Numerical study of nanofluids condensation heat transfer in a square microchannel

ABSTRACT

This paper presents a numerical study of nanofluids condensation heat transfer inside a single horizontal smooth square tube. The numerical results are compared with the previous experimental predictions. The numerical results show that the heat transfer coefficient could be improved within 20% by increasing the volume fraction of Cu nanoparticle by 5% or by increasing the mass flux from 80 to 110 kg/m² s. Reducing the hydraulic diameter of the microchannel from 200 to 160 µm leads to an increase in the condensation average heat transfer coefficient by 10%. A new correlation estimating the Nusselt number for the condensation of nanofluids or pure vapor is proposed. It predicts average condensation heat transfer with a good agreement with those computed.     

Numerical Study of Nanofluid Condensation Heat Transfer in a Square Microchannel

This study presents a numerical study of nanofluid condensation heat transfer inside a single horizontal smooth square tube. The numerical results are compared to previous experimental predictions, and show that the heat transfer coefficient can be improved 20% by increasing the volume fraction of Cu nanoparticles by 5% or increasing the mass flux from 80 to 110 kg/m² s. Reducing the hydraulic diameter of the microchannel from 200 to 160 µm led to an increase in average condensation heat transfer coefficient of 10%. A new correlation estimating Nusselt number for condensation of nanofluids or pure vapor is proposed. It predicts average condensation heat transfer, with good agreement with the computed values.     

The Inverse Reconstruction of the Heat Transfer Coefficient for the Free Surface Water Jet

This article presents an application of inverse algorithm for reconstruction of heat transfer coefficient (HTC) for a water jet impinging a flat surface. Such an approach, allows for decoupling complex fluid flow from heat conduction in a solid impinged by jet. The approach starts with parameterization of a functional form of unknown boundary temperature and heat flux occurring at the fluid–solid interface. Later, Newton's law of cooling is used to force temporal invariability of HTC. Unknown coefficients of HTC distribution are determined from a least square fit between measured and computed temperatures. Temperatures entering the objective function are recorded by an infrared camera at the surface opposite to impinged one.     

Prediction of Heat Transfer Coefficient in Flow Boiling over Tube Bundles Using ANFIS

The applicability of the artificial intelligence technique called ANFIS (for adaptive neuro fuzzy inference system) to model the flow boiling heat transfer over a tube bundle is studied in this paper. The ANFIS model is trained and validated with the experimental data from literature. The heat flux, mass flux, and row height are taken as input and the flow boiling heat transfer coefficient as output. The developed model performance is evaluated in terms of performance parameters such as root mean square error, mean square error, correlation coefficient, variance accounted for, and computational time. The preceding parameters of the model are then determined for different combinations of type and number of membership functions. The model is found to predict experimental heat transfer coefficient within an error of ±5%. The developed model is also compared with the artificial neural network model and is found to be better in predicting the flow boiling heat transfer coefficient. The developed model is further used to observe the variation of heat transfer coefficient of the individual rows and bundle for intermediate value of parameters such as heat flux and mass flux that are not included in the analysis of experimental data. The analysis is able to provide complete information about variation of heat transfer coefficient of individual rows and the bundle with respect to heat flux and mass flux.     

Initiation of CASO4 Scale Formation on Heat Transfer Surfaces under Pool Boiling Conditions

The success of innovative fouling mitigation techniques such as ion implantation depends upon the early stage of scale formation on the heat transfer surface. This is because the first crystalline nuclei that appear on the surface during the initial period dictate how fouling would develop in latter stages. In this study, the initial period of deposition of calcium sulfate on heat transfer surfaces has been investigated under pool boiling conditions. The independent variables were heat flux and calcium sulfate concentration. The experimental results show that the time until the heat transfer coefficient reaches its intermediate maximum decreases with an increasing concentration and heat flux, and is also significantly affected by the surface finish. Neural network architectures were utilized to correlate the experimental results during the initial deposition period. A satisfactory agreement between predicted and measured heat transfer coefficients has been achieved with an average error of 8.7%.     

基于有限元方法的溴化锂降膜吸收传热传质的数值研究

吸收器是吸收式制冷系统的重要部件.溴化锂溶液的降膜吸收是吸收器中最常见的传质传热形式之一.通过对溴化锂溶液在降膜吸收过程中传质和传热特性的分析,使用基于有限元法的COMSOL Multiphysics软件,建立了溴化锂溶液和水蒸汽降膜吸收的物理数学模型,计算了液膜内部温度和质量分数的分布、界面处传质通量、界面处传热通量...     

