Fluid flow in micro-channels

We consider the problem of liquid and gas flow in micro-channels under conditions of a small Knudsen and Mach numbers, that correspond to continuum model. Data from the literature on pressure drop in circular, rectangle, triangular and trapezoidal micro-channels with hydrodynamic diameter ranging from 1.01 μm to 4010 μm are analyzed. The Reynolds number at transition from laminar to turbulent flow is considered. Attention is paid to comparison between predictions of the conventional theory and experimental data, obtained during the last decade, as well as to discussion of possible sources of unexpected effects which were revealed by a number of previous investigations.     

Flow boiling heat transfer in two-phase micro-channel heat sinks--II. Annular two-phase flow model

This paper is Part II of a two-part study devoted to measurement and prediction of the saturated flow boiling heat transfer coefficient in water-cooled micro-channel heat sinks. Part I discussed the experimental findings from the study, and identified unique aspects of flow boiling in micro-channels such as abrupt transition to the annular flow regime near the point of zero thermodynamic equilibrium quality, and the decrease in heat transfer coefficient with increasing quality. The operating conditions of water-cooled micro-channels fell outside the recommended range for most prior empirical correlations. In this paper, an annular flow model is developed to predict the saturated flow boiling heat transfer coefficient. Features unique to two-phase micro-channel flow, such as laminar liquid and vapor flow, smooth interface, and strong droplet entrainment and deposition effects, are identified and incorporated into the model. The model correctly captures the unique overall trend of decreasing heat transfer coefficient with increasing vapor quality in the low vapor quality region of micro-channels. Good agreement is achieved between the model predictions and heat transfer coefficient data over broad ranges of flow rate and heat flux.     

Flow boiling heat transfer in two-phase micro-channel heat sinks--I. Experimental investigation and assessment of correlation methods

This paper is the first of a two-part study concerning measurement and prediction of saturated flow boiling heat transfer in a water-cooled micro-channel heat sink. In this paper, new experimental results are discussed which provide new physical insight into the unique nature of flow boiling in narrow rectangular micro-channels. The micro-channel heat sink contained 21 parallel channels having a m cross-section. Tests were performed with deionized water over a mass velocity range of 135-402 kg/m² s, inlet temperatures of 30 and 60 °C, and an outlet pressure of 1.17 bar. Results indicate an abrupt transition to annular flow near the point of zero thermodynamic equilibrium quality, and reveal the dominant heat transfer mechanism is forced convective boiling corresponding to annular flow. Contrary to macro-channel trends, the heat transfer coefficient is shown to decrease with increasing thermodynamic equilibrium quality. This unique trend is attributed to appreciable droplet entrainment at the onset of annular flow regime development, and the increase in mass flow rate of the annular film by droplet deposition downstream. Eleven previous empirical correlations are assessed and deemed unable to predict the correct trend of heat transfer coefficient with quality because of the unique nature of flow boiling in micro-channels, and the operating conditions of water-cooled micro-channel heat sinks falling outside the recommended application range for most correlations. Part II of this study will introduce a new annular flow model as an alternative approach to heat transfer coefficient prediction for micro-channels.     

Studies on gas–solid heat transfer during pneumatic conveying

Interactions between solids and gas during pneumatic conveying can be utilized for variety of applications including flash drying, solids preheating etc. Experiments on air–solid heat transfer were carried out in a vertical pneumatic conveying heat exchanger of 54 mm inside diameter, using gypsum as the solid material. The effect of solids feed rate (0.6–9.9 g/s), air velocity (4.21–6.47 m/s) and particle size (231–722.5 μm) on air–solid heat transfer rate, heat transfer area and air–solid heat transfer coefficient has been studied. Empirical correlations have been proposed for the prediction of Nusselt number based on the present experimental data. The proposed correlations predict Nusselt number within an error of ±15% for the present data.     

