Couette flow with slip and jump boundary conditions

The steady plane Couette flow is analyzed within the framework of the five field equations of mass, momentum and energy for a Newtonian viscous heat conducting ideal gas in which slip and jump boundary conditions are considered. The results obtained are compared with those that follow from the direct simulation Monte Carlo method. Received July 10, 2000     

Analysis of gaseous flow in a micropipe with second order velocity slip and temperature jump boundary conditions

In this paper, second order velocity slip and temperature jump boundary conditions are used to solve the momentum and energy equations along with isoflux thermal boundary condition at the surface of the micropipe. The flow is assumed to be hydrodynamically and thermally fully developed inside the micropipe and viscous dissipation is included in the analysis. The solution yields closed form expressions for the temperature field and Nusselt number (Nu) as a function of various modeling parameters, namely, Knudsen number and Brinkman number (Br). For the given values of Br, the maximum difference of Nu between continuum flow with first order slip model and continuum and, second order slip model is found to be 35.67 and 34.62 %, respectively. Present solution exhibits good agreement with the other theoretical models.     

Convection in a porous medium with velocity slip and temperature jump boundary conditions

The onset of convection in a rarefield gas saturating a horizontal layer of a porous medium has been investigated using both Darcy and Brinkman models. It is assumed that due to rarefaction both velocity slip and temperature jump exist at the boundaries. The results show that (i) when the degree of rarefaction increases the critical Rayleigh number as well as the critical wave number for the onset of convection increases, (ii) stabilizing effect of temperature jump is more than that of velocity slip, (iii) Darcy model is seen to be the most stable one when compared to Brinkman model or the pure gaseous layer (i.e. in the absence of porous medium).     

Unsteady Couette flow of a micropolar fluid with slip

The unsteady Couette flow of an isothermal incompressible micropolar fluid between two infinite parallel plates is investigated. The motion of the fluid is produced by a time-dependent impulsive motion of the lower plate while the upper plate is set at rest. A linear slip, of Basset type, boundary condition on both plates is used. Two particular cases are discussed; in the first case we have assumed that the plate moves with constant speed and in the second case we have supposed that the plate oscillates tangentially. The solution of the problem is obtained in the Laplace transform domain. The inversion of the Laplace transform is carried out numerically using a numerical method based on Fourier series expansion. Numerical results are represented graphically for the velocity, microrotation, and volume flux for various values of the time, slip and micropolar parameters.     

Newtonian plane Couette flow with dynamic wall slip

Meccanica - The occurrence of slip complicates the estimation of the viscosity in rheometric flows. Thus, special analyses and experimental protocols are needed in order to obtain reliable...     

Burnett simulation of flow and heat transfer in micro Couette flow using second-order slip conditions

The conventional Burnett equations with second-order velocity slip and temperature jump conditions were applied to the steady-state micro Couette flow of a Maxwellian monatomic gas. An analytical approach as well as a relaxation method was used to determine the velocity slip and temperature jump at the wall. Convergent solutions to the Burnett equations were obtained on arbitrary fine numerical grids for all Knudsen numbers (Kn) up to the limit of the equations’ validity. The Burnett equations with second-order slip conditions indicate a much better agreement with DSMC data over the first-order slip conditions at high Kn. The convergent Burnett solutions were obtained in orders of magnitude quicker than that with the corresponding DSMC simulation. The augmented Burnett equations were also introduced to model the flow but no obvious improvement in the results was found.     

Stokes equations with penalised slip boundary conditions

We consider the finite-element approximation of Stokes equations with slip boundary conditions imposed with the penalty method. In the case of a smooth curved boundary, our numerical results suggest that curved finite elements, regularised normal vectors or reduced integration techniques can be used to avoid a Babuska’s-type paradox and ensure the convergence of finite-element approximations to the exact solution. Convergence orders with these remedies are also compared.     

SQUEEZE FILM FLOW WITH NONLINEAR BOUNDARY SLIP

A nonlinear boundary slip model consisting of an initial slip length and a critical shear rate was used to study the nonlinear boundary slip of squeeze fluid film confined between two approaching spheres. It is found that the initial slip length controls the slip behavior at small shear rate, but the critical shear rate controls the boundary slip at high shear rate. The boundary slip at the squeeze fluid film of spherical surfaces is a strongly nonlinear function of the radius coordinate. At the center or far from the center of the squeeze film, the slip length equals the initial slip length due to the small shear rate. However, in the high shear rate regime the slip length increases very much. The hydrodynamic force of the spherical squeeze film decreases with increasing the initial slip length and decreasing the critical shear rate. The effect of initial slip length on the hydrodynamic force seems less than that of the critical shear rate. When the critical shear rate is very small the hydrodynamic force increases very slowly with a decrease in minimum film thickness. The theoretical predictions agree well with the experiment measurements.     

