A novel solution for pressure drop in singly connected microchannels of arbitrary cross-section

This paper outlines a novel approximate solution for determining the pressure drop of fully developed, laminar, single-phase flow in singly connected microchannels of arbitrary cross-section. Using a “bottom-up” approach, it is shown that for constant fluid properties and flow rate in fixed cross-section channels, the Poiseuille number is only a function of geometrical parameters of the cross-section, i.e., perimeter, area, and polar moment of inertia. The proposed model is validated with experimental data for rectangular, trapezoidal, and triangular microchannels. The model is also compared against numerical results for a wide variety of channel cross-sections including: hyperellipse, trapezoid, sine, square duct with two adjacent round corners, rhombic, circular sector, circular segment, annular sector, rectangular with semi-circular ends, and moon-shaped channels. The model predicts the pressure drop for the cross-sections listed within 8% of the values published.     

A superposition approach to study slip-flow forced convection in straight microchannels of uniform but arbitrary cross-section

This work presents a superposition approach to investigate forced convection in microducts of arbitrary cross-section, subject to H1 and H2 boundary conditions, in the slip-flow regime with further complication of a temperature jump condition assumption. It is shown that applying an average slip velocity and temperature jump definition, one can still use the no-slip/no-jump results with some minor modifications. Present results for slip-flow in microchannels of parallel plate, circular, and rectangular cross-sections are found to be in complete agreement with those in the literature. Application of this methodology to microchannels of triangular cross-section is also verified by comparing the present results with those obtained numerically by undertaking the commercially available software CFD-ACE.     

Viscous dissipation effects on thermal transport characteristics of combined pressure and electroosmotically driven flow in microchannels

This study investigates the influence of viscous dissipation on thermal transport characteristics of the fully developed combined pressure and electroosmotically driven flow in parallel plate microchannels subject to uniform wall heat flux. Closed form expressions are obtained for the transverse distributions of electrical potential, velocity and temperature and also for Nusselt number. From the results it is realized that the Brinkman number has a significant effect on Nusselt number. Generally speaking, to increase Brinkman number is to decrease Nusselt number. Although the magnitude of Joule heating can affect Brinkman number dependency of Nusselt number, however the general trend remains unchanged. Depending on the value of flow parameters, a singularity may occur in Nusselt number values even in the absence of viscous heating, especially at great values of dimensionless Joule heating term. For a given value of Brinkman number, as dimensionless Debye–Huckel parameter increases, the effect of viscous heating increases. In this condition, as dimensionless Debye–Huckel parameter goes to infinity, the Nusselt number approaches zero, regardless of the magnitude of Joule heating. Furthermore, it is realized that the effect of Brinkman number on Nusselt number for pressure opposed flow is more notable than purely electroosmotic flow, while the opposite is true for pressure assisted flow.     

Viscous dissipation effect on entropy generation in curved square microchannels

The viscous dissipation effect on the thermodynamic performance of the curved square microchannels in laminar flow is numerically investigated. The classical Navier-Stokes equations are adopted; aniline and ethylene glycol are selected as the working fluids. The results show that the heat transfer entropy generation number and frictional entropy generation number augment relatively under viscous dissipation effect for the case of fluid heated, and the opposite results can be found for the case of fluid cooled. The heat transfer entropy generation number increases with Reynolds number at large Reynolds number region under viscous dissipation effect when ethylene glycol is heated. The total entropy generation number extremum exists for aniline, and the extremum happens earlier when aniline is heated than when aniline is cooled. The smaller the curvature radius is, the earlier the extremum appears. The extremum does not occur for ethylene glycol due to the predomination of frictional entropy generation in the total entropy generation.     

