Gaseous slip flow forced convection through ordered microcylinders

This is a theoretical study dealing with longitudinal gaseous slip flow forced convection between a periodic bunch of microcylinders arranged in regular array. The selected geometry has applications in microscale pin fin heat sinks used for cooling of microchips. The flow is considered to be hydrodynamically and thermally fully developed. The two axially constant heat flux boundary conditions of H1 and H2 are considered in the analysis. The velocity and temperature discontinuities at the boundary are incorporated into the solutions using the first order slip boundary conditions. The method considered is mainly analytical in which the governing equations and three of the boundary conditions are exactly satisfied. The remaining symmetry condition on the right-hand boundary of the typical element is applied to the solution through the point matching technique. The results show that both the Poiseuille number and the Nusselt number are decreasing functions of the degree of rarefaction characterized by the Knudsen number. While an increase in the blockage ratio leads to a higher Poiseuille number, the functionality of the Nusselt number on this parameter is not monotonic. At small and moderate values of the blockage ratio, the Nusselt number is higher for a higher blockage ratio, whereas the opposite may be right for higher values of this parameter. It is also observed that the angular variations of the parameters are reduced at smaller blockage ratios. Accordingly, the H1 and H2 Nusselt numbers are the same for small and moderate blockage ratios.     

Pressure distributions of gaseous slip flow in straight and uniform rectangular microchannels

This paper presents analytical derivations of the pressure distribution in straight and uniform rectangular microchannels in the slip flow regime and new experimental data in those channels. The flow is to be steady state, two-dimensional, isothermal, and to have negligible transverse velocities with a first order slip boundary condition. The measured pressure distributions of airflows are compared with newly derived analytical results. There is close agreement between the measurements and calculation by the slip flow formula. The dimensionless location of the maximum deviation from the linear pressure distribution is found analytically and compared with the measurements. This dimensionless location of the maximum deviation increases with the increasing pressure ratios in the slip flow regime. The effect of several parameters such as the channel aspect ratio and the Knudsen number on the locations of maximum deviation from linearity are investigated. The nonlinearity of the pressure distribution is also discussed.     

Second-order gaseous slip flow models in long circular and noncircular microchannels and nanochannels

This paper significantly extends previous studies to the transition regime by employing the second-order slip boundary conditions. A simple analytical model with second-order slip boundary conditions for a normalized Poiseuille number is proposed. The model can be applied to either rarefied gas flows or apparent liquid slip flows. The developed simple models can be used to predict the Poiseuille number, mass flow rate, tangential momentum accommodation coefficient, pressure distribution of gaseous flow in noncircular microchannels and nanochannels by the research community for the practical engineering design of microchannels and nanochannels. The developed second-order models are preferable since the difficulty and “investment” is negligible compared with the cost of alternative methods such as molecular simulations or solutions of Boltzmann equation. Navier–Stokes equations with second-order slip models can be used to predict quantities of engineering interest such as the Poiseuille number, tangential momentum accommodation coefficient, mass flow rate, pressure distribution, and pressure drop beyond its typically acknowledged limit of application. The appropriate or effective second-order slip coefficients include the contribution of the Knudsen layers in order to capture the complete solution of the Boltzmann equation for the Poiseuille number, mass flow rate, and pressure distribution. It could be reasonable that various researchers proposed different second-order slip coefficients because the values are naturally different in different Knudsen number regimes. It is analytically shown that the Knudsen’s minimum can be predicted with the second-order model and the Knudsen value of the occurrence of Knudsen’s minimum depends on inlet and outlet pressure ratio. The compressibility and rarefaction effects on mass flow rate and the curvature of the pressure distribution by employing first-order and second-order slip flow models are analyzed and compared. The condition of linear pressure distribution is given.     

Theoretical analysis of the frictional losses in magnetohydrodynamic microflows considering slippage

In this article, we study the frictional losses in magnetohydrodynamic (MHD) microflows by analyzing the Poiseuille number defined through the Darcy–Weisbach friction factor. We consider two-dimensional fully developed flow models characteristic of MHD micropumps including the Hartmann braking effect and the existence of slippage. Unlike the purely hydrodynamic case, in MHD flows the Poiseuille number depends not only on the aspect ratio but also on the physical properties of the fluid and the externally applied magnetic field. Three different combinations of boundary conditions (slip and no-slip) are investigated. Calculations show that the Poiseuille number is considerably reduced as the dimensionless slip length is increased, while it increases as Hartmann number does. The obtained results are consistent with previous models and are helpful for the design of magnetohydrodynamic microflow devices.