Free-convection flow about a wedge under mixed thermal boundary conditions and a magnetic field

A similarity analysis was performed to investigate the laminar free-convection boundary-layer flow in the presence of a transverse magnetic field over a wedge with mixed thermal boundary conditions. Boundary-layer velocity and temperature profiles were determined numerically for various values of the Prandtl number and the magnetic parameter. The results show that the magnetic field retards the velocity profiles and increases the skin friction. The temperature profiles were expanded with increasing values of the magnetic parameter resulting in higher surface temperatures. A transformation relating the similarity solutions of the boundary-layer velocity and temperature profiles associated with different values of the mixed thermal boundary condition parameter was obtained.     

Unsteady incompressible Couette flow in a uniform transverse magnetic field

Summary The unsteady plane Couette flow of an incompressible, viscous and infinitely conducting fluid in a uniformly imposed transverse magnetic field is studied. The problem is solved in general in a series form by means of a finite Fourier transform, and explicit solutions for two special cases are worked out.     

On flows of third-grade fluids with non-linear slip boundary conditions

We prove the existence and uniqueness of steady flows of incompressible fluids of grade three subject to slip and no-slip boundary conditions in bounded domains. The slip boundary condition is a non-linear generalization of the Navier slip boundary condition and permits situations in which the solid boundary undergoes non-rigid tangential motion. The existence proof is based on a fixed point method in which the boundary-value problem is decomposed into four linear problems.     

Exact solution for compressive flow of viscoplastic fluids under perfect slip wall boundary conditions

Based on the perfect slip condition between rigid walls and fluids, the compressive flow of Herschel-Bulkley fluids and biviscous fluids was studied. The explicit expressions of stresses and fluid velocity were given. To move the rigid walls for a Herschel-Bulkley fluid with the yield stress (τ₀), the mean pressure applied onto the rigid wall should be larger than 2τ₀/. No yield surface exists in the interior of the fluids when flow occurs. For a biviscous fluid, a critical load was given. The fluid behaves like the Bingham fluid when the external applied load onto the wall is larger than the critical load, otherwise the fluid is Newtonian. Received: 10 June 1997 Accepted: 22 September 1997     

Hydromagnetic oscillatory Couette flow in rotating system with induced magnetic field

This paper presents a study of hydromagnetic Couette flow of an incompress- ible and electrically conducting fluid between two parallel rotating plates, one of which is oscillating in its own plane. A uniform transverse magnetic field is used, and the induced magnetic field is taken into account. The exact solution to the governing equations is obtained in a closed form. The solution to the problem in the case of vanishing and small finite magnetic Prandtl numbers is also derived from the general solution. The asymp- totic behavior of the solution for large values of the frequency parameter is analyzed to gain some physical insights into the flow pattern. Expressions for the shear stress at both the oscillatory and stationary plates due to primary and secondary flows and mass flow rate in the primary and secondary flow directions are also obtained. The results of the fluid velocity and the induced magnetic field are presented. The shear stresses on the plates due to the primary and secondary flows and the corresponding mass flow rates are presented in a tabular form.     

Non-Newtonian biomagnetic fluid flow through a stenosed bifurcated artery with a slip boundary condition

The effects of a velocity slip and an external magnetic field on the flow of biomagnetic fluid(blood) through a stenosed bifurcated artery are investigated by using ANSYS FLUENT. Blood is regarded as a non-Newtonian power-law fluid, and the magnetization and electrical conductivity are considered in the mathematical model.The no-slip condition is replaced by the first-order slip condition. The slip boundary condition and magnetic force are compiled in the solver by the user-defined function(UDF)...     

Thermal slip boundary conditions in vibrational nonequilibrium flows

This paper deals with new thermal jump boundary conditions at the wall in polyatomic gas flows. The calculations and results especially concern vibrational nonequilibrium conditions when the dissociation effects may be neglected. First the usual conditions are briefly described. Then the boundary conditions proposed in the paper are justified on the basis of previous experimental results and by developing direct heat flux calculations at the wall. Analytical expressions and numerical values of the various fluxes are presented.     