Slip flow in elliptic microchannels

Microscale fluid dynamics has received intensive interest due to the emergence of Micro-Electro-Mechanical Systems (MEMS) technology. When the mean free path of the gas is comparable to the channel's characteristic dimension, the continuum assumption is no longer valid and a velocity slip may occur at the duct walls. The elliptic cross-section is one useful channel shape that may be produced by microfabrication. The elliptic microchannels have potential practical applications in MEMS. Slip flow in elliptic microchannels has been examined and a detailed theoretical analysis has been performed. A solution is obtained using elliptic cylinder coordinates and the separation of variables method. A simple model is developed for predicting the Poiseuille number in elliptic microchannels for slip flow. The developed model may be used to predict mass flow rate and pressure distribution of slip flow in elliptic microchannels.     

Viscous dissipation effect on entropy generation for non-Newtonian fluids in microchannels

An analytical study on the viscous dissipation effect on entropy generation in fully developed forced convection for single phase non-Newtonian fluid flow in circular microchannels is reported. In the first-law analysis, closed form solutions of the temperature distributions in the radial direction for the models with and without viscous dissipation term in the energy equation are obtained. In the second-law analysis, the two models are compared by analyzing their relative deviations in dimensionless entropy generation and Bejan number for different Brinkman number and power-law index. The findings show that under certain conditions the viscous dissipation effect on entropy generation in microchannels is significant and should not be neglected.     

Steady evaporating flow in rectangular microchannels

Analytical and numerical solutions are presented for steady evaporating flow in open microchannels having a rectangular cross section and a uniform depth. The flow, driven by the axial gradient of capillary pressure, generally consists of an entry region where the meniscus is attached to the top corners of the channel followed by a jump-like transition to a corner-flow region in which the meniscus progressively recedes into the bottom corners of the channel. Illustrative numerical solutions are used to guide the derivation of an easily applied analytical approximation for the maximum sustainable heat flux or capillary limit.     

Condensation flow patterns in silicon microchannels

A simultaneous visualization and measurement experiment was carried out to investigate condensation flow patterns of steam flowing through an array of trapezoidal silicon microchannels, having a hydraulic diameter of 82.8 μm and a length of 30 mm. The degassed and deionized water steam flowing in the microchannels was cooled by flowing water of 8 °C from the bottom. The silicon microchannels were covered with a thin transparent pyrex glass from the top which enabled the visualization of flow patterns. Experiments were performed at different inlet pressures ranging from 4.15 × 10⁵ Pa to 1.25 × 10⁵ Pa (with corresponding mass fluxes decreasing from 47.5 g/cm² s to 19.3 g/cm² s) while the outlet pressure was maintained at a value of 10⁵ Pa. Different condensation flow patterns such as fully droplet flow, droplet/annular/injection/slug-bubbly flow, annular/injection/slug-bubbly flow, and fully slug-bubbly flow were observed in the microchannels. At a given inlet pressure and mass flux, the flow pattern depended on both the location and time. Of particular interest is that the vapor injection flow, consisting of a series of bubble growth and detachment activities, appeared and disappeared periodically. During the disappearance period of injection flow, the slug-bubbly flow at downstream changed to the single-phase liquid flow due to the reversed flow of outlet condensate, while the annular flow at upstream changed to the vapor flow due to the effect of incoming vapor. Therefore, two-phase flow and single-phase flow appeared alternatively in the microchannels, causing large fluctuations of wall temperatures as well as other measurements. It was also found that the occurrence of vapor injection flow moved from the outlet toward the inlet as the mass flux was decreased. The vapor injection flow and its induced condensation instabilities in microchannels are reported here for the first time.     

