Theory of heat transfer during condensation in microchannels

A theoretical model for condensation in microchannels takes account of the effects of gravity and streamwise shear stress on the condensate surface as well as the transverse pressure gradient due to surface tension in the presence of change in condensate surface curvature. Numerical solutions of the relevant conservation equations have been obtained for various channel shapes, dimensions, vapor-to-surface temperature differences and vapor mass fluxes. The theory is reviewed and updated. The effect of channel inclination is included and new results are presented. When using boundary conditions of uniform vapor and surface temperature it is found that, over a certain length of channel, the local mean (around the channel perimeter) heat-transfer coefficient is essentially independent of gravity and vapor shear stress. For the surface tension dominated regime, an equation for the Nusselt number as a function of a single dimensionless group, analogous to that occurring in the simple Nusselt theory except that the gravity term is replaced by a surface tension term, has been derived both on the basis of dimensional analysis and by approximate theory. The equation represents all of the data satisfactorily. This is a step towards the goal of representing the solutions, including those conditions where shear stress and gravity play important roles, by relatively simple dimensionless algebraic equations, valid for any fluid and channel geometry, for convenient use in design and optimization.     

Transition from annular flow to plug/slug flow in condensation of steam in microchannels

A visualization study has been conducted to investigate the transition from annular flow to plug/slug flow in the condensation of steam in two different sets of parallel microchannels, having hydraulic diameters of 90 μm and 136 μm, respectively. The steam in the parallel microchannels was cooled on the bottom by forced convection of water and by natural convection of air from the top. It is found that the location, where the transition from annular flow to plug/slug flow takes place, depends on mass flux and cooling rate of steam. The effects of mass flux and cooling rate on the occurrence frequency of the injection flow in a single microchannel, having a hydraulic diameter of 120 μm and 128 μm, respectively, are investigated. It is found that two different shapes of injection flow occur in the smooth annular flow in microchannels: injection flow with unsteady vapor ligament occurring at low mass flux (or high cooling rate) and injection flow with steady vapor ligament occurring at high mass flux (or low cooling rate). It is also found that increase of steam mass flux, decrease of cooling rate, or decrease of the microchannel diameter tends to enhance instability of the condensate film on the wall, resulting in occurrence of the injection flow further toward the outlet with an increase in occurrence frequency.     

Augmentation of outside tube heat transfer coefficient during condensation of steam over horizontal copper tubes

An experimental investigation has been carried out to find the condensing side heat transfer coefficient, h_o, during condensation of steam over a plain tube, a circular integral-fin tube(CIFT) and a spine integral-fin tube(SIFT). The CIFT and SIFT have enhanced the h_o by a factor of 2.5 and 3.2 respectively. The experimental values of h_o for CIFT were compared with those predicted from different models. The Honda and Nozu model underpredicted the values of h_o in a range of 10 to 20 percent.     

Visualization study of steam condensation in triangular microchannels

A visualization experiment is conducted to investigate the condensation of steam in a series of triangular silicon microchannels. The results indicate that droplet, annular, injection and slug-bubbly flow are the dominant flow patterns in these triangular silicon microchannels. With increased mass flow rate, or an increase in the hydraulic diameter under the same Reynolds number, the location at which the injection occurred is observed to move towards the channel outlet. The frequency of the injection increases, i.e. the flow of condensation instability is higher with increased inlet vapor Reynolds number, condensate Weber number and the prolongation of the injection location, or with a decrease in the hydraulic diameter of the channel. In addition, the wall temperature of the channel decreases along the condensation stream. The total pressure drop, the average condensation heat transfer coefficient and the average Nusselt number are observed to be larger with increased inlet vapor Reynolds number. Moreover, it is found that the condensation heat transfer is enhanced by a reduction in the channel scale.     

