slip on unsteady axisymmetric flow of Carreau nanofluid over a radially stretching surface

The unsteady magnetohydrodynamic (MHD) axisymmetric flow of Carreau nanofluid over a radially stretching sheet is investigated numerically in this article. Recently devised model for nanofluid namely Buongiorno’s model incorporating the effects of Brownian motion and thermophoresis is adopted here. Additionally, partial velocity slip and convective boundary condition are considered. Mathematical problem is modeled with the help of momentum, energy and nanoparticles concentration equations using suitable transformation variables. The numerical solutions for the transformed highly nonlinear ordinary differential equations are computed for both shear thinning and shear thickening fluids. For numerical computations, an effective numerical approach namely the Runge-Kutta Felhberg integration scheme is adopted. Effects of involved controlling parameters on the temperature and nanoparticles concentration are examined. Numerical computations for the local Nusselt number and local Sherwood number are also performed. It is interesting to note that the strong magnetic field has the tendency to enhance the thermal and concentration boundary layer thicknesses. Additionally, the local Nusselt and Sherwood numbers depreciate by improving values of unsteadiness parameter, magnetic parameter, velocity slip parameter and thermophoresis parameter in shear thickening and shear thinning fluids.

The new analytical study for boundary-layer slip flow and heat transfer of nanofluid over a stretching sheet

In this article, the semi-analytical/numerical technique known as the homotopy analysis method (HAM) is employed to derive solutions for partial slip effects on the heat transfer of nanofluids over a stretching sheet. An accurate analytical solution is presented which depends on the Prandtl number, slip factor, Lewis number, Brownian motion number, and thermophoresis number. The variation of the reduced Nusselt and reduced Sherwood numbers with Brownian motion number, and thermophoresis number for various values Prandtl number, slip factor, Lewis number is presented in tabular and graphical forms. The results of the present article show the flow velocity and the surface shear stress on the stretching sheet and also reduced Nusselt number and reduced Sherwood number are strongly influenced by the slip parameter. It is found that hydrodynamic boundary layer decreases and thermal boundary layer increases with slip parameter. Comparison of the present analysis is made with the previously existing literature and an appreciable agreement in the values is observed for the limiting case.

MHD mixed convection of Cu–water nanofluid in a two-sided lid-driven porous cavity with a partial slip

ABSTRACTA numerical simulation of magneto-hydrodynamic mixed convection flow and heat transfer of Cu–water nanofluid in a square cavity filled with a Darcian porous medium with a partial slip is numerically investigated. The left and right walls of the cavity are moving up with a constant speed in vertical direction, and the partial slip effect is considered along these walls. The top and bottom walls of the cavity are assumed to be adiabatic. The right vertical wall of the cavity is assumed to be kept at a lower temperature, while the left vertical wall is kept at a higher temperature. The developed equations of the mathematical model are nondimensionalized and then solved numerically subject to appropriate boundary conditions by the finite-volume method. A parametric study is performed and a set of graphical results is presented and discussed to demonstrate interesting features of the solution.

MHD mixed convection of localized heat source/sink in a nanofluid-filled lid-driven square cavity with partial slip

Magneto-hydrodynamic mixed convection in a lid-driven square cavity filled with Cu–water nanofluid is investigated in this paper. Partial slip effect is considered along the lid driven horizontal walls. A segment of the left wall is considered as a heat source, meanwhile a heat sink is placed on the right wall of cavity. The remainder cavity walls are thermally insulated. A control finite volume method is adopted as a numerical appliance of the present study. The study is achieved by controlling the effect of a set of pertinent parameters, these are; the size and position of the heat source/sink (B = 0.2–0.8, D = 0.3–0.7, respectively), the Hartman number (Ha = 0–100), Richardson number (Ri = 0.001–10), nanoparticle volume fraction (ϕ=0.0−0.1), partial slip parameter (S=1−∞), and the lid-direction of the horizontal walls (λ = ±1) where the positive sign means lid-driven to the right while the negative sign means lid-driven to the left. The results show that the shortest length of the heat source/sink localized midway of the vertical walls give the maximum convective heat transfer, and the best direction of the horizontal walls is that when they are both lid-driven to the left. For very strong applied magnetic field, the lid-direction becomes inactive.

