Second-order Slip Effects Research Articles

Impact of Second-Order Slip on Radiative Magnetohydrodynamics Rotating Flow in Channel

In our current investigation, we have discussed the effects of second-order slip and radiation on the flow of a generalized rotating fluid inside a channel in the presence of a magnetic field. The flow equations are transformed into a set of ordinary differential equations with the help of suitable similarity transformations, and the resultant coupled nonlinear ordinary differential equations are solved analytically. Using the obtained results, the effects of the involved physical parameters on the flow dynamics are examined and described physically. In addition, Pearson’s coefficient of correlation has been utilized to measure the linear association between different variables. The impact of emerging dimensionless parameters such as Hartman number, rotation parameter, radiation parameter, viscosity parameter, first- and second-order slip parameter, Schmidt number, and suction parameter on the Nusselt number and Sherwood number have all been investigated using a slope linear regression approach across the whole data points. The t-test approach has been adopted to explore the relationship between various involved physical parameters.

MHD flow study of viscous fluid through a complex wavy curved surface due to bio-mimetic propulsion under porosity and second-order slip effects

The steady laminar flow of viscous fluid from a curved porous domain under a radial magnetic field is considered. The fluid flow by a curved domain is due to peristaltic waves present at the boundary walls. The whole analysis is based on porosity (Darcy number) effects. Moreover, the effects of second-order slip on the rheology analysis are also discussed. Due to the complex nature of the flow regime, we have governed the rheological equations by using curvilinear coordinates in the fixed frame. The physical influence of magnetic (Hartmann number) and porosity (Darcy number) parameters on the rheological features of peristaltic transportation are argued in detailed (in the wave frame). Additionally, in the current study, the complex wavy pattern on both boundary walls of the channel is used. The whole rheological study is based on ancient, but medically valid, assumptions of creeping phenomena and long wavelength assumptions. Analytical solutions of the governing equations are obtained by using the simple integration technique in Mathematica software 11.0. The core motivation of the present analysis is to perceive the physical influence of embedded parameters, such as the dimensionless radius of the curvature parameter, magnetic parameter, porosity parameter, different amplitude ratios of complex peristaltic waves, first- and second-order slip parameters, on the axial velocity, pressure gradient, local wall shear stress, tangential component of the extra-stress tensor, pumping and trapping phenomena.

A mathematical model for bioconvection flow of Williamson nanofluid over a stretching cylinder featuring variable thermal conductivity, activation energy and second-order slip

The significant bioconvection phenomenon with the utilization of nanoparticles encountered fundamental industrial and technological applications in recent years. This communication addressed the bioconvection phenomenon in the flow of magnetized Williamson nanoparticles with additional features of activation energy and heat absorption/generation. The analysis has been suggested by imposing the interesting features of the second-order slip effects and convective Nield boundary constraints. The flow problem based on the relevant laws results in a set of partial differential equations which are further retarded into ordinary differential forms. The numerical approach based on shooting algorithm is introduced to impose the numerical solution by using MATLAB software. The flow parameters governed with the flow equations are graphically explored with associated physical consequences. The numerical division for local Nusselt number, local Sherwood number and motile number is presented while assigning diverse values to the involved parameters. The reported theoretical simulations can be more effective to enhance the thermal extrusion processes and solar energy systems. It is observed that the presence of first- and second-order slip parameters significantly controls the associated boundary layers of velocity, temperature, concentration and gyrotactic microorganism profiles.

Generalized second-order slip for unsteady convective flow of a nanofluid: a utilization of Buongiorno’s two-component nonhomogeneous equilibrium model

AbstractThe unsteady convective boundary layer flow of a nanofluid along a permeable shrinking/stretching plate under suction and second-order slip effects has been developed. Buongiorno’s two-component nonhomogeneous equilibrium model is implemented to take the effects of Brownian motion and thermophoresis into consideration. It can be emphasized that, our two-phase nanofluid model along with slip concentration at the wall shows better physical aspects relative to taking the constant volume concentration at the wall. The similarity transformation method (STM), allows us to reducing nonlinear governing PDEs to nonlinear dimensionless ODEs, before being solved numerically by employing the Keller-box method (KBM). The graphical results portray the effects of model parameters on boundary layer behavior. Moreover, results validation has been demonstrated as the skin friction and the reduced Nusselt number. We understand shrinking plate case is a key factor affecting non-uniqueness of the solutions and the range of the shrinking parameter for which the solution exists, increases with the first order slip parameter, the absolute value of the second order slip parameter as well as the transpiration rate parameter. Besides, the second-order slip at the interface decreases the rate of heat transfer in a nanofluid. Finally, the analysis for no-slip and first-order slip boundary conditions can also be retrieved as special cases of the present model.

