Viscous flow in variable cross-section microchannels of arbitrary shapes

This paper outlines a novel approximate model for determining the pressure drop of laminar, single-phase flow in slowly-varying microchannels of arbitrary cross-section based on the solution of a channel of elliptical cross-section. A new nondimensional parameter is introduced as a criterion to identify the significance of frictional and inertial effects. This criterion is a function of the Reynolds number and geometrical parameters of the cross-section; i.e., perimeter, area, cross-sectional polar moment of inertia, and channel length. It is shown that for the general case of arbitrary cross-section, the cross-sectional perimeter is a more suitable length scale. An experimental investigation is conducted to verify the present model; 5 sets of rectangular microchannels with converging–diverging linear wall profiles are fabricated and tested. The collected pressure drop data are shown to be in good agreement with the proposed model. Furthermore, the presented model is compared with the numerical and experimental data available in the literature for a hyperbolic contraction with rectangular cross-section.     

Numerical simulation of heat transfer enhancement in wavy microchannel heat sink

In this paper, heat transfer and water flow characteristics in wavy microchannel heat sink (WMCHS) with rectangular cross-section with various wavy amplitudes ranged from 125 to 500 μm is numerically investigated. This investigation covers Reynolds number in the range of 100 to 1000. The three-dimensional steady, laminar flow and heat transfer governing equations are solved using the finite-volume method (FVM). The water flow field and heat transfer phenomena inside the heated wavy microchannels is simulated and the results are compared with the straight microchannels. The effect of using a wavy flow channel on the MCHS thermal performance, the pressure drop, the friction factor, and wall shear stress is reported in this article. It is found that the heat transfer performance of the wavy microchannels is much better than the straight microchannels with the same cross-section. The pressure drop penalty of the wavy microchannels is much smaller than the heat transfer enhancement achievement. Both friction factor and wall shear stress are increased proportionally as the amplitude of wavy microchannels increased.     

Optimization of anode performance in the ethanol electrochemical reforming for clean hydrogen production

Carbon-based fuel electrochemical reforming is considered as a promising hydrogen production method. Ethanol is one of the most appropriate carbon-based fuels. In this work, anode performance, especially the flow, ethanol electro-oxidization and energy consumption in the ethanol electrochemical reforming is numerically studied and experimental verified. Take the straight serpentine channel with square cross-section as a base structure in the electrochemical cell (EC), the effects of channel geometry and operating parameters are analyzed. Another five different configurations of flow channels, as well as another three different cross-sections are designed and explored. Results indicate that at the same cross-section area, the wider channel provides the higher effective area for proton transfer, and thereby improves the electrode reactions. The appropriate decrease of inlet velocity or increase of input voltage promotes the anode reaction and reduces the pressure drop in channel, while the operating temperature has the opposite effects on ethanol conversion and pressure drop. The arc channel is found optimal considering its highest ethanol conversion, although its pressure drop is a bit higher. The sector cross-section with uniform flow field distribution is found most favorable for the straight serpentine channel considering the ethanol electro-oxidization. These findings will favor the improvement of EC.     

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.     

Influence of channel geometry on the performance of a counter flow microchannel heat exchanger

Microchannel heat exchangers (MCHE) can be made with channels of various geometries. Their size and shape may have considerable effect on the thermal and hydraulic performance of a heat exchanger. In this paper numerical simulation is carried out to solve 3D developing flow and 3D conjugate heat transfer of a balanced counter flow microchannel heat exchanger (CFMCHE) to evaluate the effect of size and shape of channels on the performance of CFMCHE for the same volume of heat exchanger. The effect of shape of the channels on its performance is studied for different channel cross-sections such as circular, square, rectangular, iso-triangular and trapezoidal. Results show that for the same volume of a heat exchanger, increasing the number of channels lead to increase in both effectiveness and pressure drop. Moreover circular channels give the best overall performance (thermal and hydraulic) among various channel shapes. New correlations are developed to predict the value of heat exchanger effectiveness and performance index as a function of relative size of channels with overall heat exchanger volume, Reynolds number and thermal conductivity ratio.     

Validation of a Second-Order Slip Flow Model in Rectangular Microchannels

An analytical slip-flow model based on second-order boundary conditions was proposed for gaseous flow in rectangular microchannels. An experimental setup has been designed for the measurement of gaseous micro flow rates under controlled temperature and pressure conditions. Data relative to nitrogen and helium flows through rectangular microchannels, from 4.5 to 0.5 μm in depth and with aspect ratios from 1–9%, are presented and analyzed. A method is proposed to eliminate the main source of uncertainty, which is the imprecision when measuring the dimensions of the microchannel cross-section. It is shown that in rectangular microchannels, the proposed second-order model is valid for Knudsen numbers up to about 0.25, whereas the first-order model is no longer accurate for values higher than 0.05. The best fit is found for a tangential momentum accommodation coefficient σ = 0.93, both with helium and nitrogen.     