Marangoni凝结表面传热系数的影响因素分析

对水和酒精混合蒸气在竖直平板上的凝结传热进行了研究。利用液膜覆盖率,分别按考虑和忽略浓度边界层扩散热阻计算了凝结表面传热系数,并将计算结果与实验值进行了比较。结果发现同时考虑液膜导热热阻及浓度边界层扩散热阻的计算值在极小酒精质量分数时高于实验值,在较小酒精质量分数时和实验值接近,但是在高酒精质量分数时低于实验值。由此可见计算凝结表面传热系数时,在小酒精质量分数条件下扩散热阻可以忽略,但在高酒精质量分数条件下扩散热阻对整个热阻的贡献较大,必须考虑其对传热的影响。     

Heat transfer in trapezoidal microchannels of various aspect ratios

Heat transfer in the thermal entrance region of trapezoidal microchannels is investigated for hydrodynamically fully developed, single-phase, laminar flow with no-slip conditions. Three-dimensional numerical simulations were performed using a finite-volume approach for trapezoidal channels with a wide range of aspect ratios. The sidewall angles of 54.7° and 45° are chosen to correspond to etch-resistant planes in the crystal structure of silicon. Local and average Nusselt numbers are reported as a function of dimensionless length and aspect ratio. The effect of Prandtl number upon the thermal entrance condition is explored. The fully developed friction factors are computed and correlated as a function of channel aspect ratio. Correlations are also developed for the local and average Nusselt numbers in the thermal entrance region as a function of a dimensionless axial length variable.     

Dropwise condensation heat transfer of steam on a polytethefluoroethylene film

bouctionThe higher heat tranSfer phae due todroPwise condensation as cOmPared with filIncondensation had bo inveshgated extensively by manyresearchers durin the past sixty years["n. Grea PrOgI'esshad been Inade in understanding the IneCanisms fordroPwise condensation pessP'q, However unscondensation mode had not been widely aPPlied toPIaedcal heat exchanger devices due tO the crucialProblem of han an effeChve method formanhaurin the bopwise condensation sbos.ReCetly, the successful aP…     

The effective use of heat transfer additives for steam condensation

Reported herein are the results of the experimental investigations on the effect of small amounts of heat transfer additives (C_add<1000 ppm) on steam condensation in a bundle of horizontal tubes that are internally cooled. The condenser was designed with 12 tubes in an array of three horizontals and four verticals with a 2-in. horizontal and 1.5-in. vertical in-line pitch. By using effective additives, the condensation heat transfer rate can be augmented as much as 30% as compared with heat transfer that operated without additives under the same operating condition. The steam condensation, which occurred in our experiments while using effective additives, was mostly dropwise like. When heat transfer additives function effectively, the condensate-droplets become more dispersed and have a smaller shape than those produced without additives. These droplets, unlike traditional turbulence, start at the top portion of the condenser tubes and cover most of the tubes. Such a flow behavior can be explained by the Marangoni effect (in terms of thermodynamic equilibrium) in connection with obtained surface tension data. Furthermore, we extend our discussion to the dynamic effect of surface tension in the steam condensation process and propose a general criterion for selecting effective additives. In our experiments, we noted that the use of heat transfer additives such as 2-ethyl-1-hexanol for steam condensation was highly effective.     

Numerical simulation for steady annular condensation flow in triangular microchannels

A steady one-dimensional model for annular condensation flow in triangular microchannels is developed. The curvature radius distribution of the condensate stream along the channel has been determined numerically. The results indicate that the curvature radius of the liquid phase would increase rapidly at the beginning, and then as the condensation process progresses along the length of the microchannels, the radius increase would proceed more slowly. At the end of the condensation flow, the radius increases rapidly again. A smaller contact angle and heat flux or a larger hydraulic diameter and steam pressure will all result in a longer condensation length.     

Visualization study of steam condensation in wide rectangular silicon microchannels

A visualization study is conducted to investigate condensation flow in wide rectangular silicon microchannels with the hydraulic diameter of 90.6 μm and width/depth ratio of 9.668. Droplet-annular compound flow, injection flow, and vapor slug-bubbly flow are observed along the channel, which differ from that in other cross-sectional shape microchannels. In the droplet-annular compound flow region, the vertical walls (short side) of the channel are completely covered by the condensate, while droplet condensation still exists on the horizontal wall (long side) of the channel. The location of the injection flow will be postponed with the increasing inlet vapor Reynolds number. The injection frequency will increase with the increasing inlet vapor Reynolds number and condensate Weber number. More specifically, the frequency in the wide rectangular microchannels is lower than that in triangular microchannels having the same hydraulic diameter. It is confirmed that the cross-sectional shape of the microchannel plays a significant role on the instability of condensation flow. In addition, the correlation of Nusselt number is also presented.     

