Pressure-Driven Gas Flows in Micro Channels with a Slip Boundary:A Numerical Investigation

In this paper,flow of slightly rarefied compressible nitrogen in microchannels has been investigated numerically for low values of Reynolds and Mach numbers.The 2D governing equations were solved using Finite Element Method with first-order slip boundary conditions(Comsol Multiphysics software).A validation was performed by comparing with similar configuration from the literature.It was found that our model can accurately predict the pressure driven flow in microchannels.Several interesting findings are reported about the Relative pressure,longitudinal velocity,Mach number,effect of gas rarefaction and flow rate.

Slip effects on shearing flows in a porous medium

This paper deals with the magnetohydrodynamic （MHD） flow of an Oldroyd 8-constant fluid in a porous medium when no-slip condition is no longer valid. Modified Darcy＇s law is used in the flow modelling. The non-linear differential equation with non-linear boundary conditions is solved numerically using finite difference scheme in combination with an iterative technique. Numerical results are obtained for the Couette, Poiseuille and generalized Couette flows. The effects of slip parameters on the velocity profile are discussed.

Near continuum boundary layer flows at a flat plate

The problem of boundary layer flows at a flat plate surface with velocity-slip and temperature-jump boundary conditions is analyzed. With the velocity slip conditions, there are multiple physical factors lumped together, and the boundary layer solutions significantly change their behaviors. The self-similarity in the solutions degenerates, however, the problem is still an ordinary differential equation which can be solved. Shooting methods are applied to solve the flowfield. The results include velocity and temperature for both the surface and flowfield. Unlike the traditional Blasius fiat plate boundary layer solutions which are self-similar through all the plate boundary layer, the new solutions indicate that the front tip is actually a singularity point, especially at locations within one mean flee path from the leading edge.

Scaling group transformation for MHD boundary layer flow over permeable stretching sheet in presence of slip flow with Newtonian heating effects

Taking into account the slip flow effects, Newtonian heating, and thermal radiation, two-dimensional magnetohydrodynamic （MHD） flows and heat transfer past a permeable stretching sheet are investigated numerically. We use one parameter group transformation to develop similarity transformation. By using the similarity transformation, we transform the governing boundary layer equations along with the boundary conditions into ordinary differential equations with relevant boundary conditions. The obtained ordinary differential equations are solved with the fourth-fifth order Runge-Kutta- Fehlberg method using MAPLE 13. The present paper is compared with a published one. Good agreement is obtained. Numerical results for dimensionless velocity, temperature distributions, skin friction factor, and heat transfer rates are discussed for various values of controlling parameters.

Effects of slip condition on MHD stagnation-point flow over a power-law stretching sheet

The steady two-dimensional magnetohydrodynamic stagnation flow towards a nonlinear stretching surface is studied. The no-slip condition on the solid boundary is replaced with a partial slip condition. A scaling group transformation is used to get the invariants. Using the invariants, a third-order ordinary differential equation corresponding to the momentum is obtained. An analytical solution is obtained in a series form using a homotopy analysis method. Reliability and efficiency of series solutions are shown by the good agreement with numerical results presented in the literature. The effects of the slip parameter, the magnetic field parameter, the velocity ratio parameter, the suction velocity parameter, and the power law exponent on the flow are investigated. The results show that the velocity and shear stress profiles are greatly influenced by these parameters.

Water slip flow in superhydrophobic microtubes within laminar flow region

The fabrication of superhydrophobic surfaces and the studies on water flow characteristics therein are of great significance to many industrial areas as well as to science and technology development. Experiments were car- ried out to investigate slip characteristics of water flowing in circular superhydrophobic microtubes within lam- inar flow region. The superhydrophobic microtubes of stainless steel were fabricated with chemical etching- fluorination treatment. An experimental setup was designed to measure the pressure drop as function of water flow rate. For comparison, superhydrophilic tubes were also tested. Poiseuille number Po was found to be smaller for the superhydrophobic microtubes than that for superhydrophilic ones. The pressure drop reduc- tion ranges from 8% to 31%. It decreases with increasing Reynolds number when Re 〈 900, owing to the transition from Cassie state to Wenze] state. However, it is almost unchanged with further increasing Re after Re 〉 900. The slip length in superhydrophobic microtubes also exhibits a Reynolds number dependence similarly to the pressure drop reduction. The relation between slip length and Darcy friction factor is theoretically analyzed with consideration of surface roughness effect, which was testified with the experimental results.