Experimental Study of Flow Patterns,Pressure Drop,and Flow Instabilities in Parallel Rectangular Minichannels

Abstract

Flow boiling heat transfer in parallel minichannels and microchannels is one of the solutions proposed for cooling high heat flux systems. The associated increase in the pressure drop poses a problem that needs to be studied in detail before the small diameter channels can be implemented in practical systems. The pressure drop fluctuations and the flow instability in a network of parallel channels connected by a common header also need to be addressed for the stable operation of flow boiling systems. The current work focuses on studying the flow patterns, pressure drop fluctuations, and flow instabilities in a set of six parallel rectangular minichannels, each with 333μm in hydraulic diameter. Deionized and degassed water was used for all the experiments. The pressure fluctuations are recorded and signal analysis is performed to find the dominant frequencies and their amplitudes. These pressure fluctuations are then mapped to their corresponding flow patterns observed using a high speed camera. The results help us to relate pressure fluctuations to different flow characteristics and their effect on flow instability.     

Three-dimensional thermal analysis of heat sinks with circular cooling micro-channels

The pressure drop and thermal characteristics of heat sinks with circular micro-channels are investigated using the continuum model consisting of the conventional Navier-Stokes equations and the energy conservation equation. Developing flow (both hydrodynamically and thermally) is assumed in the fluid region and three-dimensional conjugate heat transfer is assumed in the solid region. Thermal results based on this approach are shown to be in good agreement with existing experimental data. Effects of various geometrical parameters, material properties, and Reynolds number on the thermal performance of the sink were investigated. A comparison between circular and rectangular channels at the same Reynolds number and hydraulic diameter showed that sinks with rectangular channels have lower thermal resistance, while sinks with circular channels dissipate more heat per unit pumping power.     

Porous copper fiber sintered felts with surface microchannels for methanol steam reforming microreactor for hydrogen production

In this study, a laser micro-milling technique was introduced into the fabrication process of surface microchannels with different geometries and dimensions on the porous copper fiber sintered felts (PCFSFs). The PCFSFs with surface microchannels as catalyst supports were then used to construct a new type of laminated methanol steam reforming microreactor for hydrogen production. The microstructure morphology, pressure drop, velocity and permeability of PCFSF with surface microchannels were studied. The effect of surface microchannel shape (rectangular, stepped, and polyline) and catalyst loading amount on the reaction performance of methanol steam reforming microreactor for hydrogen production was further investigated. Our results show that the PCFSF with rectangular microchannels demonstrated a lower pressure drop, higher average velocity and higher permeability compared to the stepped and polyline microchannel. Furthermore, the PCFSF with rectangular microchannels also exhibited the highest methanol conversion and H₂ flow rate. The best reaction performance of methanol steam reforming microreactor for hydrogen production was obtained using PCFSF with rectangular microchannels when 0.5 g catalyst was loaded.     

ADIABATIC GAS–LIQUID FLOW IN MICROCHANNELS

This article presents a review of adiabatic two-phase flow in minichannels and microchannels. Differences between them are identified and explained based on this review and our own research. Several channels of decreasing diameter were used in our experiments to determine the effect of the channel size on the two-phase flow of nitrogen gas and water. The effect of channel geometry was examined by characterizing the two-phase flow in a circular and square microchannel of similar size. Only slug flow was observed in the microchannels. Four new sub-classes of slug flow were subsequently defined. A new correlation was developed for the time-averaged void fraction data in the microchannels. The two-phase pressure drop in microchannels was predicted by treating the two phases as being separate with a large velocity difference. Regarding the effect of microchannel geometry, the transition boundaries on the two-phase flow regime maps were shifted for the slug flow subcategories.     

Influence of channel shape on the thermal and hydraulic performance of microchannel heat sink

Microchannel heat sinks (MCHS) can be made with channels of various shapes. Their size and shape may have remarkable influence on the thermal and hydrodynamic performance of MCHS. In this paper, numerical simulations are carried out to solve the three-dimensional steady and conjugate heat transfer governing equations using the Finite-Volume Method (FVM) of a water flow MCHS to evaluate the effect of shape of channels on the performance of MCHS with the same cross-section. The effect of shape of the channels on MCHS performance is studied for different channel shapes such as zigzag, curvy, and step microchannels, and it is compared with straight and wavy channels. The MCHS performance is evaluated in terms of temperature profile, heat transfer coefficient, pressure drop, friction factor, and wall shear stress. Results show that for the same cross-section of a MCHS, the temperature and the heat transfer coefficient of the zigzag MCHS is the least and greatest, respectively, among various channel shapes. The pressure drop penalty for all channel shapes is higher than the conventional straight MCHS. The zigzag MCHS has the highest value of pressure drop, friction factor, and wall shear stress followed by the curvy and step MCHS, respectively.     