Flow and heat transfer to Sisko fluid with partial slip

In this paper we study the partial slip effects on the flow and heat transfer of an incompressible non-Newtonian fluid over a nonlinear stretching sheet. The velocity slip boundary condition based on the Sisko constitutive fluid model is introduced. Suitable dimensionless variables are used to convert the governing partial differential equations into ordinary differential equations. Numerical solutions of these equations are obtained by the Runge–Kutta Fehlberg method. Additionally, the exact analytical solutions are presented in some special cases. The computational results for the velocity, temperature, skin-friction coefficient, and Nusselt number are presented in graphical and tabular forms. To validate the numerical results obtained, a comparison is made with the exact analytical solutions. The analysis of the results obtained shows that enhancement in the velocity slip parameter reduces the velocity as well as the momentum boundary layer thickness. However, quite the opposite is true with the temperature and corresponding thermal boundary layer thickness.

Combine effects of Magnetohydrodynamics (MHD) and partial slip on peristaltic Blood flow of Ree–Eyring fluid with wall properties

In this article, combine effects of Magnetohydrodynamics and partial slip on Blood flow of Ree–Eyring fluid through a porous medium have been investigated. The walls of the non-uniform porous channel are considered as compliant. The governing equation of Ree–Eyring fluid for blood flow are simplified using long wavelength and low Reynolds number approximation. The obtained resulting equation are solved analytically and exact solution has been obtained. The impact of different physical parameters such as Hartmann number, slip parameter, porous parameter, wall rigidity parameter, wall tension and mass characterization parameter are taken into account. It is found that velocity distribution increases due to slip effects while its behavior is opposite for Hartmann number. Trapping mechanism has also taken under consideration by drawing contour streamlines.

Effect of partial slip on an unsteady MHD mixed convection stagnation-point flow of a micropolar fluid towards a permeable shrinking sheet

The objective of the present study was to investigate the partial slip effect on an unsteady two-dimensional mixed convection stagnation point flow towards a permeable shrinking sheet. The governing equations are reduced to a system of non-dimensional partial differential equations using a semi-similarity transformation, before being solved numerically by using Keller-box method. The features of the flow characteristics for different values of the governing parameters are analysed and discussed. The results indicate that the momentum, thermal and concentration boundary layer thicknesses increase with increasing mixed convection parameter for opposing flow, whereas the opposite effect is observed for assisting flow. The results also show that the surface velocity is higher when there is slip at a sheet compared to its absent. Further, the study indicates that the boundary layer thicknesses become thicker and thicker with increasing shrinking parameter, while the opposite effect is observed with increasing Hartmann number. Comparison with previously published work for special cases is performed and found to be in excellent agreement.

Mixed convection in a nanofluid filled-cavity with partial slip subjected to constant heat flux and inclined magnetic field

Mixed convection in a lid-driven square cavity filled with Cu-water nanofluid and subjected to inclined magnetic field is investigated in this paper. Partial slip effect is considered along the lid driven horizontal walls. A constant heat flux source on the left wall is considered, meanwhile the right vertical wall is cooled isothermally. The remainder cavity walls are thermally insulted. A control finite volume method is used as a numerical appliance of the governing equations. Six pertinent parameters were studied these; the orientation of the magnetic field (Φ=0–360°), Richardson number (Ri=0.001–1000), Hartman number (Ha=0–100), the size and position of the heat source (B=0.2–0.8, D=0.3–0.7, respectively), nanoparticles volume fraction (ϕ=0.0–0.1), and the lid-direction of the horizontal walls (λ=±1) where the positive sign means lid-driven to the right while the negative sign means lid-driven to the left. The results show that the orientation and the strength of the magnetic field can play a significant role in controlling the convection under the effect of partial slip. It is also found that the natural convection decreases with increasing the length of the heat source for all ranges of the studied parameters, while it is do so due to the vertical distance up to Hartman number of 50, beyond this value the natural convection decreases with lifting the heat source narrower to the top wall.

Stagnation-Point Flow towards a Stretching Vertical Sheet with Slip Effects

The effects of partial slip on stagnation-point flow and heat transfer due to a stretching vertical sheet is investigated. Using a similarity transformation, the governing partial differential equations are reduced into a system of nonlinear ordinary differential equations. The resulting equations are solved numerically using a shooting method. The effect of slip and buoyancy parameters on the velocity, temperature, skin friction coefficient and the local Nusselt number are graphically presented and discussed. It is found that dual solutions exist in a certain range of slip and buoyancy parameters. The skin friction coefficient decreases while the Nusselt number increases as the slip parameter increases.

