Direct simulation of roughness effects on rarefied and compressible flow at slip flow regime

A two dimensional numerical simulation is performed for incompressible and compressible fluid flows through microchannels in slip flow regime with consideration of slip and temperature jump boundary conditions. The wall roughness is simulated in two cases with triangular microelements and random shaped micro peaks distributed on wall surfaces to study the effects of roughness shape and distribution on the flow field. Various Mach and Knudsen numbers have been used to investigate the effects of rarefaction as well as compressibility. It is found that rarefaction has a more significant effect on the flow field in microchannels with higher relative roughness. It is also found that the effect of compressibility will be more noticeable when relative roughness increases. In addition a high influence of roughness distribution and shape can be seen for both compressible and incompressible flows. The numerical results have also been checked with available theoretical and experimental relations and a good agreement has been achieved.     

Slip flow and heat transfer in microbearings with fractal surface topographies

The effects of random surface roughness on slip flow and heat transfer in microbearings are investigated. A three-dimensional random surface roughness model characterized by fractal geometry is used to describe the multiscale self-affine roughness, which is represented by the modified two-variable Weierstrass–Mandelbrot (W–M) functions, at micro-scale. Based on this fractal characterization, the roles of rarefaction and roughness on the thermal and flow properties in microbearings are predicted and evaluated using numerical analyses and simulations. The results show that the boundary conditions of velocity slip and temperature jump depend not only on the Knudsen number but also on the surface roughness. It is found that the effects of the gas rarefaction and surface roughness on flow behavior and heat transfer in the microbearing are strongly coupled. The negative influence of roughness on heat transfer found to be the Nusselt number reduction. In addition, the effects of temperature difference and relative roughness on the heat transfer in the bearing are also analyzed and discussed.     

滑移区气体-颗粒流动与传热特性研究

针对气体-颗粒微尺度流动与传热过程开展数值模拟研究,所构建模型中气体处理为可压缩、变物性流体,并在颗粒表面采用速度滑移和温度跳跃边界条件以考虑气体稀薄效应。在数值模拟基础上,研究分析稀薄效应对颗粒与其周围气体流动与换热的影响程度,并进一步提出新的阻力系数与传热努谢尔特数关联式。研究结果表明,气体稀薄效应将减小颗粒阻力系数,同时抑制颗粒与其周围气体的传热过程。     

A universal entrance nusselt number for internal slip flow

A universal finite Nusselt number is found for laminar slip flow heat transfer at the entrance of a conduit. The Nusselt number expression is valid for both isothermal and isoflux thermal boundary conditions and for any conduit geometry. The value of the entrance Nusselt number is found to be dependent on two nondimensional parameters that include effects of rarefaction, fluid properties, and the fluid/wall interaction.     

微通道内气体-近壁颗粒流动传热数值模拟研究

数值模拟了微通道受限空间内气体-近璧颗粒流动与传热过程,所建模型考虑微尺度气体的可压缩与交物性特征,且在通道和颗粒壁面采用速度滑移和温度跳跃边界条件以考虑滑移区气体动量/能量非连续效应.在此基础上,计算分析了克努森数(Kn)和颗粒偏移比对颗粒表面拖曳力系数(CD)以及传热努塞尔数(Nu)的影响规律.研究结果表明:受气体...     

The effect of creep flow on two-dimensional isoflux microchannels

Microchannel convective heat transfer and friction loss characteristics are numerically evaluated for gaseous, two-dimensional, steady state, laminar, constant wall heat flux flows. The effects of Knudsen number, accommodation coefficients, second-order slip boundary conditions, creep flow, and hydrodynamically/thermally developing flow are considered. These effects are compared through the Poiseuille number and the Nusselt number. Numerical values for the Poiseuille and Nusselt numbers are obtained using a continuum based three-dimensional, unsteady, compressible computational fluid dynamics algorithm that has been modified with slip boundary conditions. To verify the numerical results, analytic solutions of the hydrodynamically and thermally fully developed momentum and energy equations have been derived subject to both first- and second-order slip velocity and temperature jump boundary conditions. The resulting velocity and temperature profiles are then utilized to obtain the microchannel Poiseuille and Nusselt numbers as a function of Knudsen number, first- and second-order velocity slip and temperature jump coefficients, Brinkman number, and the ratio of the thermal creep velocity to the mean velocity. Excellent agreement between the numerical and analytical data is demonstrated. Second-order slip terms and creep velocity are shown to have significant effects on microchannel Poiseuille and Nusselt numbers within the slip flow regime.     