Channel cross section effect on heat transfer performance of oblique finned microchannel heat sink

In the present work, the effect of channel cross section on the heat transfer performance of an oblique finned micro-channel heat sink was investigated. Water and Al₂O₃/water nanofluid of volume fraction 0.25% were used as a coolant. The oblique finned microchannels are designed with three channel cross-sections namely square, semicircle and trapezoidal. The primary work of this paper is to study the heat transfer and hydrodynamic characteristics in the oblique finned microchannel. The experimental setup and procedure are validated using water as coolant in a micro-channel heat sink. Heat transfer and flow characteristics are examined for three cross-sections of varying mass flux. The trapezoidal channel cross-section increases the considerable heat transfer rate improvement for both water and nanofluid by 3.133% and 5.878% compared to square and semicircle cross section. Also, the pressure drop is higher in the trapezoidal cross-section over the square and semicircle cross section. This is due to increase in friction loss of trapezoidal cross section. The results indicate that trapezoidal cross-section oblique finned micro-channel is more suitable for heat transfer in the electronic cooling application.     

Fluid flow and convective heat transfer in flat microchannels

This study investigates the design, construction and instrumentation of an experimental microchannel, with a rectangular cross-section and large aspect ratio, that allows characterization of the flow and convective heat transfer under well defined and precise conditions and makes it possible to vary the hydraulic diameter of the microchannel. The flow friction coefficient is estimated by direct pressure drop measurements inside the microchannel in a zone where the flow is fully developed. Since the wall thermal conditions inside the microchannel can not be measured directly, their estimation requires temperature measurements in the wall thickness and an inverse heat conduction method. The thermal and hydrodynamic results obtained by varying the hydraulic diameter between 1 mm and 100 μm do not deviate from the theory or empirical correlations for large-scale channels. These results let us confirm that for smooth walls the continuum mechanics laws for convection and fluid mechanics remain valid in microchannels of hydraulic diameter greater than or equal to 100 μm.     

Experimental and numerical study on the flow characteristics in curved rectangular microchannels

In this paper, the flow characteristics in curved rectangular microchannels with different aspect ratios and curvature ratios for Re numbers ranging from 80 to 876 are investigated. The obtained experimental results are compared with simulated values based on classical Navier–Stokes equations and available correlation in the literature. An empirical equation based on experimental data is proposed to provide a better prediction of the frictional pressure drop in the curved rectangular microchannels.     

Adiabatic two-phase flow in rectangular microchannels with different aspect ratios: Part I – Flow pattern,pressure drop and void fraction

An aspect ratio is an important parameter for two-phase flow in a rectangular microchannel. To study the aspect ratio effect on the flow pattern, pressure drop and void fraction, experiments of adiabatic liquid water and nitrogen gas two-phase flow in rectangular microchannels were conducted. The widths and heights of rectangular microchannels are 510 μm × 470 μm, 608 μm × 410 μm, 501 μm × 237 μm and 503 μm × 85 μm. Therefore, the aspect ratios of the rectangular microchannels are 0.92, 0.67, 0.47 and 0.16; and the hydraulic diameters of the rectangular microchannels were 490, 490, 322 and 143 μm, respectively. Experimental ranges were liquid superficial velocities of 0.06–1.0 m/s and gas superficial velocities of 0.06–71 m/s. Visible rectangular microchannels were fabricated using a photosensitive glass. And pressure drop in microchannels was directly measured through embedded ports. The visualization of the flow pattern was carried out with a high-speed camera and a long distance microscope. Typical flow patterns in the rectangular microchannels observed in this study were bubble flow, transitional flow (multiple flow) and liquid ring flow. As the aspect ratio decreased, the bubble flow regime became dominant due to the confinement effect and the thickness of liquid film in corner was decreased. A void fraction in the rectangular microchannels has a linear relation with the volumetric quality. And the two-phase flow becomes homogeneous with decreasing aspect ratio owing to the reduction of the liquid film thickness. Like Zhang et al.’s [19] correlation, as the confinement number increased, the C-value in Lockhart and Martinelli correlation decreased. And a frictional pressure drop in the rectangular microchannels was highly related with the flow pattern.     

