On the mechanism of macrolayer formation in nucleate pool boiling at high heat flux

In nucleate boiling at high heat flux, a liquid layer, known as the ‘macrolayer’, is trapped between the heating surface and the vapour masses. An analysis of the mechanism of formation of this macrolayer is presented. Based on the analysis, a theoretical expression has been derived for the initial thickness of the macrolayer. The agreement between the theoretical values of the initial macrolayer thickness and the experimental values published in the literature is reasonably good.     

Non-heating simulation of pool-boiling critical heat flux

This paper presents a non-heating experimental method that simulates the critical heat flux (CHF) phenomenon in pool boiling. In the experiments, with providing controlled air flow through the holes on a plate submerged in a pool of water, the liquid sublayer (macrolayer) thickness and bubble departure frequency have been successfully measured by a conductance probe. The CHF is reasonably predicted by applying the measured parameters to a liquid macrolayer dryout model. The measured trends of the macrolayer thickness and bubble departure frequency with air mass flux are also consistent with the present understanding. As a result of this experimental study, it is expected that the non-heating method would be useful to investigate the various parametric effects on pool and flow boiling CHF, with avoiding the difficulty in heating and large electric power requirement even for complex geometries.     

Macrolayer formation and mechanisms of nucleate boiling,critical heat flux,and transition boiling

The drying process of a macrolayer on a 15 mm diameter boiling surface was observed with high speed video in the region of nucleate and of transition boiling close to the critical heat flux (CHF). It was found that the macrolayer rests beneath a large vapor mass. It partially dries in nucleate boiling and completely dries in transition boiling at the detachment of the vapor mass. The macrolayer thickness at CHF and in transition boiling was determined on the basis of the energy balance relation proposed by Katto and Yokoya. The macrolayer thickness at low heat flux was obtained by decreasing CHF with downward-facing heating surfaces and agreed well with the correlation proposed previously by the present authors. The macrolayer thickness in transition boiling with a vertical surface also agrees fairly well with the correlation, when the heat flux at macrolayer formation, given on the nucleate boiling curve, is extrapolated to surface superheat of transition boiling and when the surface temperature at macrolayer formation is equal to a time-averaged value. © 1998 Scripta Technical, Heat Trans Jpn Res, 27(2): 155–168, 1998     

Measurement of surface dryout near heating surface at high heat fluxes in subcooled pool boiling

The authors have conducted measurements of liquid–vapor behavior in the vicinity of a heating surface for saturated and subcooled pool boiling on an upward-facing copper surface by using a conductance probe method. A previous paper [A. Ono, H. Sakashita, Liquid–vapor structure near heating surface at high heat flux in subcooled pool boiling, Int. J. Heat Mass Transfer 50 (2007) 3481–3489] reported that thicknesses of a liquid rich layer (a so-called macrolayer) forming in subcooled boiling are comparable to or thicker than those formed near the critical heat flux (CHF) in saturated boiling. This paper examines the dryout behavior of the heating surface by utilizing the feature that a thin conductance probe placed very close to the heating surface can detect the formation and dryout of the macrolayer. It was found that the dryout of the macrolayer formed beneath a vapor mass occurs in the latter half of the hovering period of the vapor mass. Two-dimensional measurements conducted at 121 grid points in a 1-mm × 1-mm area at the center of the heating surface showed that the dryout commences at specific areas and spreads over the heating surface as the heat flux approaches the CHF. Furthermore, transient measurements of wall void fractions from nucleate boiling to transition boiling were conducted under the transient heating mode, showing that the wall void fraction has small values (<10%) in the nucleate boiling region, and then steeply increases in the transition boiling region. These findings strongly suggest that the macrolayer dryout model is the most appropriate model of the CHF for saturated and subcooled pool boiling of water on upward facing copper surfaces.     

The effect of heated wall thickness and materials on nucleate boiling at high heat flux

The present work is to numerically investigate the effect of heater side factors on the nucleate boiling at high heat flux, which is characterized by the existence of macrolayer. Two-region equations are proposed to study both thermo-capillary driven flow in the liquid layer and heat conduction in the solid wall. The numerical results indicate that the thermo-capillary driven flow in the macrolayer and evaporation at the vapor-liquid interface constitute a very efficient heat transfer mechanism to explain the high heat transfer coefficient of nucleate boiling heat transfer near CHF. For a very thin wall and/or wall with a poor thermal conductivity (heat side factors) are found to have significant effect on flow pattern in the liquid layer and the temperature distribution in the heated wall.     