     

Analytical solution of mixed electromagnetic/pressure driven gaseous flows in microchannels

The influences of wall-slip/jump conditions on the fluid flow and heat transfer for hydrodynamically and thermally fully developed electrically conducting gaseous flow subject to an electromagnetic field inside a parallel plate microchannel with constant heat flux at walls are studied under the assumptions of a low-magnetic Reynolds number. The governing equations are non-dimensionalized and then analytical solutions are derived for the friction and the heat transfer coefficients. The fluid flow and the heat transfer characteristics obtained in the analytical solutions are discussed in detail for different parameters such as the Knudsen, Hartmann, and Brinkman numbers. The velocity profiles verify that even with a constant Knudsen number, applying a stronger electromagnetic field gives rise to an increase in the slip velocity. The results also reveal that on increasing the Hartmann number, the heat transfer rate as well as the friction factor is enhanced, whereas it tends to suppress the movement of the fluid. Further, it is found that the Nusselt and the Poiseuille numbers are less sensitive to the electromagnetic field effects with increase in rarefaction.     

Numerical simulation of gas flow in rough microchannels: hybrid kinetic–continuum approach versus Navier–Stokes

The flow field in a rough microchannel is numerically analyzed using a hybrid solver, dynamically coupling kinetic and Navier–Stokes solutions computed in rarefied and continuum subareas of the flow field, respectively, and a full Navier–Stokes solver. The rough surface is configured with triangular roughness elements, with a maximum relative roughness of 5 % of the channel height. The effects of Mach number, Knudsen number (or Reynolds number) and roughness height are investigated and discussed in terms of Poiseuille number and mass flow rate. Discrepancies between full Navier–Stokes and hybrid solutions are analyzed, assessing the range of validity of Navier–Stokes equations provided with first-order slip boundary conditions for modeling gas flow along a rough surface. Results indicate that the roughness increases Poiseuille number and decreases mass flux in comparison with those for the smooth microchannel. Increasing rarefaction results in further enhancement of roughness effect. At the same time, the compressibility effect is more noticeable than the roughness one, although the compressibility effect is alleviated by increase in the rarefaction. It was found that, although the Navier–Stokes solution of the flow in a smooth channel is accurate up to Kn = 0.1, when relative roughness height is higher than 1.25 % significant errors already appear at Kn = 0.02.     

Double-disk rotating viscous micro-pump with slip flow

In this paper numerical solution was provided for the 2D, axisymmetric Navier-Stokes equations coupled with energy equation for gaseous slip flow between two micro rotating disks pump. A first-order slip boundary condition was applied to all internal solid walls. The objective is to study the effect of Knudsen number, rotational Reynolds number and gap height on pump head, flow rate, coefficient of moments and overall micro-pump efficiency. Pump head, flow rate, coefficient of moments and pump efficiency were calculated for various pump operating conditions when the mass flow rate is applied at the pump inlet port. Detailed investigations were performed for rotational Reynolds number equals to 10. Effect of gap height between the two disks was studied. Effect of rotational Reynolds number on maximum flow rate and maximum pressure rise was simulated. The present numerical results for no-slip were compared with previously published experimental and theoretical data and found to be in a very good agreement. Knudsen number Kn values were found to be major parameters that affect the performance of pump. Pump performance decreases with increasing Kn. Optimal pump performance occurs around middle point of pump operating range. Pump operating range decreases with increasing Kn numbers. Pump performance is found to experience a steep degradation for Kn approaching 0.1. Maximum flow rate increases with rotational speed almost linearly. Maximum pressure rise also increases with rotational speed. Reducing gap height results in increasing maximum pressure rise, while increasing gap height results in larger maximum flow rate.     

An improved model of carbon nanotube conveying flow by considering comprehensive effects of Knudsen number

Although the theoretical model of carbon nanotube conveying flow has been evolving from under macroscale theory framework to under nanoscale theory framework, for now, the small-scale effects have yet to be considered thoroughly. Herein, after extending the compatibility condition, we propose an improved model. Compared with the previous models, the improved model is not only dependent on the nonlocal parameter, but also comprehensively takes all the factors related to Knudsen number, namely effective viscosity, slip boundary condition and non-uniform flow profile, into account. Based on this model, a formula of critical flow velocity is derived in addition to numerical results and our model gives a considerably decreased critical flow velocity. Besides, when Knudsen number and nonlocal parameter increase, the critical flow velocity goes down dramatically, which indicates that the effects of Knudsen number cannot be neglected, and we demonstrate that the dispute over nonlocal parameter may impair the reliability of theoretical prediction of critical flow velocity. We also find that the effects of nonlocal parameter and Knudsen number on critical flow velocity are probably uncoupled.     

