SLIP FLOW IN RECTANGULAR MICROTUBES

Heat Transfer to Newtonian and Non-Newtonian Fluids in Rectangular Ducts

The behavior of hydrodynamically fully developed and thermally developing laminar flow of Newtonian fluids in rectangular ducts with arbitrary aspect ratio and equal heating on adjacent walls, subject to the H2 boundary condition, is studied numerically. The developing Nusselt number is obtained for a wide range of duct aspect ratios. The limiting solution of Nu(H2) as Z approaches infinity was found to agree excellently with those found in the literature. 8 refs.

The heat and mass transfer due to the steady laminar and incompressible micropolar fluid flow through a rectangular duct with the slip flow and convective boundary conditions are numerically calculated. The fluid moves under an external magnetic field applied on a plane perpendicular to the axis of the duct. The governing nonlinear partial differential equations of momentum, microrotation, induction, and the energy are solved simultaneously by the finite difference method. The effect of various numbers and parameters such as Reynolds, magnetic Reynolds, Hartmann, coupling, Brinkman numbers, the slip flow and convective parameters are presented in graphs. Some comparisons with previous works are included.

Poiseuille number, the product of friction factor and Reynolds number (fRe) for quasi-fully-developed gas microchannel flow in the slip flow regime, was obtained numerically based on the arbitrary-Lagrangian-Eulerian method. Two-dimensional compressible momentum and energy equations were solved for a wide range of Reynolds and Mach numbers for constant wall temperatures that are lower or higher than the inlet temperature. The channel height ranges from 2 μm to 10 μm and the channel aspect ratio is 200. The stagnation pressure pstg is chosen such that the exit Mach number ranges from 0.1 to 1.0. The outlet pressure is fixed at atmospheric conditon. Mach and Knudsen numbers are systematically varied to determine their effects on fRe. The correlation for fRe for the slip flow is obtained from that of fRe of no-slip flow and incompressible theory as a function of Mach and Knudsen numbers. The results are in excellent agreement with the available experimental measurements. It was found that fRe is a function of Mach and Knudsen numbers and is different from the values by 96/(1+12Kn) obtained from the incompressible flow theory.

Experimental and numerical study of friction factor for a modified power law fluid in a rectangular duct

We report on a refined macroscopic model for slightly compressible gas slip flow in porous media developed by upscaling the pore-scale boundary value problem. The macroscopic model is validated by comparisons with an analytic solution on a two-dimensional (2-D) ordered model structure and with direct numerical simulations on random microscale structures. The symmetry properties of the apparent slip-corrected permeability tensor in the macroscale momentum equation are analysed. Slip correction at the macroscopic scale is more accurately described if an expansion in the Knudsen number, beyond the first order considered so far, is employed at the closure level. Corrective terms beyond the first order are a signature of the curvature of solid–fluid interfaces at the pore scale that is incompletely captured by the classical first-order correction at the macroscale. With this expansion, the apparent slip-corrected permeability is shown to be the sum of the classical intrinsic permeability tensor and tensorial slip corrections at the successive orders of the Knudsen number. All the tensorial effective coefficients can be determined from intrinsic and coupled but easy-to-solve closure problems. It is further shown that the complete form of the slip boundary condition at the microscale must be considered and an important general feature of this slip condition at the different orders in the Knudsen number is highlighted. It justifies the importance of slip-flow correction terms beyond the first order in the Knudsen number in the macroscopic model and sheds more light on the physics of slip flow in the general case, especially for large porosity values. Nevertheless, this new nonlinear dependence of the apparent permeability with the Knudsen number should be further verified experimentally.

Rarefied gas flow and heat transfer in the entrance region of rectangular microchannels are investigated numerically in the slip flow regime. A control-volume based numerical scheme is used to solve the Navier-Stokes and energy equations with velocity slip and temperature jump conditions at the walls. The effects of variations in Reynolds number (0.1 ≤ Re ≤ 100 ), channel aspect ratio ( 0 ≤ α* ≤ 1 ) and Knudsen number (0 ≤ Kn ≤ 0.1) are studied on the flow development, slip flow heat transfer, and key parameters like the friction factor and the Nusselt number. For simultaneously developing flow and heat transfer, major reductions in friction coefficients and heat transfer rates are observed in the entrance region due to rarefaction effects, which also extend to the fully developed region, however at much lower levels.Copyright © 2005 by ASME

In this work we use a three dimensional Molecular Dynamics simulation method to study the effect of different geometries and Knudsen number regimes on the gas flow in micro-nanochannels. Argon molecules have been used for the simulations. Thermal wall and diffusive-specular wall types were used for the boundaries of the channels. The velocity profiles in the channel were obtained and analyzed with three different channel geometries that are commonly used in the industry: circular, rectangular (square), and slit channel. We found that when using the same driving force, the maximum velocity of the flow increases when the geometry changes in the order from circular geometry to rectangular geometry to slit geometry, where the latter becomes 1.2∼1.5 times as large compared with either the rectangular or circular channel. While the absolute values of the velocity profiles show a distinct difference according to the different geometries, geometry effect on the shape of the velocity profile also shows interesting features. Rectangular tube shows much flatter profile compared with the other two channels. Also the effect of the size of the channels and different Knudsen numbers on the velocity profiles is investigated. Two different sizes were used here: 100nm and 10nm corresponding to typical sizes of a nano channel and carbon nanotubes. We found that the Knudsen number has an effect on the slip and maximum flow velocity for the slit geometry even for higher Knudsen number. For the Kn higher than approximately 3, it was found that the Knudsen number has a small influence on the slip flow velocity for the circular channel and rectangular channel than for lower Knudsen number.