Performance of annular fins with different profiles subject to variable heat transfer coefficient

Performance of annular fins of different profiles subject to locally variable heat transfer coefficient is investigated in this paper. The performance of the fin expressed in terms of fin efficiency as a function of the ambient and fin geometry parameters has been presented in the literature in the form of curves known as the fin-efficiency curves for different types of fins. These curves, that are essential in any heat transfer textbook, have been obtained based on constant convection heat transfer coefficient. However, for cases in which the heat transfer from the fin is dominated by natural convection, the analysis of fin performance based on locally variable heat transfer coefficient would be of primer importance. The local heat transfer coefficient as a function of the local temperature has been obtained using the available correlations of natural convection for plates. Results have been obtained and presented in a series of fin-efficiency curves for annular fins of rectangular, constant heat flow area, triangular, concave parabolic and convex parabolic profiles for a wide range of radius ratios and the dimensionless parameter m based on the locally variable heat transfer coefficient. The deviation between the fin efficiency calculated based on constant heat transfer coefficient, reported in the literature, and that presently calculated based on variable heat transfer coefficient, has been estimated and presented for all fin profiles with different radius ratios.     

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.     

Study on condensation heat transfer characteristics of wet paper in steam heating process

Effects of suction pressure and permeability on the steam heating characteristics of the wet paper are studied. Experimental results show that suction pressure enhances the energy absorption in the wet paper and effects of suction pressure strongly appear in the high-permeability paper, and also absorbed energy rate is decreased with increasing in heating time. From the numerical simulation results it is found that increase in moisture content and decrease of pressure gradient reduce the absorbed energy rate. Dimensionless numbers are derived from the basic equations to summarize the experimental and numerical simulation results.     

Boiling heat transfer in rectangular microchannels with reentrant cavities

This paper investigates flow boiling of water in microchannels with a hydraulic diameter of 227 μm possessing 7.5 μm wide reentrant cavities on the sidewalls. Average two-phase heat transfer coefficients and CHF conditions have been obtained over a range of effective heat fluxes (28–445 W/cm²) and mass velocities (41–302 kg/m² s). High Boiling number and Reynolds number have been found to promote convective boiling, while Nucleate Boiling dominated at low Reynolds number and Boiling number. A criterion for the transition between nucleate and convective boiling has been provided. Existing correlations did not provide satisfactory agreement with the heat transfer coefficient but did predict CHF conditions well.     

Investigation of heat transfer in rectangular microchannels

An experimental investigation was conducted to explore the validity of classical correlations based on conventional-sized channels for predicting the thermal behavior in single-phase flow through rectangular microchannels. The microchannels considered ranged in width from 194 μm to 534 μm, with the channel depth being nominally five times the width in each case. Each test piece was made of copper and contained ten microchannels in parallel. The experiments were conducted with deionized water, with the Reynolds number ranging from approximately 300 to 3500. Numerical predictions obtained based on a classical, continuum approach were found to be in good agreement with the experimental data (showing an average deviation of 5%), suggesting that a conventional analysis approach can be employed in predicting heat transfer behavior in microchannels of the dimensions considered in this study. However, the entrance and boundary conditions imposed in the experiment need to be carefully matched in the predictive approaches.     

Fully developed electro-osmotic heat transfer in microchannels

Thermally fully developed, electro-osmotically generated convective transport has been analyzed for a parallel plate microchannel and circular microtube under imposed constant wall heat flux and constant wall temperature boundary conditions. Such a flow is established not by an imposed pressure gradient, but by a voltage potential gradient along the length of the tube. The result is a combination of unique electro-osmotic velocity profiles and volumetric heating in the fluid due to the imposed voltage gradient. The exact solution for the fully developed, dimensionless temperature profile and corresponding Nusselt number have been determined analytically for both geometries and both thermal boundary conditions. The fully developed temperature profiles and Nusselt number are found to depend on the relative duct radius (ratio of the Debye length to duct radius or plate gap half-width) and the magnitude of the dimensionless volumetric source.     