Evaporation of macrolayer in nucleate boiling near burnout

The mechanism of nucleate boiling heat transfer near burnout has been investigated by studying the evaporation of the liquid macrolayer underneath the vapor mass. It is proved that heat conduction across the macrolayer and evaporation at the free surface is not a mode efficient enough to account for the major portion of heat transfer. The alternative model proposed is a macrolayer primarily consumed through evaporation of much thinner microlayers at the bottom of vapor stems penetrating the macrolayer. Analysis based upon the proposed mechanism shows that the macrolayer does not totally dry out in a vapor-mass cycle before boiling crisis. Other mechanisms accountable for the consumption of the macrolayer are also discussed.     

Studies on pool boiling heat transfer: Macrolayer thickness in transition boiling

Macrolayer thicknesses in transition boiling were determined from the energy balance relation q_tr = ρ_lH_fgδ_l·f , based on measurements of q_tr (the time-averaged heat flux in transition boiling) and f (the detachment frequency of vapor masses) for water and ethanol boiling on vertical and horizontal 15-mm-diameter surfaces under atmospheric pressure. The macrolayer thickness for the vertical surface, designed to prevent liquid contact with the periphery of the surface during the vapor mass hovering, agreed well with the correlation proposed previously by the present authors, when the heat flux at macrolayer formation is obtained from a nucleate boiling curve extrapolated to the superheat of transition boiling. The macrolayer on the horizontal surface was apparently thickened due to the inflow of bulk liquid beneath the growing vapor masses. © 1999 Scripta Technica, Heat Trans Jpn Res, 27(8): 568–583, 1998     

Critical Heat Flux of Boiling Heat Transfer in a Moderate Narrow Space

INTanDUCTI0NBoilingheattransferandcriticalheatflux(CHF)inaconfinednarrowspacehavebeenstudiedexperi-melltallybyanumberofinvestigatorsinthepastfewdecades.However,thereisnoanypopularlyacceptedmodelintheheattransferinnarrowspaceboiling,althoughsomepopularknowledgeabouttheboilingheattransferinthenarrowspacehavebeenacceptedbymanyresearchers.Theknowledgecanbecon-cludedasthatthenucleateboilingheattransferisenhancedatlowheatfluxregionanddeterioratedathighheatfiuxregi0nespeciallyatCHF.Theenhanceme…     

Recirculation model of kettle reboiler

The present paper deals with the simulation of a kettle reboiler. Considering rectangular tube sheet, concept of internal recirculation developed in a kettle reboiler during boiling, changes in physico-thermal property of liquid and liquid vapour mixture with temperature and pressure and using empirical correlations, a hydrodynamic model has been developed to determine pressure drop, vapour quality, recirculation rate, boiling regime, and heat transfer coefficient at various tube rows of the bundle.Results show, recirculation rate in a reboiler has been found to vary with the heat flux and pressure. Further, at a given value of heat flux and pressure vapour quality, mass flux, and heat transfer coefficient have been found to increase gradually from bottom to top tube row of the bundle.     

Studies on pool boiling heat transfer (modification of correlation of macrolayer thickness and measurements of macrolayer thickness at low heat fluxes)

The macrolayer thickness at critical heat flux has been determined based on the energy balance relation q_CHF=ρ_lH_fgδ_l·f, with measurements of the critical heat flux and the detachment frequency of vapor masses (coalesced bubbles) for various liquids at pressures from 0.05 MPa to 0.35 MPa for upward and vertical 20 mm diameter disk heaters. The macrolayer thickness correlation proposed in the fourth report of this series by Kumada and Sakashita [Trans. JSME, 58 (552) (1992), 2505] was modified with the data obtained in the present report. Macrolayer thicknesses at low heat fluxes for water and ethanol under atmospheric pressure were also measured while changing the orientation of the heating surface from vertical to downward. The measured macrolayers at low heat fluxes were thinner than those obtained from existing data measured by a probe method in the nucleate boiling region and agreed fairly well with the proposed correlation. © 1997 Scripta Technica, Inc. Heat Trans Jpn Res, 25 (8): 522–536, 1996     