Non-linear analyses of flow boiling in microchannels

Recently, four unstable boiling cases with different fluctuating amplitudes were observed in parallel silicon microchannels having a hydraulic diameter of 186 μm. These were: the liquid/two-phase alternating flow (LTAF) at two different heat fluxes, the continuous two-phase flow (CTF) at medium heat flux and medium mass flux, and the liquid/two-phase/vapor alternating flow (LTVAF) at high heat flux and low mass flux. In this paper, data of these unstable boiling cases are analyzed using the following methods: correlation coefficient, attractor reconstruction, correlation dimension and largest Lyapunov exponent. The processes responsible for appearance of chaotic oscillations in microchannels, such as nucleation, stability of bubbly flow, vapour core stability and vapour-phase flow stability, are discussed. It is shown that under certain conditions, the microchannels system works as a thermal oscillator. It was found that heat supplied to the microchannels increases the heating surface temperature while the appearance of the two-phase flow inside the channels decreases the heating surface temperature. The mechanism involving an increase in heating surface temperature is supported by phenomena of blocking the liquid flow in microchannels by the two-phase flow.     

Characterization of electroosmotic flow in rectangular microchannels

In this paper, the electroosmotic displacing process between two solutions (namely the same electrolyte of different concentrations) in a rectangular microchannel is studied theoretically and experimentally. Firstly, the electric potential and velocity field in a rectangular microchannel are obtained by solving the governing equations. Fourier transform method is used to solve the electrolyte concentration profile equation. The electric current versus time curve through the microchannel is predicted based on the concentration profile obtained. The current monitoring technique is then used to study the electroosmotic displacing process. The results from the measured current–time relations agree well with those from the prediction, suggesting a reliable theoretical model developed in this study.     

Experimental investigation of flow friction for liquid flow in microchannels

In this paper, investigations on the liquid flow in microchannels with different experimental methods are presented. The experiments were carried out in channels with hydraulic diameter ranging from 30 μm to 344 μm at Reynolds number ranging from 20 to 4000. Based on the experimental data collected and those available in the literature, comparisons and analysis have been carried out to evaluate the possible phenomena occurring in the liquid flow in microchannels. Results obtained show that characteristics of flow in microchannels agree with conventional behaviors predicted by Navier-Stokes equations in the region of those dimensions tested. In this paper, the detailed explanations on experimental results are discussed.     

Numerical simulation of two-fluid electroosmotic flow in microchannels

This paper presents a numerical scheme for stratified two-liquid electroosmotic flows. The simulation results highlight that using the electroosmotic effects can control the interface location of a pressure-driven two-liquid flow. A finite volume method is used to solve the coupled electric potential equation and Navier–Stokes equation together.The validity of the numerical scheme is evaluated by comparing its predictions with the results of the analytical solutions in the fully developed regions. The liquid–liquid interface developments due to the favorably and adversely applied electric field are examined.     

三角形微槽中的气体滑移流动特性

针对三角形微槽利用正交函数法求解了带一阶滑移边界条件的N-S方程,对不可压燃气体在等腰三角形和等边三角形微槽道内的充分发展层流滑移流动特性进行了理论分析,获得了三角形微槽内的速度分布和阻力特性的分析解,计算结果表明,正交函数法适用于三角形微槽内滑移流动特性的分析计算,在滑移流区,三角形微槽边界上出现滑移流动,且随着Knudsen数（气体分子的平均自由程与流道特征尺寸之比）的增大,壁面上的滑移速度越大,流动阻力随之减小,但三角形微槽的三个角区边界上的滑移速度增加较小,三角形微槽的高宽比对无量纲阻力常数随Kn的变化关系影响很小。     

Local measurement of flow boiling in structured surface microchannels

Experiments were conducted to investigate flow boiling in 200 μm × 253 μm parallel microchannels with structured reentrant cavities. Flow morphologies, boiling inceptions, heat transfer coefficients, and critical heat fluxes were obtained and studied for mass velocities ranging from G = 83 kg/m² s to G = 303 kg/m² s and heat fluxes up to 643 W/cm². Comparisons of the performance of the enhanced and plain-wall microchannels were performed. The microchannels with reentrant cavities were shown to promote nucleation of bubbles and to support significantly better reproducibility and uniformity of bubble generation. The structured surface was also shown to significantly reduce the boiling inception and to enhance the critical heat flux.     