Effect of developing flow and thermal regime on momentum and heat transfer in micro-scale heat sink

A developing micro-channel heat transfer and fluid flow has been investigated experimentally in rectangular micro-channels of D_h = 440 μm, having water as a working fluid. Infrared technique was used to design and built a micro-channel test section that incorporate internal fluid temperature measurements. The new method that provides information about the fluid temperature distribution inside the channel and provides validation for the methods used to determine the local and average Nusselt numbers. The experimental results have been compared with theoretical predictions from the literature and results obtained by numerical modeling of the present experiment. The experimental results of pressure drop and heat transfer confirm that including the entrance effects, the conventional theory is applicable for water flow through micro-channels.These results differ from the conclusions of several researches. It was shown that data presented by some researches can be due to entrance effects. The present results highlight the importance of accounting for common phenomena that are often negligible for standard flows such as accounting for profile of inlet velocity, axial heat conduction, effect of the design inlet and outlet manifolds.This paper, to the best of knowledge, is the first presentation on the method of the bulk fluid temperature measurements along micro-channel using IR technique, and calculation of the local heat transfer coefficient based on the local heat flux and the local temperature difference between the heated wall and the bulk fluid temperature.     

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.     

Analysis of microchannel heat sink performance using nanofluids

In this study, silicon microchannel heat sink performance using nanofluids as coolants was analyzed. The nanofluid was a mixture of pure water and nanoscale Cu particles with various volume fractions. The heat transfer and friction coefficients required in the analysis were based on theoretical models and experimental correlations. In the theoretical model, nanofluid was treated as a single-phase fluid. In the experimental correlation, thermal dispersion due to particle random motion was included. The microchannel heat sink performances for two specific geometries, one with W_ch = W_fin = 100 μm and L_ch = 300 μm, the other with W_ch = W_fin = 57 μm and L_ch = 365 μm, were examined. Because of the increased thermal conductivity and thermal dispersion effects, it was found that the performances were greatly improved for these two specific geometries when nanofluids were used as the coolants. In addition to heat transfer enhancement, the existence of nanoparticles in the fluid did not produce extra pressure drop because of small particle size and low particle volume fraction.     

Flow condensation in parallel micro-channels – Part 2: Heat transfer results and correlation technique

This second part of a two-part study concerns heat transfer characteristics for FC-72 condensing along parallel, square micro-channels with a hydraulic diameter of 1 mm, which were formed in the top surface of a solid copper plate. Heat from the condensing flow was rejected to a counter flow of water through channels brazed to the underside of the copper plate. The FC-72 condensation heat transfer coefficient was highest near the channel inlet, where the annual liquid film is thinnest. The heat transfer coefficient decreased along the micro-channel because of the film thickening and eventual collapse of the annular regime. Notable heat transfer enhancement was observed for annular flow regions of the micro-channel associated with interfacial waves. Comparing the present data to predictions of previous annular condensation heat transfer correlations shows correlations intended for macro-channels generally provide better predictions than correlations intended specifically for mini/micro-channels. A new condensation heat transfer coefficient correlation is proposed for annular condensation heat transfer in mini/micro-channels. The new correlation shows excellent predictive capability based on both the present FC-72 data and a large database for mini/micro-channel flows amassed from eight previous sources.     

Prediction of the onset of nucleate boiling in microchannel flow

The onset of nucleate boiling in the flow of water through a microchannel heat sink was investigated. The microchannels considered were 275 μm wide by 636 μm deep. Onset of nucleate boiling was identified with a high-speed imaging system and the heat flux at incipience was measured under various flow conditions. An analytical model was developed to predict the incipient heat flux as well as the bubble size at the onset of boiling. The closed-form solution obtained sheds light on the impact of the important system parameters on the incipient heat flux. The model predictions yield good agreement with the experimental data.     

Viscous heating in liquid flows in micro-channels

Many experimental works on forced convection through micro-channels evidenced that when the hydraulic diameter is less than 1 mm, conventional theory can no longer be considered as suitable to predict the pressure drop and convective heat transfer coefficients. This conclusion seemed valid for both gas and liquid flows. Sometimes the authors justified this claim by invoking “new” micro-effects. On the contrary, in this paper the explanation of the experimental results obtained for micro-channels in terms of friction factors will be researched inside the conventional theory (Navier-Stokes equations). In particular, this paper will focus on the role of viscous heating in fluids flowing through micro-channels. A criterion will be presented to draw the limit of significance for viscous dissipation effects in micro-channel flows. The role of the cross-sectional geometry on viscous dissipation will be highlighted and the minimum Reynolds number for which viscous dissipation effects can no longer be neglected will be calculated as a function of the hydraulic diameter and of the micro-channel geometry for different fluids. It will be demonstrated how viscous effects can explain some experimental results on the Poiseuille numbers in micro-channels, which recently appeared in the open literature.     