Convective radiative plane Poiseuille flow of nanofluid through porous medium with slip: An application of Stefan blowing

Effects of second order slip on plane Poiseuille nanofluid under the influence of Stefan blowing in a channel are discovered in this study. The starring role of heat transfer, magnetic field and porosity are all together taken into account. The mathematical modeling is performed via Buongiorno's model. The effectual reliability of analytical solutions derived by homotopy analysis method is verified through h-curves as well as by means of residual errors norms in each case. Impact of physical factors is examined via graphs numerical tables. The slowing down effects of Stefan blowing are significantly seen for velocity and temperature profiles whereas opposite characteristic for the case of nanoparticle concentrations is noticed. Also an extra sensitivity in the field of velocity is observed for second- order slip as compared to first order -slip.

Effects of second-order slip and drag reduction in boundary layer flows

Abstract In this paper, boundary layer flow over a moving flat plate with second-order velocity slip, injection and applied magnetic field is analyzed. The governing partial differential equations are converted in to a nonlinear ordinary differential equation through an appropriate similarity transformation. The resulting nonlinear equation is solved via homotopy analysis method (HAM). Errors ranging from 10–7 to 10–10 are reported for a relatively few terms. The effects of the pertinent parameters on the velocity and the shear stress are presented graphically and discussed. In the absence of magnetic field and the two slip parameters, the results are found to be in excellent agreement with the available results in the literature. It is expected that the results obtained will not only provide useful information for industrial applications but also complement the earlier works.

Hall current, Newtonian heating and second-order slip effects on convective magneto-micropolar fluid flow over a sheet

This research deals with an analysis of the Hall current effect on the mixed convective magneto-micropolar fluid flow over a permeable stretching/shrinking sheet. Impact of the Newtonian heating parameter is analyzed in the slip flow regime. The nonlinear equations of the fluid flow are derived with the help of a similarity transform and its solutions are obtained by Optimal Homotopy Analysis Method (OHAM). For limiting cases, obtained results are in excellent agreement with the available exact and numerical results in the literature. The graphical and tabular representations of the obtained results show significant effects of the physical parameters on the magneto-micropolar fluid flow and heat transfer characteristics. In particular, it is observed that, as the sheet stretches, a change in the Hall current parameter yields a higher horizontal velocity component for the lower value of the magnetic field parameter; while it produces a higher and shorter transverse velocity profile at high intensity of the magnetic field. In Magnetohydrodynamics (MHD) generators, Hall effects are an important consideration to analyze the heat transfer phenomenon with high temperature conducting fluids.

MHD forced convection ow and heat transfer of ferro fluids over a moving at plate with uniform heat flux and second-order slip effects

In this study, the problem of two-dimensional forced convection MHD flow and heat transfer of ferro fluids over a moving at plate with the influence of uniform heat flux and secondorder slip eff ects is considered. By applying the similarity transformation, the governing equations are reconstructed into the similarity equations and the resulting equations are solved via shooting technique. Then, we implement a stability analysis in order to verify which solutions are stable and physically realizable. The e ects of the magnetic parameter,moving parameter, mass transfer parameter, rst-order surface slip parameter, second-order surface slip parameter and volume fraction of solid ferroparticles on the dimensionless velocity, temperature, skin friction and Nusselt numbers are discussed in the form of tabular and graphical presentation. For this present study, we consider the results based on three preferred ferroparticles, namely magnetite, cobalt ferrite and Mn-Zn ferrite in water- and kerosene-based fluids. The results display the existence of dual solutions for a plate moving towards the origin in which the rst solution is stable and physically realizable, while the second solution is not. Moreover, it is demonstrated that the magnetic, moving, mass transfer and slip eff ects together with the volume fraction of ferro fluids delay the boundary layer separation.

Effects of second-order slip on the flow of a fractional Maxwell MHD fluid

The magnetohydrodynamic (MHD) flow of a generalized Maxwell fluid induced by a moving plate has been investigated, where the second-order slip between the wall and the fluid in the wall is considered. The fractional calculus approach is used to establish the constitutive relationship model of the non-Newtonian fluid model. Exact analytical solutions for the velocity field and shear stress in terms of Fox H-function are obtained by means of the Laplace transform. The solutions for the generalized Maxwell second-order slip model without magnetic field, the MHD flow of generalized Maxwell flow without slip effects or first-order slip model can be derived as the special cases. Furthermore, the influence of the order of fractional derivative, the magnetic body force, the slip coefficients and power index on the velocity and shear stress are analyzed and discussed in detail. The results show that the velocity corresponding to flows with slip condition is lower than that for flow with non-slip conditions, and the velocity with second-slip condition is lower than that with first-order slip condition.