Unsteady Casson nanofluid flow over a stretching sheet with thermal radiation, convective and slip boundary conditions

In this paper we report on combined Dufour and Soret effects on the heat and mass transfer in a Casson nanofluid flow over an unsteady stretching sheet with thermal radiation and heat generation. The effects of partial slip on the velocity at the boundary, convective thermal boundary condition, Brownian and thermophoresis diffusion coefficients on the concentration boundary condition are investigated. The model equations are solved using the spectral relaxation method. The results indicate that the fluid flow, temperature and concentration profiles are significantly influenced by the fluid unsteadiness, the Casson parameter, magnetic parameter and the velocity slip. The effect of increasing the Casson parameter is to suppress the velocity and temperature growth. An increase in the Dufour parameter reduces the flow temperature, while an increase in the value of the Soret parameter causes increase in the concentration of the fluid. Again, increasing the velocity slip parameter reduces the velocity profile whereas increasing the heat generation parameter increases the temperature profile. A validation of the work is presented by comparing the current results with existing literature.

Partial slip effect in flow of magnetite-Fe3O4 nanoparticles between rotating stretchable disks

This paper addresses the flow of magnetic nanofluid (ferrofluid) between two parallel rotating stretchable disks with different rotating and stretching velocities. Water based fluid comprising magnetite-Fe3O4 nanoparticles is addressed. Velocity slip and temperature jump at solid–fluid interface are also taken into account. Appropriate transformations reduce the nonlinear partial differential system to ordinary differential system. Convergent series solutions are obtained. Effects of various pertinent parameters on the velocity and temperature profiles are shown and evaluated. Computations for skin friction coefficient and Nusselt number are presented and examined for the influence of involved parameters. It is noted that tangential velocity of fluid decreases for larger velocity slip parameter. Fluid temperature also reduces for increasing value of thermal slip parameter. Surface drag force and heat transfer rate at lower disk are enhanced when magnetic field strength is increased.

Effect of Mass and Partial Slip on Boundary Layer Flow of a Nanofluid over a Porous Plate Embedded In a Porous Medium

Effect of Mass and Partial Slip on Boundary Layer Flow of a Nanofluid over a Porous Plate Embedded In a Porous Medium

Effect of Partial Slip on Peristaltic Flow of a Sisko Fluid with Mild Stenosis through a Porous Medium

Effect of Partial Slip on Peristaltic Flow of a Sisko Fluid with Mild Stenosis through a Porous Medium

Hydromagnetic slip flow of nanofluid over a curved stretching surface with heat generation and thermal radiation

The objective of the present study is to discuss the flow and heat transfer in a two-dimensional boundary layer flow of an electrically conducting nanofluid over a curved stretching sheet coiled in a circle of radius R. In addition the effects of thermal radiation, heat generation and partial slip are also incorporated. Two types of nanofluid particles namely, Cu and Ag are discussed with water as a base fluid. The mathematical model of the flow situation under consideration is developed using a curvilinear coordinates system which results in a set of partial differential equations. A similarity solution of the governing flow and heat transfer problem is obtained numerically by shooting method. Physical quantities of interest are investigated including fluid velocity, temperature, skin-friction coefficient and the local Nusselt number. Comparison of the present results with the existing results in the literature for the flat surface i.e. (k→∞) is also given.

Steady MHD Boundary-layer Slip Flow and Heat Transfer of Nanofluid over a Convectively Heated of a Non-linear Permeable Sheet

The present study investigates the theoretical analysis on steady viscous incompressible MHD laminar boundary-layer flow and heat transfer of an electrically conducting nanofluid over a convectively heated nonlinear permeable sheet with partial slip using homotopy analysis method. The present model used for the nanofluid incorporates the combined effects of magnetic field, partial slip, Biot number, suction/injection, non-linear parameter, Brownian motion, and thermophoresis. We use local similarities variable, the governing equations which are nonlinear partial differential equations was transformed into a system couple of nonlinear ordinary differential equation, which are solved semi-analytical by using homotopy analysis method. Graphically results obtained for the velocity, temperature, and nanoparticle concentration profiles are displayed for various values of the existing parameters controlling the fluid flow: Slip parameter ζ, Magnetic field M, Biot number Bi, suction/injection parameter s, Brownian motion parameter Nb, and thermophoresis parameter Nt. It was found that the Biot number increase the dimensionless temperature profile. Numerical results obtained are compared with the previous published results found on literatures are in good agreement and are discussed quantitatively.