Heat transfer characteristics of gaseous flows in microtube with constant heat flux

Heat transfer characteristics of gaseous flows in a microtube with constant heat flux whose value is positive or negative are investigated on two-dimensional compressible laminar flow for no-slip regime. The numerical methodology is based on the Arbitrary–Lagrangian–Eulerian (ALE) method. The computations are performed for tubes with constant heat flux ranging from −10⁴ to 10⁴ W m⁻². The tube diameter ranges from 10 to 100 μm and the aspect ratio of the length and diameter is 200. The stagnation pressure, p_stg is chosen in such away that the Mach number at the exit ranges from 0.1 to 0.7. The outlet pressure is fixed at the atmosphere. The wall and bulk temperatures in microtubes with positive heat flux are compared with those of negative heat flux case and also compared with those of the incompressible flow in a conventional sized tube. In the case of fast flow, temperature profiles normalized by heat flux have different trends whether heat flux is positive or negative. A correlation for the prediction of the wall temperature of the gaseous flow in the microtube is proposed. Supplementary runs with slip boundary conditions for the case of D = 10 μm conducted and rarefaction effect is discussed. With increasing Ma number, the compressibility effect is more dominant and the rarefaction effect is relative insignificant where Kn number is less than Kn = 0.0096. And, the magnitudes of viscous dissipation term and compressibility term are investigated along the tube length.     

Variance analysis of estimates and measurements of terrestrial heat flow

A components-of-variance-analysis is applied to compare heat flow estimates with heat flow measurements. Three types of heat flow data are analysed; they are: “between depth interval within well” variances, “between well site-within region” variances and “between region” variances. “Between depth interval-within well” heat flow variances are typically greater for estimates than for measurements, implying a greater unsystematic uncertainty with the interval heat flow estimates as compared to the interval measurements. “Between well site-within region” variances of heat flow are about the same, or in some cases less, for groups of estimated data as compared with groups of measured data. Therefore unsystematic uncertainties for good heat flow estimates at sites within a region should compare favourably with similar uncertainties for heat flow measurements at sites within a region. Both the “F” test and the “between region” heat flow variances suggest that estimates and measurements of heat flow can reasonably differentiate between regions of different heat flow.Some of the estimated and measured data groups are from the same region. The very limited number of heat flow estimates and measurements available indicate that the mean of estimates and the mean of deep measurements in the northern Colorado Plateau are in close agreement. While this suggests the possibility that a number of carefully calculated heat flow estimates may reasonably define the mean heat flow for a region, more data in other regions will be needed to support the concept.     

Heat Transfer Characteristics of Gaseous Flows in Micro-Channel with Negative Heat Flux

Two-dimensional compressible momentum and energy equations are solved to obtain the heat transfer characteristics of gaseous flows in micro-channels with constant heat flux for which the value is negative for no-slip flow. The numerical methodology is based on the Arbitrary-Lagrangian-Eulerian method. The computations are performed for channels with constant heat flux ranging from ?10⁴ to ?10² W/m². The channel height ranges from 10 to 100 μ m and the aspect ratio of the channel height and length is 200. The stagnation pressure is chosen such that the exit Mach number ranges from 0.1 to 0.7. The outlet pressure is fixed at the atmosphere. The wall and bulk temperatures in micro-channels with negative heat flux are compared with those of positive heat flux cases obtained in our previous work and also those of the incompressible flow in a conventional sized channel. In the case of fast flow, temperatures normalized by heat flux have different trends whether heat flux value is positive or negative. A correlation for the prediction of the wall temperature of the gaseous flow in the micro-channel is proposed. The rarefaction effect is investigated for the cases of channel height of 10 μ m with slip boundary conditions. The magnitudes of viscous dissipation term and compressibility term are also investigated. The effect of each term on heat transfer characteristics is discussed.     