Development of a distributed-parameter model for the evaporation system in a supercritical W-shaped boiler

In this paper, a distributed parameter model of an evaporation system in a supercritical W-shaped once-through boiler is developed based on the 3-D temperature distribution. The mathematical model was formulated to predict the distributions of the heat flux and the metal-surface temperature while considering a non-uniform distribution of the surface heat transfer and the frictional resistance coefficient. The results show that the heat flux distribution on the front water wall has three high heat flux zones in the W-shaped boiler, and the peak of the heat transfer coefficient moves to the peak of the heat flux gradually with the increment of load at supercritical pressure. The maximum deviation of the metal temperature is nearly 94 °C for different loads. This distributed parameter model is fit for the in-situ operating status of the boiler, and it provides a reference for the heat transfer of a supercritical system.     

Condensing heat transfer and pressure drop characteristics of hydrocarbon refrigerants

This paper presents the experimental results of condensing heat transfer coefficients and pressure gradients of HC refrigerants (e.g. R-1270, R-290 and R-600a) and R-22 in horizontal double pipe heat exchangers, having two different internal diameters of 12.70 mm and 9.52 mm (OD), respectively. Both the local condensing heat transfer coefficients and pressure drops (inside the tube) of hydrocarbon refrigerants were higher than R-22. The average condensing heat transfer coefficient increased with the mass flux. The experimental heat transfer coefficients agreed with the correlations of Shah, Travis and Cavallini–Zecchin’s to within ±20%. These results can be useful in the design of new heat exchangers involving hydrocarbon refrigerants for future air-conditioning systems.     

Heat Transfer and Flow Pattern Characteristics for HFE-7100 Within Microchannel Heat Sinks

This study investigates the heat transfer characteristics and flow pattern for the dielectric fluid HFE-7100 within multiport microchannel heat sinks with hydraulic diameters of 480 μm and 790 μm. The test results indicate that the heat transfer coefficient for the smaller channel is generally higher than that of the larger channel. It is found that the heat transfer coefficients are roughly independent of heat flux and vapor quality for a modest mass flux ranging from 200 to 400 kg m^?2 s^?1 at a channel size of 480 μm and there is a noticeable increase of heat transfer coefficient with heat flux for hydraulic diameters of 790 μm. The difference arises from flow pattern. However, for a smaller mass flux of 100 kg m^?2 s^?1, the presence of flow reversal at an elevated heat flux for hydraulic diameters of 480 μm led to an appreciable drop of heat transfer coefficient. For a larger channel size of 790 μm, though the flow reversal is not observed at a larger heat flux, some local early partial dryout still occurs to offset the heat flux contribution and results in an unconceivable influence of heat flux. The measured heat transfer coefficients for hydraulic diameters of 790 μm are well predicted by the Cooper correlation. However, the Cooper correlation considerably underpredicts the test data by 35–85% for hydraulic diameters of 480 μm. The influence of mass flux on the heat transfer coefficient is quite small for both channels.     

Heat Flux Correlation for Spray Cooling in the Nonboiling Regime

An experimental facility was developed to investigate the nonboiling heat transfer performance of water spray cooling. The effects of mass flux and wall temperature on heat transfer coefficient and heat flux were experimentally studied. It was found that heat transfer coefficient increased with the increasing of mass flux and wall temperature. Generalized correlations were developed for the Nusselt number related to wall temperature and the average Nusselt number as a function of the spray Reynolds number and the nondimensional temperature with an absolute error of 4% and 15% when the Reynolds number is more than 440. Compared with the data of Oliphant et al., it was observed that the usage field of the correlations could be extended to Reynolds number greater than 240.     

Heat exchanger design considering variable overall heat transfer coefficient: An artificial neural network approach

This study presents an artificial neural network approach in combination with numerical methods to calculate the heat transfer area assuming a nonlinear variation of the global heat transfer coefficient as a consequence of the thermophysical properties of the fluids, the geometry of the surfaces, and other factors. The development of the article is presented in two applications. The first application takes up the database described by Allan P. Colburn, four possibilities are proposed using functions from the field of artificial neural networks to create several approaches. The second application is presented to verify the goodness of the proposed methodology, the artificial neural network model is applied in an experimental data set of double-pipe vertical heat exchangers, the comparison between the calculated and experimental heat transfer area shows a relative percentage error smaller than 2.8%. The results in the applications are evidence of the competitiveness of the artificial neural network for the prediction of the heat transfer area considering a variable overall heat transfer coefficient.     