Entropy generation of viscous dissipative nanofluid flow in microchannels

An analytical study on the viscous dissipation effect on entropy generation in laminar fully developed forced convection of water–alumina nanofluid in circular microchannels is reported. In the first-law analysis, closed form solutions of the temperature distributions in the radial direction for the models with and without viscous dissipation term in the energy equation are obtained. The results show that the heat transfer coefficient decreases with nanoparticle volume fraction largely in the laminar regime of nanofluid flow in microchannel when the viscous dissipation effect is taken into account. In the second-law analysis, the two models are compared by analyzing their relative deviations in entropy generation for different Reynolds number and nanoparticle volume fraction. When the viscous dissipation is taken into account, the temperature distribution is prominently affected and consequently the entropy generation ascribable to the heat transfer irreversibility is significantly increased. The increase of entropy generation induced by the increase of nanoparticle volume fraction is attributed to the increase of both the thermal conductivity and viscosity of nanofluid which causes augmentation in the heat transfer and fluid friction irreversibilities, respectively. By incorporating the viscous dissipation effect, both thermal performance and exergetic effectiveness for forced convection of nanofluid in microchannels dwindle with nanoparticle volume fraction, contrary to the widespread conjecture that nanofluids possess advantage over pure fluid associated with higher overall effectiveness from the aspects of first-law and second-law of thermodynamics.     

Analytical solution of gaseous slip flow in long microchannels

In this paper we provide solution of the Navier–Stokes equations for gaseous slip flow in long microchannels with a second-order accurate slip boundary condition at the walls. The obtained solution is general enough to allow evaluation of various slip models proposed in the literature. We compare our solution against the first-order accurate slip boundary condition and show that the solution has a weak dependence on Reynolds number, which was neglected in the earlier theory. It is emphasized that first-order slip models do not predict the “Knudsen paradox” (appearance of a minima in normalized volume flux at Knudsen number approximately unity), or a change in curvature of centerline pressure at Knudsen numbers of 0.16. A comparison with Boltzmann’s solution suggests that the derived solution agrees reasonably well up to Knudsen number approximately 5, which shows that the validity of Navier–Stokes to rarefied gases can possibly be increased by using a high order slip boundary condition and proper choice of the slip coefficients. This result is significant from the perspective of numerical simulations of rarefied gases.     

Boiling nucleation and two-phase flow patterns in forced liquid flow in microchannels

Using microfabrication techniques, a microscale platinum heater was fabricated on a Pyrex glass wafer and located in a shallow, but nearly trapezoidal microchannel with a hydraulic diameter of $D_{\mathrm{h}}$ = 56 microns fabricated on another glass wafer. Using a high-speed digital CCD video camera and microscope, the boiling nucleation temperature and two-phase flow patterns were observed and examined at different mass flow rates. The nucleation temperature was found to be reasonably close to the theoretical values as predicted by a 3D numerical heat transfer simulation with the measured bulk temperature of the microheater. The stability of the developed flow indicated three clearly distinguishable two-phase flow regimes: bubbly, wavy and annular. To avoid problems observed in the past, care was taken to ensure that the results were not influenced by the entrance and/or exit regions of the test section. The observed variations in the two-phase flow patterns were compared with the results of a model developed using a stability analysis of the liquid film.     

Melting of a phase change material in concentric horizontal annuli of arbitrary cross-section

Results are presented of a finite element computational study of the free convection-dominated melting of a pure phase change material contained in concentric horizontal annuli of the following configurations: (a) square external tube with a circular tube inside — annulus type A and (b) circular external tube with a square tube inside — annulus type B. Effects of the Rayleigh number as well as heating of the inside, outside or both walls at a temperature above the melting point of the material were studied. Flow and temperature patterns within the melt, local heat flux distributions at the heating surface and the cumulative energy charged as a function of time are presented and discussed.     

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.