Measurement and prediction of pressure drop in a two-phase micro-pin-fin heat sink

This study concerns pressure drop in a two-phase heat sink containing an array of staggered square micro-pin-fins having a 200 × 200 μm² pin cross-section by a 670 μm pin height. Three inlet temperatures of 30, 60 and 90 °C, and six maximum mass velocities for each inlet temperature, ranging from 183 to 420 kg/m² s, were tested. Frictional pressure drop in the boiling region is deemed the dominant pressure drop component. The Lockhart–Martinelli correlation for laminar liquid–laminar vapor combination in conjunction with a previous single-phase friction factor correlation can adequately predict the data. Micro-pin-fins offer better flow stability than parallel micro-channels.     

Effects of choking on flow and heat transfer in micro-channels

The gas flows through micro-channels are encountered in many engineering applications such as the cooling devices of electronic chips, semiconductors, micro-electro-mechanical systems (MEMS), etc. Many works have been performed to investigate the flow and heat transfer characteristics generally occurring in the micro channels. According to these investigations, the majority of heat was transferred in the entrance region of the channel, due to high strain rate of the developing flow. These findings are valid only for unchoked micro channel flows. Once the gas flow is choked, the major flow features may be changed but no detailed works have been carried out to date. In these regards, the choked flow characteristics should be known to investigate the heat transfer phenomena in the micro channel flows. In the present study, numerical simulations have been used to provide detailed flow and heat transfer characteristics of micro-channel gas flows. The main objectives of the present effort are to understand the evolution of choking inside micro-channels with isothermally-heated-walls and to elucidate the regions of high heat transfer. The results obtained show that for choked flow conditions, high heat transfer is generated at both the entrance and the exit of the micro-channel. The exit effects like increased strain rate, high temperature gradient and the thinning of the boundary layer cause a rapid increase in heat transfer at the exit of the micro-channel. The location where the flow is choked is practically important in determining the heat transfer phenomena at the vicinity of the channel exit.     

Recent developments in EHD Enhanced Heat Transfer

This paper considers that the case for using electrohydrodynamic (EHD) enhancement of heat transfer has been established, especially in thermodynamic renewable energy applications where temperature levels are relatively low. It goes on to establish the basis on which nucleate boiling heat transfer is enhanced by EHD forces at surfaces designed to improve condensation, giving experimental results for a six-tube, shell/tube heat exchanger boiling R12 at “Io-fin” surfaces as well as for single-tube tests using “Thermoexcel” and “Gewa-T” surfaces.     

Convection film boiling on horizontal cylinders

Free, mixed and forced convection film boiling on a horizontal cylinder in a saturated or subcooled liquid is studied theoretically using a single model based on a two-phase laminar boundary layer integral method. The vapour flow is described accurately by including the inertia and convection terms in the momentum and energy equations, in order to study convection film boiling in the cases of very high superheat. Different film boiling cases are then analysed with this model. The case of high superheat and low subcooling was first analysed by comparing the model with an experiment consisting in the quenching of wires with very high superheat: the model was able to predict the measured heat transfer from the cylinder with errors less than 30%, performing better than previous models or correlations. Additional calculations in other high superheat conditions have also been performed and compared with a model which does not include the inertia and convection terms in order to have a more quantitative idea of their effects on the heat transfers. The case of low superheat and high subcooling is then analysed by comparing the model with other forced convection experiments with cylinders at lower temperatures. By analysing different experiments, it is found that there are in fact two different forced convection film boiling sub-regimes characterised by relatively “low” or “high” heat transfers, and that the existence of these sub-regimes is probably linked with the stability of the vapour film during film boiling. The model results compare quite well with the experimental data which belong to the “stable” sub-regime but, on the other hand, the model largely underestimates the heat transfer for experimental data which belongs to the “unstable” sub-regime. Finally, the model is compared to some free convection experimental data. The model was able to predict the measured heat transfers from the cylinder with errors less than 30% both in saturated and subcooled cases.     