Fundamental data on the gas–liquid two-phase flow in minichannels

We report on the results of investigations into the characteristics of an air–water isothermal two-phase flow in minichannels, that is, in capillary tubes with inner diameters of 1 mm, 2.4 mm, and 4.9 mm, also in capillary rectangular channels with an aspect ratio of 1 to 9. The directions of flow were vertical upward, horizontal and vertical downward. Based on the authors 15 years of fundamental research into the gas–liquid two-phase flows in circular tubes and rectangular channels, we summarized the characteristics of the flow phenomena in a minichannel with special attention on the flow patterns, the time varying holdup and the pressure loss. The effects of the tube diameters and aspect ratios of the channels on these flow parameters and the flow patterns were investigated. Also the correlations of the holdup and the frictional pressure drop were proposed.     

Adiabatic two-phase flow in rectangular microchannels with different aspect ratios: Part II – bubble behaviors and pressure drop in single bubble

One of the major flow patterns in a microchannel is an elongated bubble flow, which is similar to a long slug bubble. Behaviors and pressure drop for a single bubble in a rectangular microchannel were studied. Based on the experiments in Part I of this paper, data for liquid superficial velocities of 0.06–0.8 m/s, gas superficial velocities of 0.06–0.66 m/s and AR of 0.92, 0.67, 0.47 and 0.16 were analyzed. The velocity, length, number, and frequency of the single bubble in the rectangular microchannel were obtained from image processing based on a unit cell model. The bubble velocities were proportional to total superficial velocity. As the aspect ratio decreased, the portion of the bubble area increased due to the corner effect. New correlation of the bubble velocity for different aspect ratio was proposed. Also, bubble and liquid slug length, the number of the unit cell and bubble frequency were analyzed with different aspect ratios. The pressure drop for the single bubble in the rectangular microchannels was evaluated using the information of the bubble behavior. The pressure drop in the single elongated bubble was proportional to the bubble velocity. The pressure drop in the single elongated bubble in the rectangular microchannel increased as the aspect ratio decreased.     

Gas/Liquid Flow in Plate-and-Frame Heat Exchangers - Part II: Two-Phase Multiplier and Flow Pattern Analysis

Pressure drop data measured during adiabatic two-phase flow in a plate-and-frame heat exchanger (PHE) are normalized with respect to the single-phase liquid pressure drop to give two-phase multipliers. A curve-fitted equation defines this relationship, which is a strong function of the Lockhart-Martinelli parameter. C coefficients are shown to be strong functions of both the Lockhart-Martinelli parameter and liquid viscosity, making this correlation unsuited to predictions of pressure drop in PHEs. Interfacial structure, observed during air-water downflow in replica channels (dC = 3 mm), is categorized into five flow patterns. These have a number of similarities with structures reported for circular and rectangular channels of similarly low hydraulic diameter. The transition boundaries between the patterns are shown to be a function of the chevron angle.     

Constructal optimization of the geometry of an array of micro-channels

This paper documents the geometric optimization of an array of circular and non-circular ducts. The optimization was carried out numerically using finite volume method. As optimal dimensions were independent of the array configuration, the numerical simulation was performed on a unit cell. Numerical optimization for circular, square and isosceles right triangle cross-sections of channels was performed. Based on the results of this investigation, some correlations were proposed to predict the optimal hydraulic diameter and dimensionless heat transfer per unit volume. In addition to examining the effect of pressure drop on these parameters, it was showed that among the different geometries of this study, square cross-section has the most efficiency for a given volume. The numerical results of the present study were compared with approximate results reported in the literature which a good agreement was observed.     

Voltage loss and fluctuation in proton exchange membrane fuel cells: The role of cathode channel plurality and air stoichiometric ratio

Water management is a critical issue in the development of proton exchange membrane (PEM) fuel cells with robust operation. Liquid water can accumulate and flood the gas delivery microchannels and the porous electrodes within PEM fuel cells and deteriorate performance. Since the liquid distribution fluctuates in time for two-phase flow, the rate of oxygen transport to the cathode catalyst layer also fluctuates, resulting in unstable power density and efficiency. This paper reports experimental data on the mean voltage loss and the voltage fluctuations during constant current operation as a function of both the number of parallel microchannels and the air flow rate stoichiometric ratio. We define channel plurality as a flow field design parameter to describe the number of channels per unit of active area. The voltage loss was found to scale proportionally to channel plurality divided by the air stoichiometric ratio. The amplitude of the voltage fluctuations was found to be linearly proportional to channel plurality and inversely proportional to the air stoichiometric ratio squared. By analyzing pressure drop data and power spectra, we conclude that the voltage fluctuations are well-correlated with two-phase flow instabilities in the cathode's parallel microchannels. Finally, a scaling analysis is presented for generalizing the results for fuel cells having different active area and channel cross-section.