A multiplicative decomposition of Poiseuille number on rarefaction and roughness by lattice Boltzmann simulation

Poiseuille number of rarefied gas flow in channels with designed roughness is studied and a multiplicative decomposition of Poiseuille number on the effects of rarefaction and roughness is proposed. The numerical methodology is based on the mesoscopic lattice Boltzmann method. In order to eliminate the effect of compressibility, the incompressible lattice Boltzmann model is used and the periodic boundary is imposed on the inlet and outlet of the channel. The combined bounced condition is applied to simulate the velocity slip on the wall boundary. Numerical results reveal the two opposite effects that velocity gradient and friction factor near the wall increase as roughness effect increases; meanwhile, the increments of the rarefaction effect and velocity slip lead to a corresponding decrement of friction factor. An empirical relation of Poiseuille number which contains the two opposite effects and has a better physical meaning is proposed in the form of multiplicative decomposition, and then is validated by available experimental and numerical results.     

The influence of slip conditions, wall properties and heat transfer on MHD peristaltic transport

The effects of both wall slip conditions and heat transfer on peristaltic flow of MHD Newtonian fluid in a porous channel with elastic wall properties have been studied under the assumptions of long-wavelength and low-Reynolds number. The analytical solution has been derived for the stream function and temperature. The results for velocity, temperature, stream function and heat transfer coefficient obtained in the analysis have been evaluated numerically and discussed briefly. The numerical result shows that more trapped bolus appears with increasing Knudsen number.     

Mixed convection in a wall plume

The mixed convection flow that arises due to a finite heated element located on a vertical adiabatic surface in an external flow, aligned with the surface, is studied analytically. The problem is of particular interest in electronic circuitry cooling and in heat removal in various manufacturing systems. The boundary layer flow is studied to determine the heat transfer from the heated element, the temperature decay downstream and the flow field that results. Numerical results are obtained, employing finite difference methods for a wide range of the mixed convection parameter. The pure natural convection problem is studied first and the results obtained are compared with earlier studies on wall plumes. The effect of mixed convection on the heat transfer and fluid flow characteristics is studied in detail. The temperature at the heated element surface is studied as a function of the mixed convection parameter. The effect of the inclusion of radiative loss on the temperature and flow fields is also examined.     

Magnetohydrodynamic flow with slippage in an annular duct for microfluidic applications

In this paper, we investigate theoretically the 3D laminar flow of an electrolyte in an annular duct driven by a Lorentz force. The duct is formed by two concentric electrically conducting cylinders limited by insulating bottom and top walls. A uniform magnetic field acts along the axial direction, while a potential difference is applied between the cylinders so that a radial electric current traverses the fluid. The interaction of the current and the magnetic field produces a Lorentz force that drives an azimuthal flow. The steady flow is solved using a Galerkin method with Bessel–Fourier series in the radial direction and trigonometric series along the vertical direction, allowing different combinations of slip conditions at the walls. The orthogonality of both series with the general boundary conditions of the third kind is used to find an analytic approximation. Velocity patterns and flow rates are explored by varying the aspect ratio of the duct and the gap between the cylinders, as well as the slippage at the walls. Results can provide useful information for optimization and design of annular microfluidic devices.     

Pressure-driven electrokinetic slip flows of viscoelastic fluids in hydrophobic microchannels

This work investigates the steady-state slip flow of viscoelastic fluids in hydrophobic two-dimensional microchannels under the combined influence of electro-osmotic and pressure gradient forcings with symmetric or asymmetric zeta potentials at the walls. The Debye–Hückel approximation for weak potential is assumed, and the simplified Phan-Thien-Tanner model was used for the constitutive equation. Due to the different hydrophobic characteristics of the microchannel walls, we study the influence of the Navier slip boundary condition on the fluid flow, by considering different slip coefficients at both walls and varying the electrical double-layer thickness, the ratio between the applied streamwise gradients of electric potential and pressure, and the ratio of the zeta potentials. For the symmetric case, the effect of the nonlinear Navier slip model on the fluid flow is also investigated.     