Heat transfer during pool boiling based on evaporation from micro and macrolayer

An analytical model of heat transfer based on evaporation from the micro and macrolayers to the vapor bubble during pool boiling is developed. Evaporation of microlayer and macrolayer during the growth of individual bubbles is taken care of by using temporal and spatial variation of temperature in the liquid layer. Change of bubble shape during the entire cycle of bubble growth and departure is meticulously considered to find out the rate of heat transfer from the solid surface to the boiling liquid. Continuous boiling curve is developed by considering the bubble dynamics and decreasing thickness of liquid layer along with the increase of dry spot radius. Transient variation of macrolayer and microlayer thickness is predicted along with their effect on CHF. Present model exhibits a good agreement with reported experimental data as well as theories.     

Flow boiling in a 1.1 mm tube with R134a: Experimental results and comparison with model

A detailed comparison of flow boiling heat transfer results in a stainless steel tube of 1.1 mm internal diameter with results of a three-zone flow model are presented in this paper. The working fluid is R134a. Other parameters were varied in the range: mass flux 100–600 kg/m² s; heat flux 16–150 kW/m² and pressure 6–12 bar.The experimental results demonstrate that the heat transfer coefficient increases with heat flux and system pressure, but does not change with vapour quality when the quality is less than about 50% for low heat and mass flux values. The effect of mass flux is observed to be insignificant. For vapour quality values greater than 50% and at high heat flux values, the heat transfer coefficient does not depend on heat flux and decreases with vapour quality. This could be caused by dryout. The three-zone evaporation model predicts the experimental results fairly well, especially at relatively low pressure. However, the dryout region observed at high quality is highly over-predicted by the model. The sensitivity of the performance of the model to the three optimised parameters (confined bubble frequency, initial film thickness and end film thickness) and some preliminary investigation relating the critical film thickness for dryout to measured tube roughness are also discussed.     

Monodisperse Spray Cooling of Small Surface Areas at High Heat Flux

Spray cooling is an effective method to remove high heat fluxes from electronic components. To understand the physical mechanisms, this work studies heat transfer rates from single and dual nozzle distilled water sprays on a small heated surface (1.3 mm × 2 mm). Thermal ink jet atomizers generate small droplets, 33 μm diameter, at known frequencies, leading to controlled spray conditions with a monodisperse stream of droplets interacting with the hot surface. Of particular interest in this work is the dissipated heat flux and its relation to the liquid film thickness, the surface superheat, and the cooling mass flow rate. Experimental results show the heat flux scales to the cooling mass flow rate. In comparison to published spreading–splashing correlations, these experiments indicate that the drops impinge on the liquid film and spread without generating splashing, leading to high-efficiency stable heat transfer. Surface temperatures range from 120 to 140°C. In addition, the liquid film thickness is investigated in relation to the heater superheat and a stable thin film is seen at superheats beyond 20°C. The efficiency of the spray system is inversely related to the film thickness and may be due to ejection of liquid from the surface due to bursting of vapor bubbles.     

On the occurrence of two-stage combustion in alkali metals

Pool combustion experiments have been conducted for three alkali metals, namely, lithium (Li), sodium (Na) and potassium (K). Lithium and sodium are found to show a two-stage combustion behaviour which has been reported for a number of other metals. Here, the combustion is characterized by a sporadic rise in the flame temperature accompanied by a bright glow. Potassium is found to burn in vapour phase combustion in all cases without sporadic temperature excursions. In the present study, this different burning behaviour is attributed to the formation of thick oxide agglomerates in the case of Li and Na through the pores of which oxygen/metal vapour has to diffuse for combustion to occur. In such cases, a second stage of vapour phase combustion occurs when the oxide agglomerate is heated sufficiently so that the vapour of the liquid metal trapped in the pores breaks through to the surface. In the case of potassium, a self-cleaning mechanism, attributable to the high solubility of the metal oxides in liquid potassium and the relatively low melting point of the potassium oxides, enables a clear liquid surface to be exposed throughout for vapour phase combustion to prevail always. Recorded temperature profiles, SEM analysis of the oxide agglomerates as well as calculations of the metal–oxygen equilibrium thermo-chemistry for the three metals confirm this scenario.     