Determination of Slip Length in Couette Flow Based on an Analytical Simulation Incorporating Surface Interaction

An analytical simulation based on a new model incorporating surface interaction is conducted to study the slip phenomenon in the Couette flow at different scales. The velocity profile is calculated by taking account of the micro-force between molecules and macro-force from the viscous shearing effect, as they contribute to the achieve- ment of the slip length. The calculated results are compared with those obtained from the molecular dynamics simulation, showing an excellent agreement. Further, the effect of the shear rate on the slip is investigated. The results can well predict the fluid flow behaviors on a solid substrate, but has to be proved by experiment.

Hydrothermal performance analysis of various surface roughness configurations in trapezoidal microchannels at slip flow regime

The effects of various surface roughness geometrical properties including roughness height(5%,10%,15%),number(3,6),and shape(rectangular and triangular)on the flow and heat transfer of slip-flow in trapezoidal microchannels were investigated.The effects of mentioned parameters on the heat transfer coefficient through the microchannel,average Nusselt number and pressure drop for Reynolds number of 5,10,15 and 20 were examined.The obtained results showed that increasing the roughness height and number increases the pressure drop due to higher stagnation effects before and after roughness elements and decreases the Nusselt number due to higher recirculation zones effects than obstruction effects.The most reduction in Nusselt number and the most increment in pressure drop occur at the roughness height of 15%,roughness number of 6 and Reynolds number of 20 by about 10.6%and 52.8%than the smooth microchannel respectively.

Slip flow in an annular sector duct using radial eigenfunctions

The fully developed slip flow in an annular sector duct is solved by expansions of eigenfunctions in the radial direction and boundary collocation on the straight sides. The method is efficient and accurate. The flow field for slip flow differs much from that of no-slip flow. The Poiseuille number increases with increased inner radius, opening angle, and decreases with slip.

Viscous Slip MHD Flow over a Moving Sheet with an Arbitrary Surface Velocity

The magnetohydrodynamic（MHD） flow induced by a stretching or shrinking sheet under slip conditions is studied.Analytical solutions based on the boundary layer assumption are obtained in a closed form and can be applied to a flow configuration with any arbitrary velocity distributions. Seven typical sheet velocity profiles are employed as illustrating examples. The solutions to the slip MHD flow are derived from the general solution and discussed in detail. Different from self-similar boundary layer flows, the flows studied in this work have solutions in explicit analytical forms. However, the current flows require special mass transfer at the wall, which is determined by the moving velocity of the sheet. The effects of the slip parameter, the mass transfer at the wall, and the magnetic field on the flow are also demonstrated.

Numerical study of homogeneous–heterogeneous reactions on stagnation point flow of ferrofluid with non-linear slip condition

This study deals with the stagnation point flow of ferrofluid over a flat plate with non-linear slip boundary condition in the presence of homogeneous-heterogeneous reactions.Three kinds of ferroparticles,namely,magnetite(Fe_3O_4),cobalt ferrite(CoFe_2O_4) and manganese zinc ferrite(Mn-ZnFe_2O_4) are taken into account with water and kerosene as conventional base fluids.The developed model of homogeneous-heterogeneous reactions in boundary layer flow with equal and unequal diffusivities for reactant and autocatalysis is considered.The governing partial differential equations are converted into system of non-linear ordinary differential equations by mean of similarity transformations.These ordinary differential equations are integrated numerically using shooting method.The effects of pertinent parameters on velocity and concentration profiles are presented graphically and discussed.We found that in the presence of Fe_3O_4-kerosene and CoFe_2O_4-kerosene,velocity profiles increase for large values of α and β whereas there is a decrement in concentration profiles with increasing values of if and K_s.Furthermore,the comparison between non-magnetic(A1_2O_3) and magnetic Fe_3O_4 nanoparticles is given in tabular form.