Boiling heat transfer and critical heat flux of ethanol–water mixtures flowing through a diverging microchannel with artificial cavities

This paper presents an experimental study on the convective boiling heat transfer and the critical heat flux (CHF) of ethanol–water mixtures in a diverging microchannel with artificial cavities. The results show that the boiling heat transfer and the CHF are significantly influenced by the molar fraction (x_m) as well as the mass flux. For the single-phase convection region except for the region near the onset of nucleate boiling with temperature overshoot, the single-phase heat transfer coefficient is independent of the wall superheat and increases with a decrease in the molar fraction. After boiling incipience, the two-phase heat transfer coefficient is much higher than that of single-phase convection. The two-phase heat transfer coefficient shows a maximum in the region of bubbly-elongated slug flow and deceases with a further increase in the wall superheat until approaching a condition of CHF, indicating that the heat transfer is mainly dominated by convective boiling. A flow-pattern-based empirical correlation for the two-phase heat transfer coefficient of the flow boiling of ethanol–water mixtures is developed. The overall mean absolute error of the proposed correlation is 15.5%, and more than 82.5% of the experimental data were predicted within a ±25% error band. The CHF increases from x_m = 0–0.1, and then decreases rapidly from x_m = 0.1–1 at a given mass flux of 175 kg/m² s. The maximum CHF is reached at x_m = 0.1 due to the Marangoni effect, indicating that small additions of ethanol into water could significantly increase the CHF. On the other hand, the CHF increases with increasing the mass flux at a given molar fraction of 0.1. Moreover, the experimental CHF results are compared with existing CHF correlations of flow boiling of the mixtures in a microchannel.     

Nucleate Boiling Enhancements on Porous Graphite and Microporous and Macro–Finned Copper Surfaces

Enhancements in nucleate boiling heat removal with dielectric liquids, by increasing either the bubbles nucleation sites density and/or the wetted surface area, are desirable for immersion cooling of high-power computer chips. This article presents the results of recent investigations of nucleate boiling enhancement of FC-72, HFE-7100, and PF-5060 dielectric liquids on porous graphite, copper microporous surfaces, and copper surfaces with square corner pins, 3 mm × 3 mm in cross-section and 2, 3, and 5 mm tall. All surfaces have a footprint measuring 10 × 10 mm. These investigations examined the effects of liquid subcooling up to 30 K and surface inclination, from upward-facing to downward-facing, on nucleate boiling heat transfer coefficient and critical heat flux. Natural convection of dielectric liquids for cooling chips while in the stand-by mode, at a surface average heat flux <20 kW/m², is also investigated for the different surfaces.     

Comparison of Whole-Domain and Sequential Algorithms for Function Specification Method in the Inverse Heat Transfer Problem of Laminar Convective Pipe Flow

This article compares the application of the whole-domain function specification method (WDFSM) and the sequential function specification method (SFSM) to the inverse problem of transient conjugate heat transfer of laminar forced convection in a circular pipe. The two inverse methods are used to estimate the time-varying inlet temperature and the outer-wall heat flux simultaneously on the basis of temperature measurements taken at two different locations within the pipe flow. The numerical results reveal that the estimations obtained from the WDFSM method are marginally better than those obtained from the SFSM approach.     

Experimental study on static/circulatory flash evaporation

Comparative study on heat and mass transfer properties of static/circulatory flash evaporation, i.e., non-equilibrium fraction (NEF), evaporated mass and heat transfer coefficient, was presented based on two experimental systems. NEF evolution in static flash was newly fitted by error function equation, based on which a unified calculating model for heat and mass transfer properties of both flashes was set up initially. At last, heat transfer coefficient was redefined as average heat flux released from unit volume of waterfilm under unit superheat. Results suggested that this coefficient was a time-depended function and a peak value existed in its evolution versus time.     