Application of the Green function method to flow-thermoelastic forced vibration analysis of viscoelastic carbon nanotubes

In this paper, the Green function method (GFM) is implemented for forced vibration analysis of carbon nanotubes (CNTs) conveying fluid in thermal environment. The Eringen’s nonlocal elasticity theory is used to take into account the size effect of CNT with modeling the CNT wall–fluid flow interaction by means of slip boundary condition and Knudsen number (Kn). The derived governing differential equations are solved by GFM which demonstrated to have high precision and computational efficiency in the vibration analysis of CNTs. The validity of the present analytical solution is confirmed by comparing the results with those reported in other literature, and good agreement is observed. The analytical examinations are accomplished, while the emphasis is placed on considering the influences of nonlocal parameter, boundary conditions, temperature change, structural damping of the CNT, Knudsen number, fluid velocity and visco-Pasternak foundation on the dynamic deflection response of the fluid-conveying CNTs in detail.     

Application of a parallel DSMC technique to predict flowcharacteristics in microfluidic filters

Using a parallel implementation of the direct simulation Monte Carlo (DSMC) method, periodic MEMS microfilters are studied in detail. The dependence of the flow characteristics on geometry, Knudsen number, pressure difference, spacing between the filter elements, and accommodation coefficients are investigated. By comparing DSMC results with the widely used analytical formulas, the validity range of the analytical approaches is evaluated. The simulation results show that velocity slip exists both on the filter channel walls and on the filter membrane and results in an increased flow rate. Velocity slip increases strongly with decreasing accommodation coefficients. For long channels, this results in a strong increase in flow rate; whereas for short channels, the increase in flow rate is limited. For the filter separations considered in this paper, we observe that separation between filter channels does not influence the flow rate within each channel     

Mixed convective heat and mass transfer in a vertical wavy channel with traveling thermal waves and porous medium

We investigate the problem of mixed convection heat and mass transfer through a vertical wavy channel with porous medium. The flow is generated by the periodic thermal waves prescribed at the wavy walls of the channel. The equations of momentum energy and concentration are solved subject to a set of appropriate boundary conditions by assuming that the solution consists of a mean part and a perturbed part. The effects of various pertinent parameters on flow, heat and mass transfer characteristics are discussed numerically and explained graphically.     

Double-diffusive and Soret-induced convection of a micropolar fluid in a vertical channel

This paper reports an investigation of the fully developed natural convection heat and mass transfer of a micropolar fluid in a vertical channel. Asymmetric temperature and concentration boundary conditions are applied to the walls of the channel. The cases of double diffusion and Soret-induced convection are both considered. The governing parameters for the problem are the buoyancy ratio and the various material parameters of the micropolar fluid. The resulting non-dimensional boundary value problem is solved analytically in closed form using MAPLE software. A numerical solution of the time dependent governing equations is demonstrated to be in good agreement with the analytical model. The influence of the governing parameters on the fluid flow as well as heat and solute transfers is demonstrated to be significant.     

Study of subsonic�Csupersonic gas flow through micro/nanoscale nozzles using unstructured DSMC solver

We use an extended direct simulation Monte Carlo (DSMC) method, applicable to unstructured meshes, to numerically simulate a wide range of rarefaction regimes from subsonic to supersonic flows through micro/nanoscale converging–diverging nozzles. Our unstructured DSMC method considers a uniform distribution of particles, employs proper subcell geometry, and follows an appropriate particle tracking algorithm. Using the unstructured DSMC, we study the effects of back pressure, gas/surface interactions (diffuse/specular reflections), and Knudsen number on the flow field in micro/nanoscale nozzles. If we apply the back pressure at the nozzle outlet, a boundary layer separation occurs before the outlet and a region with reverse flow appears inside the boundary layer. Meanwhile, the core region of inviscid flow experiences multiple shock-expansion waves. In order to accurately simulate the outflow, we extend a buffer zone at the nozzle outlet. We show that a high viscous force creation in the wall boundary layer prevents any supersonic flow formation in the divergent part of the nozzle if the Knudsen number exceeds a moderate magnitude. We also show that the wall boundary layer prevents forming any normal shock in the divergent part. In reality, Mach cores would appear at the nozzle center followed by bow shocks and expansion region. We compare the current DSMC results with the solution of the Navier–Stokes equations subject to the velocity slip and temperature jump boundary conditions. We use OpenFOAM as a compressible flow solver to treat the Navier–Stokes equations.     

Non-isothermal flow of rarefied gas through a long pipe with elliptic cross section

A non-isothermal rarefied gas flow trough a long tube with an elliptical cross section due to pressure and temperature gradients is studied on the basis of the S-model kinetic equation in the whole range of the Knudsen number covering both free molecular regime and hydrodynamic one. A wide range of the pipe section aspect ratio is considered. The mass flow rate is calculated as a function of the pressures and temperatures on the tube ends. The thermomolecular pressure effect has been modeled and the coefficient of the thermomolecular pressure difference has been calculated in whole range of the Knudsen number and in wide range of the pipe section aspect ratio.