In this paper, we undertake an analytical study of stresses (augmented and Onsager–Burnett) and entropy generation for the plane Poiseuille flow problem, and their variation with Knudsen number. The gas flow is assumed to be 2D laminar, fully developed, compressible, and isothermal; these assumptions make the problem amenable to analytical treatment. The variation of stresses and entropy generation has been analyzed over a large range of Knudsen number. The magnitude of stresses and entropy generation at a particular position in the channel has been considered. It is found that the augmented and OBurnett normal stresses are of opposite signs to the corresponding Navier–Stokes stresses, while the magnitude of the net normal stress increases with Knudsen number. The magnitude of the augmented Burnett shear stress is insignificant as compared to the augmented Burnett normal stresses. A close match between the augmented and OBurnett normal stresses has been found at low Knudsen number. However, an opposite variation has been observed between the augmented and Onsager shear stresses at high Knudsen number. A good comparison of the normalized mass flow rate with the reported value in the literature helps to validate our analysis. A minimum in the variation of normalized entropy generation against the Knudsen number (Kn) is observed at Kn close to unity, and is being reported for the first time. The magnitude of net entropy generation from the summation of Navier–Stokes and augmented Burnett stresses is found to be positive, even in the transition regime of gas flow. Further, an appearance of minimum or maximum in normalized net shear stress versus Knudsen number, depending upon the lateral position in the microchannel, has also been observed. Altogether, this analysis supports the validity of the Navier–Stokes equation with modified constitutive expression, even for higher Knudsen numbers. Moreover, the significant terms of Burnett stress are pointed out by the analysis, which can help in developing reduced-order model for these equations.

Due to the existence of a velocity slip and temperature jump on the solid walls, the heat transfer in microchannels significantly differs from the one in the macroscale. In our research, we have focused on the pressure driven gas flows in a simple finite microchannel geometry, with an entrance and an outlet, for low Reynolds (Re<200) and low Knudsen (Kn<0.01) numbers. For such a regime, the slip induced phenomena are strongly connected with the viscous effects. As a result, heat transfer is also significantly altered. For the optimization of flow conditions, we have investigated various temperature gradient configurations, additionally changing Reynolds and Knudsen numbers. The entrance effects, slip flow, and temperature jump lead to complex relations between flow behavior and heat transfer. We have shown that slip effects are generally insignificant for flow behavior. However, two configuration setups (hot wall cold gas and cold wall hot gas) are affected by slip in distinguishably different ways. For the first one, which concerns turbomachinery, the mass flow rate can increase by about 1% in relation to the no-slip case, depending on the wall-gas temperature difference. Heat transfer is more significantly altered. The Nusselt number between slip and no-slip cases at the outlet of the microchannel is increased by about 10%.

The aim of the present paper is to analyze the friction and mass flow in a rough microchannel using Lattice Boltzmann Method (LBM). The LBM is a kinetic method based on the particle distribution function, so it can be fruitfully used to study the flow dependence on Knudsen number including slip velocity, pressure drop in rough microchannel. The surface roughness elements are taken to be considered as a series of circular shaped riblets throughout the channel with relative roughness height up to a maximum 10% of the channel height. The friction coefficients in terms of Poiseuille number (Pn), mass flow rate and the flow behaviors have been discussed in order to study the effect of surface roughness in the slip flow regime at Knudsen number (Kn), ranging from 0.01 to 0.10. It is seen that the friction factor and the flow behaviors in a rough microchannel strongly depend on the rarefaction effect and the relative roughness height. The friction factor in a rough microchannel is higher than that in smooth channel but the mass flow rate is lower than that of smooth channel. Moreover, it is seen that the friction factor increased with relative roughness height but decreased with increasing the Kundsen number (Kn) whereas the mass flow rate is decreased with increasing both of surface roughness height and Knudsen number.

Cylindrical Couette problem with different surface temperatures: Rarefied effects

Investigation of straightforward impedance eduction in the presence of shear flow

Oscillatory flow of second grade fluid in a straight rectangular duct

Mass and flow resistance in a square ribbed microchannel have been studied numerically using the Lattice Boltzmann Method. It has been build up on two dimensional nine velocity vectors model with single relaxation time method called the Lattice Bhatnagor-Gross-Krook model. To analyze the roughness effect on the flow resistance namely the friction factor and mass flow has been discussed at the slip flow regime, <TEX>$0.01{\leq}Kn{\leq}0.10$</TEX>, where Kn is the Knudsen number. The wall roughness is considered by square microelements with a relative roughness height up to maximum 10% of channel height. The velocity profiles in terms of streamlines near the riblets are demonstrated to be responsible for the roughness effect. It is found that the roughness effect leads to increase the flow resistance with roughness height but it is decreased significantly with increasing the space between two roughness elements as well as the Knudsen number. In addition, the mass flow decreased linearly with increasing both roughness height and gap but significantly changed at the slip flow regime.