Effects of Second-Order Slip and Viscous Dissipation on the Analysis of the Boundary Layer Flow and Heat Transfer Characteristics of a Casson Fluid

The aim of the present study is to analyze numerically the steady boundary layer flow and heat transfer characteristics of Casson fluid with variable temperature and viscous dissipation past a permeable shrinking sheet with second order slip velocity. Using appropriate similarity transformations, the basic nonlinear partial differential equations have been transformed into ordinary differential equations. These equations have been solved numerically for different values of the governing parameters namely: shrinking parametersuction parameterCasson parameterfirst order slip parametersecond order slip parameter Prandtl number and the Eckert number using the bvp4c function from MATLAB. A stability analysis has also been performed. Numerical results have been obtained for the reduced skin-friction, heat transfer and the velocity and temperature profiles. The results indicate that dual solutions exist for the shrinking surface for certain values of the parameter space. The stability analysis indicates that the lower solution branch is unstable, while the upper solution branch is stable and physically realizable. In addition, it is shown that for a viscous fluida very good agreement exists between the present numerical results and those reported in the open literature. The present results are original and new for the boundary-layer flow and heat transfer past a shrinking sheet in a Casson fluid. Therefore, this study has importance for researchers working in the area of non-Newtonian fluids, in order for them to become familiar with the flow behavior and properties of such fluids.

Effects of Second-Order Slip and Magnetic Field on Mixed Convection Stagnation-Point Flow of a Maxwellian Fluid: Multiple Solutions

In this paper, we investigate the effects of second-order slip and magnetic field on the nonlinear mixed convection stagnation-point flow toward a vertical permeable stretching/shrinking sheet in an upper convected Maxwell (UCM) fluid with variable surface temperature. Numerical results are obtained using the bvp4c function from matlab for the reduced skin-friction coefficient, the rate of heat transfer, the velocity, and the temperature profiles. The results indicate that multiple (dual) solutions exist for a buoyancy opposing flow for certain values of the parameter space irrespective to the types of surfaces whether it is stretched or shrinked. It is found that an applied magnetic field compensates the suction velocity for the existence of the dual solutions. Depending on the parametric conditions; elastic parameter, magnetic field parameter, first- and second-order slip parameters significantly controls the flow and heat transfer characteristics. The illustrated streamlines show that for upper branch solutions, the effects of stretching and suction are direct and obvious as the flow near the surface is seen to suck through the permeable sheet and drag away from the origin of the sheet. However, aligned but reverse flow occurs for the case of lower branch solutions when the mixed convection effect is less significant.

Second-Order Slip Effects on Heat Transfer of Nanofluid with Reynolds Model of Viscosity in a Coaxial Cylinder

Abstract The present work makes an analysis on the effects of second-order velocity slip and temperature jump boundary conditions for third-grade nanofluid over a coaxial cylinder. In the modeling of blood-based nanofluids containing metal or metal oxide nanoparticles, the viscosity is approximated to second-order Maclaurin’s series for the first time and the effective density is handled to a combination of temperature and nanoparticles volume fraction. The governing equations are transformed into a dimensionless system of nonlinear differential equations and solved by homotopy analysis method (HAM). The accuracy and efficiency of the HAM solutions are verified by ℏ $$\hbar $$ -curves and residual error curves using package BVPh2.0. The physical interpretations are illustrated by graphs and tables. The results revealed that the Nusselt number increases with an increase of nanoparticle volume fraction. The second-order velocity slip has a significant weakened effect on the skin friction. In addition, the Brownian motion and thermophoresis movement are collaborating to increase the temperature profile.

Theory of binary spiral-grooved gas bearings

Viscous gas flow in the clearance of a bearing with spiral grooves of different depths on both working surfaces is investigated. In the boundary conditions for the velocities the first- and second-order slip effects are taken into account on the basis of the Cercignani-Slezkin method. An essentially nonlinear differential equation determining the law of pressure variation in the active zone of the bearing is derived. The theory developed is compared with experiment [1] with reference to the example of a physical model with closed center and conclusions concerning the advantages of binary models are drawn.

Second-order slip effects in Poiseuille flow

Plane Poiseuille flow of a rarefied gas was studied in the presence of both a pressure and a temperature gradient under near continuum conditions. Calculations are performed for general gas–gas and gas–surface interactions of the molecules. The second-order slip and the phenomenological coefficients of the symmetric Onsager matrix were explicitly calculated by variational techniques. The slip velocity and the contributions of the Knudsen layer to mass and heat flows are described by a second symmetric matrix.