Slip-model Performance for Underexpanded Micro-scale Rocket Nozzle Flows

In aerospace Micro-Electro Mechanical Systems （MEMS）, the characteristic length scale of the flow approaches the molecular mean free path, thus invalidating the continuum description and enforcing the use of particle methods, like the Direct Simulation Monte Carlo （DSMC）, to deal with the non-equilibrium regions. Within the slip-regime （0.01〈Kn〈-0.1） both approaches, continuum and particle-based, seem to behave well in terms of accuracy. The present study summarizes the implementation and results obtained with a 2nO-order slip boundary condition in a Navier-Stokes solver to address the rarefaction near the nozzle walls. Its assessment and application to a cold-gas micro-scale conical nozzle of 300μm throat diameter, discharging into the low-pressure freestream, constitutes the major aim of the work. The slip-model incorporates the velocity slip with thermal creep and temperature jump, thus permitting to deal with non-isothermal flows as well. Results show that the gas experiences an intense rarefaction in the lip vicinity, pointing to the limits of model validity. Furthermore, a strong Mach deceleration is observed, attributed to the rather thick subsonic boundary layer and supersonic bulk heating caused by the viscous dissipation, in contrast with the expansion to occur in large rocket nozzles during underexpanded operation.

Simultaneous effects of magnetic field and space porosity on compressible Maxwell fluid transport induced by a surface acoustic wave in a microchannel

Peristaltic motion induced by a surface acoustic wave of a viscous, compressible and electrically conducting Maxwell fluid in a confined parallel-plane microchannel through a porous medium is investigated in the presence of a constant magnetic field. The slip velocity is considered and the problem is discussed only for the free pumping case. A perturbation technique is employed to analyze the problem in terms of a small amplitude ratio. The phenomenon of a “backward flow” is found to exist in the center and at the boundaries of the channel. In the second order approximation, the net axial velocity is calculated for various values of the fluid parameters. Finally, the effects of the parameters of interest on the mean axial velocity, the reversal flow, and the perturbation function are discussed and shown graphically. We find that in the non-Newtonian regime, there is a possibility of a fluid flow in the direction opposite to the propagation of the traveling wave. This work is the most general model of peristalsis created to date with wide-ranging applications in biological, geophysical and industrial fluid dynamics.

Erratum to“Simultaneous effects of magnetic field and space porosity on compressible Maxwell fluid transport induced by a surface acoustic wave in a microchannel”

We would like to acknowledge the misprinted terms in our published paper“Simultaneous effects of magnetic field and space porosity on compressible Maxwell fluid transport induced by a surface acoustic wave in a microchannel”[Chin.Phys.B 22124702(2013)].Since only two misprints exist and the main results of the published paper are correct,we present the correct equations in this erratum.

Discrete Boltzmann Method with Maxwell-Type Boundary Condition for Slip Flow

The rarefied effect of gas flow in microchannel is significant and cannot be well described by traditional hydrodynamic models. It has been known that discrete Boltzmann model(DBM) has the potential to investigate flows in a relatively wider range of Knudsen number because of its intrinsic kinetic nature inherited from Boltzmann equation.It is crucial to have a proper kinetic boundary condition for DBM to capture the velocity slip and the flow characteristics in the Knudsen layer. In this paper, we present a DBM combined with Maxwell-type boundary condition model for slip flow. The tangential momentum accommodation coefficient is introduced to implement a gas-surface interaction model.Both the velocity slip and the Knudsen layer under various Knudsen numbers and accommodation coefficients can be well described. Two kinds of slip flows, including Couette flow and Poiseuille flow, are simulated to verify the model.To dynamically compare results from different models, the relation between the definition of Knudsen number in hard sphere model and that in BGK model is clarified.

Slip Flow on Graphene:Current Status and Perspective

Fast fluid transport on graphene has attracted a growing body of research due to a wide range of potential applications including thermal management,water desalination,energy harvesting,and lab-on-a-chip.Here,we critically review the theoretical,simulational,and experimental progress regarding the fluid slippage on graphene.Based on the summary of the past studies,we give perspectives on future research directions towards complete understanding and practical applications of slip flow on graphene.