Thermal and hydrodynamic analysis of gaseous flow in trapezoidal silicon microchannels

Thermal and hydrodynamic character of a hydrodynamically developed and thermally developing flow in trapezoidal silicon microchannels is analyzed. The continuum momentum and energy equations, with the velocity slip and temperature jump condition at the solid walls, are solved numerically in a square computational domain obtained by transformation of the trapezoidal geometry. The effects of rarefaction, aspect ratio and a parameter representing the fluid/wall interaction on thermal and hydrodynamic character of flow in trapezoidal microchannels are explored. It is found that the friction factor decreases if rarefaction and/or aspect ratio increase. It is also found that at low rarefactions the very high heat transfer rate at the entrance diminishes rapidly as the thermally developing flow approaches fully developed flow. At high rarefactions, heat transfer rate does not exhibit considerable changes along the microchannel, no matter the flow is developing or not.     

Three-dimensional numerical simulation of the slip flow through triangular microchannels

Three-dimensional numerical analysis for fully developed incompressible fluid flow and heat transfer through triangular microchannels over the slip flow regime is simulated in this paper. In order to study the flow through the channel, the Navier–Stokes equations are solved in conjunction with slip/jump boundary conditions. The influences of Knudsen number (0.001 < Kn < 0.1), aspect ratio (0.2 < A < 4.5), and Reynolds number (1 < Re < 15) on the fluid flow and heat transfer characteristics are extensively investigated in the paper. The numerical results reveal that the rarefaction decreases the Poiseuille number, while its effect on the Nusselt number completely depends on the interaction between velocity slip and temperature jump. It is also found that the aspect ratio has an important role in the analysis, but the variation of Reynolds number is less remarkable.     

Numerical simulation of slip flow through rhombus microchannels

Microgeometry fluid dynamics has gotten a lot interest due to the arrival of Micro-Electro-Mechanical systems (MEMS). When the mean free path of a gas and characteristic length of the channel are in the same order, continuum assumption is no longer valid. In this situation velocity slip and temperature jump occur in the duct walls. Fully developed numerical analysis for characteristic laminar slip flow and heat transfer in rhombus microchannels are performed with slip velocity, and temperature-jump boundary condition at walls. The impacts of Reynolds number (0.1 < Re < 40), velocity slip, and temperature-jump on Poiseuille number, and Nusselt number for different aspect ratio (0.15 < A < 1.0), and Knudsen number are studied in detail. The contours of non-dimensional velocity for some cases are examined as well. The results show that aspect ratio and Knudsen number have important impact on Poiseuille number, and Nusselt number in rhombus microchannels. Reynolds number has considerable influence on Nusselt number at low Reynolds number, but its influence on Poiseuille number is not very important at the studied range.     

Size effect on microscale single-phase flow and heat transfer

The present discussion will focus on the size effect induced by the variation of dominant factors and phenomena in the flow and heat transfer as the device scale decreases. Due to the larger surface to volume ratio for microchannels and microdevices, factors related to surface effects have more impact to microscale flow and heat transfer. For example, surface friction induced flow compressibility makes the fluid velocity profiles flatter and leads to higher friction factors and Nusselt numbers; surface roughness is likely responsible for the early transition from laminar to turbulent flow and the increased friction factor and Nusselt number; the relative importance of viscous force modifies the correlation between Nu and Ra for natural convection in a microenclosure and, other effects, such as channel surface geometry, surface electrostatic charges, axial heat conduction in the channel wall and measurement errors, could lead to different flow and heat transfer behaviors from that at conventional scales.     

Convective heat transfer in pressure-driven nitrogen slip flows in long microchannels: The effects of pressure work and viscous dissipation

An analytical and numerical study is carried out to examine the convective heat transfer in two-dimensional pressure-driven nitrogen slip flows in long microchannels, whose length-to-height ratios are above 500. The momentum and the energy equations are solved, where variable properties, rarefaction that involves velocity slip, thermal creep and temperature jump, pressure work, and viscous dissipation are all taken into account. Nitrogen is assumed to be a perfect gas. The effects of pressure work and viscous dissipation, which are particularly significant for long microchannels, are examined by analyzing the uniform wall temperature and the uniform wall heat flux cases. It is found that the degree of rarefaction, which is characterized by the Knudsen number, is the key factor that determines the relative importance of pressure work and viscous dissipation. It is demonstrated that, for perfect gases, rarefaction promotes the conversion of internal energy to mechanical energy. Specifically, regardless of the fluid field development, pressure work and viscous dissipation cancel out in the absence of rarefaction, while pressure work is greater than viscous dissipation with rarefaction and its dominance increases as the Knudsen number increases. It is shown that the combination of pressure work and viscous dissipation makes a significant impact on the Nusselt number in both the continuum and the rarefaction cases. Therefore, it is concluded that for convective heat transfer in internal gas flows, both pressure work and viscous dissipation need to be considered in analysis.     