The effect of heating direction on flow boiling heat transfer of R134a in micro-channels

This paper presents effects of heating directions on heat transfer performance of R134a flow boiling in micro-channel heat sink.The heat sink has 30 parallel rectangular channels with cross-sectional dimensions of 500μm width 500μm depth and 30mm length.The experimental operation condition ranges of the heat flux and the mass flux were 13.48 to 82.25 W/cm2 and 373.3 to 1244.4 kg/m2s respectively.The vapor quality ranged from 0.07 to 0.93.The heat transfer coefficients of top heating and bottom heating both were up to 25 kW/m2 K.Two dominate transfer mechanisms of nucleate boiling and convection boiling were observed according to boiling curves.The experimental results indicated that the heat transfer coefficient of bottom heating was 13.9％ higher than top heating in low heat flux,while in high heat flux,the heat transfer coefficient of bottom heating was 9.9％.higher than the top heating,because bubbles were harder to divorce the heating wall.And a modified correlation was provided to predict heat transfer of top heating.     

多管程微通道冷凝器热力性能计算方法

多管程平行流微通道冷凝器的管程设计方案对换热器管内热力性能影响较大。但目前一直尚未有对其管内换热系数和压降进行理论预测的较为简单可行方法。本文针对各管程工质流量可变,平均干度可变的多管程平行流冷凝器管内热力参数提出一种分程计算方法：在假设管壁温度不变及同管程内流量均匀分配的前提下,采用了Koyama与Wang冷凝换热模型,以及Zhang和Koyama提出的摩擦压降模型,建立了壁温与热流量之间的关系式,通过迭代求得管内平均换热系数和压降的理论值。以一个商用R134a、流程分配为12-8-8-6微通道冷凝器作为示例,用理论和实验方法分别得到了其管内冷凝平均换热系数和压降。结果表明,二者的偏差均落在30%以内。其中Koyama和Zhang 提出的模型预测偏差较小,分别为-4.96%~11.31%,0.42%~25.14%。     

A finite element analysis for inverse heat conduction problems

This paper presents an efficient inverse analysis technique based on a sensitivity coefficient algorithm to estimate the unknown boundary conditions of multidimensional steady and transient heat conduction problems. Sensitivity coefficients were used to represent the temperature response of a system under unit loading conditions. The proposed method, coupled with the sensitivity analysis in the finite element formulation, is capable of estimating both the unknown temperature and heat flux on the surface provided that temperature data are given at discrete points in the interior of a solid body. Inverse heat conduction problems are referred to as ill-posed because minor inaccuracy or error in temperature measurements cause a drastic effect on the predicted surface temperature and heat flux. To verify the accuracy and validity of the new method, two-dimensional steady and transient problems are considered. Their surface temperature and heat flux are evaluated. From a comparison with the exact solution, the effects of measurement accuracy, number and location of measuring points, a time step, and regularization terms are discussed. © 1998 Scripta Technica. Heat Trans Jpn Res, 26(6): 345–359, 1997     

A data method using the inner temperature difference to improve the stability of the inverse heat conduction problems

Abstract

This article proposes a method to construct two series systems for improving the stability of the inverse heat conduction problems (IHCP) in a finite slab. The transfer function between the surface heat flux or temperature and the inner temperature difference is respectively obtained by Laplace transform technique firstly. Then the series systems which can solve IHCP based on the inner temperature difference are constructed by replacing the unsuitable zero and pole points of the transfer function approximated by è approximation. Finally the effects of the series systems are evaluated by a typical example. The results of the evaluation show that this method can obtain the surface heat flux and temperature by the inner temperature difference, and enhance the response speed of the measurement system at the same time. In addition this method can also improve the signal to noise ratio (SNR) of the inverse solutions by selectively amplifying the high SNR parts of the inner temperature difference. The present work provides an effective method to improve the stability of IHCP.     

Modeling of convective heat transfer of a nanofluid in the developing region of tube flow with computational fluid dynamics

In this article, convective heat transfer effect on the nanofluid flow in the developing region of a tube with constant heat flux was investigated using computational fluid dynamics (CFD). For this purpose, nanofluid containing Al₂O₃ and water as a liquid single phase with two average particle sizes of 45 and 150 nm and four particle concentrations of 1, 2, 4 and 6 wt.% were used. Effect of particle size on convective heat transfer coefficient was investigated in different Reynolds numbers (500 < Re < 2500) for various axial locations of tube. According to the modeling results, an equation was obtained for Nusselt number prediction using the dimensionless numbers. The results showed that the predicted data were in very good agreement with experimental data obtained from the literature. The maximum error was around 10%.