MHD Stagnation-Point Flow and Heat Transfer with Effects of Viscous Dissipation, Joule Heating and Partial Velocity Slip.

The steady two-dimensional stagnation-point flow and heat transfer past a permeable stretching/shrinking sheet with effects of viscous dissipation, Joule heating and partial velocity slip in the presence of a magnetic field is investigated. The partial differential equations are reduced to nonlinear ordinary differential equations by using a similarity transformation, before being solved numerically by shooting technique. Results indicate that the skin friction coefficient and the local Nusselt number increase as magnetic parameter increases. It is found that for the stretching sheet the solution is unique while for the shrinking sheet there exist nonunique solutions (dual solutions) in certain range of parameters. The stability analysis shows that the upper branch solution is stable while the lower branch solution is unstable.

Effects of partial slip on the peristaltic transport of a hyperbolic tangent fluid model in an asymmetric channel

In the present analysis, we have modeled the governing equations of two dimensional hyperbolic tangent fluid model under the assumptions of long wavelength and low Reynolds number. The flow is investigated in a wave frame of reference moving with the velocity of the wave. The governing equations of hyperbolic tangent fluid have been solved using regular perturbation method. The expression for pressure rise has been calculated using numerical integrations. The behavior of different physical parameters have been discussed graphically.

Partial slip effects in flow over nonlinear stretching surface

The two-dimensional flow of a viscous nanofluid is investigated. The flow is caused by a nonlinear stretching surface with the slip effects of the velocity, the temperature, and the concentration. The fluid is electrically conducted in the presence of an applied magnetic field. Appropriate transformations reduce the nonlinear partial differential system to an ordinary differential system. The convergent solutions of the governing nonlinear problems are computed. The results of the velocity, the temperature, and the concentration fields are calculated in series forms. The effects of the different parameters on the velocity, the temperature, and the concentration profiles are shown and analyzed. The skin friction coefficient, the Nusselt number, and the Sherwood number are also computed and investigated for different embedded parameters in the problem statements.

Analysis of heat transfer due to stretching cylinder with partial slip and prescribed heat flux: A Chebyshev Spectral Newton Iterative Scheme

This study is dedicated to analyze the combined effects of partial slip and prescribed surface heat flux when the fluid is moving due to stretching cylinder. A very moderate and powerful technique Chebyshev Spectral Newton Iterative Scheme is used to determine the solution of the present mathematical model. Involved physical parameters, namely the slip parameter, Casson fluid parameter, curvature parameter and Prandtl number are utilized to control the fluid moments and temperature distribution. The results show that the fluid velocity and the skin friction coefficient on the stretching cylinder are strongly influenced by the slip parameter. It is further analyzed that hydrodynamic boundary layer decreases and thermal boundary layer increases with the slip parameter. Influence of Casson fluid parameter on temperature profile provides the opposite behavior as compared to the slip parameter. The comparison of numerical values of skin friction coefficient and the local Nusselt number is made with the results available in the literature. The accuracy and convergence of Chebyshev Spectral Newton Iterative Scheme is compared with finite difference scheme (Keller box method) through tables. The CPU time is calculated for both schemes. It is observed that CSNIS is efficient, less time consuming, stable and rapid convergent.

Hydromagnetic peristaltic transport of water-based nanofluids with slip effects through an asymmetric channel

This paper addresses the effects of applied magnetic field and partial slip effects in peristalsis of water-based nanofluids in an asymmetric flow configuration. Analysis is carried out using silver and copper nanoparticles. Viscous dissipation, mixed convection, Ohmic heating and heat generation/absorption are considered. Mathematical modeling is done employing lubrication approximations. Resulting coupled system is solved numerically. Physical quantities like axial velocity, pressure gradient, temperature and heat transfer rate are graphically analyzed. Comparison between the silver–water and copper–water nanofluids is presented and analyzed. Results show that the maximum velocity, temperature and heat transfer rate at the wall in silver–water nanofluid are comparatively greater than that of copper–water nanofluid. It is also observed that addition of nanoparticles results in a decrease in the velocity and temperature of fluid. However, the heat transfer rate at the wall is enhanced through addition of nanoparticles.