Numerical simulation of thermofluid characteristics of two-phase slug flow in microchannels

A fundamental study of heat transfer characteristics of two-phase slug flow in microchannels is carried out employing the Volume-of-Fluid (VOF) method. Despite of the fact that numerical simulations of two-phase flows in microchannels have been attempted by many investigators, most efforts seem to have failed in correctly capturing the flow physics, especially those pertaining to the slug flow regime characteristics. The presence of a thin liquid film in the order of 10 μm around the bubble is a contributing factor to the above difficulty. Typically, liquid films have a significant effect on the flow field and heat transfer characteristics. In the simulations reported in this paper, the film is successfully captured and a very high local convective heat transfer coefficient is observed in the film region. A strong coupling between the conductive heat transfer in the solid wall and the convective heat transfer in the flow field is observed and characterized. Results showed that unsteady heat transfer through the solid wall in the axial direction is comparable to that in the radial direction. Results also showed that a fully developed condition could be achieved fairly quickly compared to single-phase flows. The fully developed condition is defined based on the Peclet number (Pe) and a dimensionless length of the liquid slug. Local and time-averaged Nusselt numbers for slug flows are reported for the first time. It was found that significant improvements in the heat transfer coefficient could be achieved by short slugs where the Nusselt number was found to be 610% higher than in single-phase flows. The study revealed new findings related to slug flow heat transfer in microchannels with constant wall heat flux.     

The effect of viscous dissipation and rarefaction on rectangular microchannel convective heat transfer

The effect of viscous dissipation and rarefaction on rectangular microchannel convective heat transfer rates, as given by the Nusselt number, is numerically evaluated subject to constant wall heat flux (H2) and constant wall temperature (T) thermal boundary conditions. Numerical results are obtained using a continuum based, three-dimensional, compressible, unsteady computational fluid dynamics algorithm with slip velocity and temperature jump boundary conditions applied to the momentum and energy equations, respectively. For the limiting case of parallel plate channels, analytic solutions for the thermally and hydrodynamically fully developed momentum and energy equations are derived, subject to both first- and second-order slip velocity and temperature jump boundary conditions, from which analytic Nusselt number solutions are then obtained. Excellent agreement between the analytical and numerical results verifies the accuracy of the numerical algorithm, which is then employed to obtain three-dimensional rectangular channel and thermally/hydrodynamically developing Nusselt numbers. Nusselt number data are presented as functions of Knudsen number, Brinkman number, Peclet number, momentum and thermal accommodation coefficients, and aspect ratio. Rarefaction and viscous dissipation effects are shown to significantly affect the convective heat transfer rate in the slip flow regime.     

Thermally developing flow and heat transfer in rectangular microchannels of different aspect ratios

Laminar convective heat transfer in the entrance region of microchannels of rectangular cross-section is investigated under circumferentially uniform wall temperature and axially uniform wall heat flux thermal boundary conditions. Three-dimensional numerical simulations were performed for laminar thermally developing flow in microchannels of different aspect ratios. Based on the temperature and heat flux distributions obtained, both the local and average Nusselt numbers are presented graphically as a function of the dimensionless axial distance and channel aspect ratio. Generalized correlations, useful for the design and optimization of microchannel heat sinks and other microfluidic devices, are proposed for predicting Nusselt numbers. The proposed correlations are compared with other conventional correlations and with available experimental data, and show very good agreement.     

Numerical simulation of wall roughness on gaseous flow and heat transfer in a microchannel

A flow and heat transfer numerical simulation was performed for a 2D compressible gas flow through a microchannel in the slip regime to investigate the effects of wall roughness. The wall roughness is simulated by rectangular microelements. This effect is examined for gas flows under inlet Mach number ranging from 0.0055 to 0.202. The numerical results demonstrate that the roughness elements have a significant impact on the flow characteristics. For rarefied gases, it is found that roughness effect leads to an increase in the Poiseuille number with increasing roughness height and decreasing element spacing. The surface roughness has a more significant effect on the flow with a lower inlet Kn. Compressible gas flow is also sensitive to the height of the wall roughness elements. In addition, an increase of the relative roughness height leads to a pronounced decrease in the local heat flux for both rarefied and compressible flow. The average Nusselt numbers have a much more significant reduction for a rarefied flow than a compressible flow. The influence of wall roughness on the average heat transfer rate is smaller than that on the Poiseuille number.     