Numerical simulation of laminar flow past a circular cylinder with slip conditions

The no‐slip condition is an assumption that cannot be derived from first principles and a growing number of literatures replace the no‐slip condition with partial‐slip condition, or Navier‐slip condition. In this study, the influence of partial‐slip boundary conditions on the laminar flow properties past a circular cylinder was examined. Shallow‐water equations are solved by using the finite element method accommodating SU/PG scheme. Four Reynolds numbers (20, 40, 80, and 100) and six slip lengths were considered in the numerical simulation to investigate the effects of slip length and Reynolds number on characteristic parameters such as wall vorticity, drag coefficient, separation angle, wake length, velocity distributions on and behind the cylinder, lift coefficient, and Strouhal number. The simulation results revealed that as the slip length increases, the drag coefficient decreases since the frictional component of drag is reduced, and the shear layer developed along the cylinder surface tends to push the separation point away toward the rear stagnation point so that it has larger separation angle than that of the no‐slip condition. The length of the wake bubble zone was shortened by the combined effects of the reduced wall vorticity and wall shear stress which caused a shift of the reattachment point closer to the cylinder. The frequency of the asymmetrical vortex formation with partial slip velocity was increased due to the intrinsic inertial effect of the Navier‐slip condition. Copyright © 2011 John Wiley & Sons, Ltd.     

Rayleigh problem in slip flow with transverse magnetic field

An analytical continuum solution of the Rayleigh problem in slip flow with applied magnetic field is obtained using a modified initial condition and slip boundary conditions. The results are uniformly valid for all times and show that the velocity slip and the local skin friction coefficient remain almost unaffected by the imposition of the magnetic field for small times. They increase however with the magnetic field for large times. The present results reduce to the corresponding results of the hydrodynamic case when there is no magnetic field.Nomenclature A constant - b characteristic length - B magnetic field vector - B ₀ magntidue of the applied magnetic field normale to the plate - B _x magnitude of the induced magnetic field parallel to the plate - C slip coefficient, (2–f)/f - C _f skin friction coefficient, - C _D average drag coefficient - erfc(_x) complementary error function, - E electric field vector - f Maxwell's reflection coefficient - H _a Hartmann number, (B ₀ ² b ²/)^1/2 - nondimensional magnetic parameter - J current vector - Kn=L/b Knudsen number - L mean free path - M Mach number - p constant parameter - P _m magnetic Prandtl number, Re _m/Re= ₀ - q velocity vector - Re Reynolds number, Ub/ - Re _m magnetic Reynolds number, ₀ Ub - t time - nondimensional time, tU/b - u velocity of the fluid parallel to the plate - nondimensional velocity, u/U - U velocity of the plate - Laplace transform of - x, y coordinates along and normal to the plate respectively - y nondimensional distance, y/b - Z nondimensional parameter, 1/Re ^1/2 Kn - ratio of specific heats - boundary layer thickness - velocity slip - viscosity - ₀ magnetic permeability - kinematic viscosity - nondimensional time parameter, ( /Re)^1/2/Kn - density - electrical conductivity     

Meshless Galerkin analysis of Stokes slip flow with boundary integral equations

This paper presents a novel meshless Galerkin scheme for modeling incompressible slip Stokes flows in 2D. The boundary value problem is reformulated as boundary integral equations of the first kind which is then converted into an equivalent variational problem with constraint. We introduce a Lagrangian multiplier to incorporate the constraint and apply the moving least‐squares approximations to generate trial and test functions. In this boundary‐type meshless method, boundary conditions can be implemented exactly and system matrices are symmetric. Unlike the domain‐type method, this Galerkin scheme requires only a nodal structure on the bounding surface of a body for approximation of boundary unknowns. The convergence and abstract error estimates of this new approach are given. Numerical examples are also presented to show the efficiency of the method. Copyright © 2009 John Wiley & Sons, Ltd.     

Squeeze flow of Bingham fluids under slip with friction boundary condition

This paper develops a theoretical analysis of a Bingham fluid in slipping squeeze flow. The flow field decomposition consists in combining a central extensional flow zone in the plane of symmetry and shear flow zones near the plates. It is also considered that the slipping zone is located around a central sticking zone as previously shown from experiments. It is assumed that the shear stress at the plates is constant in the slipping zone and equals a fixed friction yield value. The squeeze force required to compress a Bingham fluid under the slipping behaviour as well as the radial evolution of the transition point between both sticking and slipping zones are finally determined.