A non-isothermal Couette slip gas flow

A steady plane subsonic compressible non-isothermal Couette gas flow is analyzed for moderately high and low Reynolds numbers.The flow channel is formed by two plates in relative motion.Two cases are considered:(a) isothermal walls where the temperatures of the plates are equal and constant and(b) with constant but different plate temperatures.The Knudsen number is Kn 0.1,which corresponds to the slip and continuum flow.The flow is defined by continuity,Navier-Stokes and energy continuum equations,along with the velocity slip and the temperature jump first order boundary conditions.An analytical solution for velocity and temperature is obtained by developing a perturbation scheme.The first approximation corresponds to the continuum flow conditions,while the others represent the contribution of the rarefaction effect.In addition,a numerical solution of the problems is given to confirm the accuracy of the analytical results.The exact analytical solution,for constant viscosity and conductivity is found for the isothermal walls case as well.It is shown that it is entirely a substitution to the exact numerical solution for the isothermal walls case.

Numerical solution of thermo-solutal mixed convective slip flow from a radiative plate with convective boundary condition

A mathematical model for mixed convective slip flow with heat and mass transfer in the presence of thermal radiation is presented. A convective boundary condition is included and slip is simulated via the hydrodynamic slip parameter. Heat generation and absorption effects are also incorporated. The Rosseland diffusion flux model is employed. The governing partial differential conservation equations are reduced to a system of coupled, ordinary differential equations via Lie group theory method. The resulting coupled equations are solved using shooting method. The influences of the emerging parameters on dimensionless velocity, tempera- ture and concentration distributions are investigated. Increasing radiative-conductive parameter accelerates the boundary layer flow and increases temperature whereas it depresses concentration. An elevation in convection-conduction parameter also accelerates the flow and temperatures whereas it reduces concentrations. Velocity near the wall is considerably boosted with increasing momentum slip parameter although both temperature and concentration boundary layer thicknesses are decreased. The presence of a heat source is found to increase momentum and thermal boundary layer thicknesses but reduces concentration boundary layer thickness. Excelle- nt correlation of the numerical solutions with previous non-slip studies is demonstrated. The current study has applications in bio- reactor diffusion flows and high-temperature chemical materials processing systems.

Rotational Slip Flow in Coaxial Cylinders by the Finite-Difference Lattice Boltzmann Methods

Recent studies on applications of the lattice Boltzmann method(LBM)and the finite-difference lattice Boltzmann method(FDLBM)to velocity slip simulations are mostly on one-dimensional(1D)problems such as a shear flow between parallel plates.Applications to a 2D problem may raise new issues.The author performed numerical simulations of rotational slip flow in coaxial cylinders as an example of 2D problem.Two types of 2D models were used.The first were multi-speed FDLBM models proposed by the author.The second was a standard LBM,the D2Q9 model.The simulations were performed applying a finite difference scheme to both the models.The study had two objectives.The first was to investigate the accuracies of LBM and FDLBM on applications to rotational slip flow.The second was to obtain an experience on application of the cylindrical coordinate system.The FDLBM model with 8 directions and the D2Q9 model showed an anisotropic flow pattern when the relaxation time constant or the Knudsen number was large.The FDLBM model with 24 directions showed accurate results even at large Knudsen numbers.

Assessment of micro-scale heat exchangers efficiency using lattice Boltzmann method and design of experiments

The study is focused on the use of nanofluids in a micro-open tall cavity,which is a type of micro heat exchanger(MHE).The cavity is heated from the bottom sidewall in a sinusoidal pattern,and the effects of four input parameters(Ra,Ha,Kn,and Vf)on heat transfer and irreversibility are investigated using numerical simulations based on Lattice Boltzmann Method(LBM).The findings of the study suggest that the local heat transfer on the bottom sidewall is strongly influenced by Ra and Ha,while the surface distribution of entropy generation is mainly dependent on Kn.The study also shows that the optimization of the magnitude and wavelength of the sinusoidal temperature can improve both local heat transfer and surface distribution of entropy generation.The results of the study provide valuable insights into the design of micro heat exchangers and suggest that the optimization of micro-porous geometries using DOE could lead to increased energy efficiency.The study contributes to our understanding of the complex interactions between input parameters in micro heat exchangers and highlights the importance of considering multiple parameters in the design process.