Effect of viscous heating on heat transfer performance in microchannel slip flow region

Based on the superposition principle, an analytical solution for steady convective heat transfer in a two-dimensional microchannel in the slip flow region is obtained, including the effects of velocity slip and temperature jump at the wall, which are the main characteristics of flow in the slip flow region, and viscous heating effects in the calculations. The cases of constant heat flux boundary conditions and one wall as adiabatic and the other wall at constant heat flux input are studied. The solution method is verified for the cases where micro-scale effects are neglected. The effects of viscous heating on the temperature profiles and on the heat transfer performance are analyzed in detail. It is concluded that the effect of viscous heating, like an internal energy source, heats the fluid along the flow direction and severely distorts the temperature profiles. The effects of key parameters, such as the Brinkman and Knudsen numbers, on the Nusselt number, which expresses the heat transfer performance are investigated.     

Fluid flow and heat transfer of liquid-liquid two phase flow in microchannels: A review

The fluid flow and heat transfer behavior of liquid–liquid two phase flows have led to significantly improve the heat transfer rates in microchannels. Both numerical and experimental studies are reviewed in this paper to gain useful insights into the effect of a number of parameters such as film thickness, Peclet number, working fluid and flow geometry on hydrodynamic and thermal behavior of microchannels using liquid-liquid two phase flow. In addition, the paper summarises information about common correlations proposed to predict the pressure drop and heat transfer coefficient in the form of Nusselt number (Nu). The present study shows that there is little agreement across the literature between measured pressure drop and Nusselt number and predictions based on these correlations. Finally, the conclusions and important summaries, and some possible future development of this field are presented.     

Three-dimensional laminar slip-flow and heat transfer in a rectangular microchannel with constant wall temperature

Three-dimensional laminar slip-flow and heat transfer in rectangular microchannels having constant temperature walls are studied numerically using the finite-volume method for thermally and simultaneously developing flows. The Navier–Stokes and energy equations are solved with velocity slip and temperature jump at the wall. A modified convection–diffusion coefficient at the wall–fluid interface is defined to incorporate the temperature-jump boundary condition. Validity of the numerical simulation procedure is established and the effect of rarefaction on hydrodynamicaly developing flow field, pressure gradient and entrance length is analyzed. A correlation for the fully developed friction factor is presented as a function of Knudsen number (Kn) and aspect ratio (α). The influence of rarefaction on the Nusselt (Nu) number is investigated for thermally and simultaneously developing flows. The effect of velocity slip is found to increase the Nu number, while the temperature-jump tends to decrease it, and the combined effect could result in an increase or a decrease in the Nu number. In the fully developed region, there could be high as 15% increase or low as 50% decrease in Nu number is plausible for the range of parameters considered in this work.     

An experimental study of flow friction and heat transfer in wavy microchannels with rectangular cross section

Experimental investigation has been conducted on the flow friction and heat transfer in sinusoidal microchannels with rectangular cross sections. The microchannels considered consist of ten identical wavy units with average width of about 205 μm, depth of 404 μm, wavelength of 2.5 mm and wavy amplitude of 0–259 μm. Each test piece is made of copper and contains 60–62 wavy microchannels in parallel. Deionized water is employed as the working fluid and the Reynolds numbers considered range from about 300 to 800. The experimental results, mainly the overall Nusselt number and friction factor, for wavy microchannels are compared with those of straight baseline channels with the same cross section and footprint length. It is found that the heat transfer performance of the present wavy microchannels is much better than that of straight baseline microchannels; at the same time the pressure drop penalty of the present wavy microchannels can be much smaller than the heat transfer enhancement. Conjugate simulation based on the classical continuum approach is also carried out for similar experimental conditions, the numerical results agree reasonably well with experimental data.     

Heat and fluid flow characteristics of gases in micropipes

In this study, laminar forced convective heat transfer of a Newtonian fluid in a micropipe is analyzed by taking the viscous dissipation effect, the velocity slip and the temperature jump at the wall into account. Hydrodynamically and thermally fully developed flow case is examined. Two different thermal boundary conditions are considered: the constant heat flux (CHF) and the constant wall temperature (CWT). Either wall heating (the fluid is heated) case or wall cooling (the fluid is cooled) case is examined. The Nusselt numbers are analytically determined as a function of the Brinkman number and the Knudsen number. Different definitions of the Brinkman number based on the definition of the dimensionless temperature are discussed. It is disclosed that for the cases studied here, singularities for the Brinkman number-dependence of the Nusselt number are observed and they are discussed in view of the energy balance.