Transient conjugate heat transfer in straight microchannels

Many theoretical and experimental studies have been carried out in order to study the flow and heat transfer in microchannels. In the recent years, numerical simulation has been applied to investigate the problem under a variety of conditions. However, much of the focus has been on steady-state problems and time-dependent transport has received relatively minor attention, despite its importance in practical electronic devices and systems. Employing a versatile commercial code, this paper aims to examine heat removal from straight rectangular microchannels affected by a time-dependent heat flux input. Both cosinusoidal variation and step-change application and removal of a uniform heat source are studied to determine the response time of the system. For the fluid phase, the two-dimensional momentum and energy equations are solved, considering temperature dependent properties and viscous dissipation. The effects of the amplitude of the heat flux variation, inlet velocity, and geometry, including the thickness of the heat sink, are investigated. Channels of smaller width are found to be more sensitive to the heat flux source, especially for higher input values. The velocity represents the most important parameter for channels of greatest width considered here, as it directly affects the fluid dynamics and the pressure drop when a time-dependent heat source is applied to the system.     

Effects of surface roughness and tube materials on the filmwise condensation heat transfer coefficient at low heat transfer rates

The laminar filmwise condensation heat transfer coefficient on the horizontal tubes of copper and stainless steel was investigated. The outside diameter of the tubes was 15.88 mm, and the tube thickness ranged from 1.07 to 1.6 mm. The polished stainless steel tube had an RMS surface roughness of 0.37 μm, and commercial stainless steel tubes had maximum surface roughness of 15 μm. The tests were conducted at saturation temperatures of 20 and 30 °C, and liquid wall subcoolings from 0.4 to 2.1 °C. The measured condensation heat transfer coefficients were significantly lower than the predicted data by the Nusselt analysis when the ratio of the condensate liquid film thickness to the surface roughness, δ / R_p–v, was relatively low. When the condensate liquid film was very thin, tube material affected the condensation heat transfer coefficient in the filmwise condensation.     

Forced convective heat transfer of nanofluids in microchannels

Convective heat transfer coefficient and friction factor of nanofluids in rectangular microchannels were measured. An integrated microsystem consisting of a single microchannel on one side, and two localized heaters and five polysilicon temperature sensors along the channel on the other side were fabricated. Aluminum dioxide (Al₂O₃) with diameter of 170 nm nanofluids with various particle volume fractions were used in experiments to investigate the effect of the volume fraction of the nanoparticles to the convective heat transfer and fluid flow in microchannels. The convective heat transfer coefficient of the Al₂O₃ nanofluid in laminar flow regime was measured to be increased up to 32% compared to the distilled water at a volume fraction of 1.8 volume percent without major friction loss. The Nusselt number measured increases with increasing the Reynolds number in laminar flow regime. The measured Nusselt number which turned out to be less than 0.5 was successfully correlated with Reynolds number and Prandtl number based on the thermal conductivity of nanofluids.     

Numerical modelling of boiling heat transfer in microchannels

In this paper we report the results of our modelling studies on two-phase forced convection in microchannels using water as the fluid medium. The study incorporates the effects of fluid flow rate, power input and channel geometry on the flow resistance and heat transfer from these microchannels. Two separate numerical models have been developed assuming homogeneous and annular flow boiling. Traditional assumptions like negligible single-phase pressure drop or fixed inlet pressure have been relaxed in the models making analysis more complex. The governing equations have been solved from the grass-root level to predict the boiling front, pressure drop and thermal resistance as functions of exit pressure and heat input. The results of both the models are compared to each other and with available experimental data. It is seen that the annular flow model typically predicts higher pressure drop compared to the homogeneous model. Finally, the model has also been extended to study the effects of non-uniform heat input along the flow direction. The results show that the non-uniform power map can have a very strong effect on the overall fluid dynamics and heat transfer.