Feasibility investigations on a novel micro-manufacturing process for fabrication of fuel cell bipolar plates: Internal pressure-assisted embossing of micro-channels with in-die mechanical bonding

In this paper, we present the results of our studies on conceptual design and feasibility experiments towards development of a novel hybrid manufacturing process to fabricate fuel cell bipolar plates that consists of multi-array micro-channels on a large surface area. The premises of this hybrid micro-manufacturing process stem from the use of an internal pressure-assisted embossing process (cold or warm) combined with mechanical bonding of double bipolar plates in a single-die and single-step operation. Such combined use of hydraulic and mechanical forming forces and in-process bonding will (a) enable integrated forming of micro-channels on both surfaces (as anode and cathode flow fields) and at the middle (as cooling channels), (b) reduce the process steps, (c) reduce variation in dimensional tolerances and surface finish, (d) increase the product quality, (e) increase the performance of fuel cell by optimizing flow-field designs and ensuring consistent contact resistance, and (f) reduce the overall stack cost. This paper explains two experimental investigations that were performed to characterize and evaluate the feasibility of the conceptualized manufacturing process. The first investigation involved hydroforming of micro-channels using thin sheet metals of SS304 with a thickness of 51 μm. The width of the channels ranged from 0.46 to 1.33 mm and the height range was between 0.15 and 0.98 mm. Our feasibility experiments resulted in that different aspect ratios of micro-channels could be fabricated using internal pressure in a controllable manner although there is a limit to very sharp channel shapes (i.e., high aspect ratios with narrow channels). The second investigation was on the feasibility of mechanical bonding of thin sheet metal blanks. The effects of different process and material variables on the bond quality were studied. Successful bonding of various metal blanks (Ni201, Al3003, and SS304) was obtained. The experimental results from both investigations demonstrated the feasibility of the proposed manufacturing technique for making of the fuel cell bipolar plates.     

The Investigation of Flow Boiling for Flows in Channels with Cross-Corrugated Walls

The problem of heat transfer for flows in channels with corrugated walls is very complicated. Previously most investigators have focused their attention on studies of forced-convection, single-phase flow, and condensation of pure vapors and vapor gas mixtures. The results of new experimental investigations into heat transfer and pressure drop, for flow boiling in channels with corrugated walls, are discussed. The experimental section was a part of a pack of an industrial plate exchanger, which contained several pressed plates with longitude corrugations located under an angle to flow direction and had many contact points on the heat transfer area. The condensation method was used for the investigations. The relationship between the heat transfer ratios of the Nusselt number for single-phase flow was obtained. This correlation compares very favorably with the similar relationship obtained for flow bubble boiling in tubes proposed by Sterman [11]. For correlation of the pressure drop data, the Martinelli-Lockart approach was used, which also correlated well with the results of this study and the results of other investigations. The relationship obtained may be used in calculations for various types of industrial units which have corrugated patterns on their heat transfer surfaces.     

Heat transfer of gas–liquid mixture in micro-channel heat sink

The main objective of the present investigation is to study heat transfer in parallel micro-channels of 0.1 mm in size. Comparison of the results of this study to the ones obtained for two-phase flow in “conventional” size channels provides information on the complex phenomena associated with heat transfer in micro-channel heat sinks. Two-phase flow in parallel micro-channels, feeding from a common manifold shows that different flow patterns occur simultaneously in the different micro-channels: liquid alone (or single-phase flow), bubbly flow, slug flow, and annular flow (gas core with a thin liquid film, and a gas core with a thick liquid film). Although the gas core may occupy almost the entire cross-section of the triangular channel, making the side walls partially dry, the liquid phase always remained continuous due to the liquid, which is drawn into the triangular corners by surface tension. With increasing superficial gas velocity, a gas core with a thin liquid film is observed. The visual observation showed that as the air velocity increased, the liquid droplets entrained in the gas core disappeared such that the flow became annular. The probability of appearance of different flow patterns should be taken into account for developing flow pattern maps. The dependence of the Nusselt number, on liquid and gas Reynolds numbers, based on liquid and gas superficial velocity, respectively, was determined in the range of Re_LS = 4–56 and Re_GS = 4.7–270. It was shown that an increase in the superficial liquid velocity involves an increase in heat transfer (Nu_L). This effect is reduced with increasing superficial gas velocity, in contrast to the results reported on two-phase heat transfer in “conventional size” channels.