Temperature measurements near a heating surface at high heat fluxes in subcooled pool boiling

In previous papers (Int J Heat Mass Transfer, 2008;50:3481–3489, 2009;52: 814–821), the authors conducted measurements of liquid–vapor structures in the vicinity of a heating surface for subcooled pool boiling on an upward‐facing copper surface by using a conducting probe method. We reported that the macrolayer dryout model is the most appropriate model of the CHF and that the reason why the CHF increases with increasing subcooling is most likely that a thick macrolayer is able to form beneath large vapor masses and the lowest heat flux of the vapor mass region shifts towards the higher heat flux. To develop a mechanistic model of the CHF for subcooled boiling, therefore, it is necessary to elucidate the effects of local subcooling on boiling behaviors in the vicinity of a heating surface. This paper measured local temperatures close to a heating surface using a micro‐thermocouple at high heat fluxes for water boiling on an upward‐facing surface in the 0 to 40 K range of subcooling. A value for the effective subcooling, defined as the local subcooling during the period while vapor masses are being formed was estimated from the detected bottom peaks of the temperature fluctuations. It was established that the effective subcooling adjacent to the surface remains at considerably lower values than the bulk liquid subcooling. This suggests that, from nucleation to coalescence, the subcooling of a bulk liquid has a smaller effect on the behavior of primary bubbles than the extent of the subcooling would appear to suggest. An empirical correlation of the effective subcooling is proposed to provide a step towards quantitative modeling of the CHF for subcooled boiling. © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20277     

Turbulent liquid film evaporation in a partially heated wall along a vertical tube

In this numerical study, the evaporative heat and mass transfer of a turbulent falling liquid film in a finite vertical tube are investigated. The liquid film flows in the tube's inner wall, whose outer wall is partially subject to thermal flux. Here, different configurations corresponding to thermal flux imposed on different external surface wall percentages are examined. External face zones where the heat flux is not applied are maintained insulated. The nonlinear set of parabolic mass, momentum, energy, and mass fraction conservation equations combined with boundary and interfacial conditions are treated numerically using implicit finite difference procedure. For falling liquid film analysis, an adapted Van Driest turbulence model is used. For the present work, it is supposed that gas flows in a laminar regime. We examine in this paper the impact of the percentage of heated surface area on flows as well as on heat and mass transfer. Obtained results for a partially heated wall are compared with those produced for an entirely heated wall.     

Caracterisation de l'evaporation profondeDeep evaporation characterizationCharakterisierung der verdampfung in der tiefe eines porösen körpersИ/sиapeниe взчne зaглyблeни

Water evaporation from an homogeneous porous media, which is submitted to radiative and convective fluxes on its interface with air, is analysed by the energy balance equations and the classical transfer equations. Two Ievels are considered: the surface of the body, or its interface with air, and the deep front of evaporation. In this first analysis, the part located between these two levels is considered only as the site of a heat conductive flux and a water vapour flux, all liquid water flux is supposed negligible compared with water vapour flux. Then, it is possible to express the density of latent heat flux and the equilibrium values which characterize the level of the evaporation front and the surface of the body, such as temperature and water vapour pressure. These expressions are functions of the characteristics of air flow, radiative balance and coefficients, mainly two unidimensional numbers one of which has been used in the study of heat-transfer phenomena by Luikov [1]; these coefficients are the Brun numbers referred to heat and mass transfer.     

Time periodic flow boiling heat transfer of R-134a and associated bubble characteristics in a narrow annular duct due to flow rate oscillation

An experiment is conducted here to investigate the effects of the imposed time periodic refrigerant flow rate oscillation in the form of nearly a triangular wave on refrigeriant R-134a flow boiling heat transfer and associated bubble characteristics in a horizontal narrow annular duct with the duct gap fixed at 2.0 mm. The results indicate that when the imposed heat flux is close to that for the onset of stable flow boiling, intermittent flow boiling appears in which nucleate boiling on the heated surface does not exist in an entire periodic cycle. At somewhat higher heat flux persistent boiling prevails. Besides, the refrigerant flow rate oscillation only slightly affects the time-average boiling curves and heat transfer coefficients. Moreover, the heated wall temperature, bubble departure diameter and frequency, and active nucleation site density are found to oscillate periodically in time as well and at the same frequency as the imposed mass flux oscillation. Furthermore, in the persistent boiling the resulting heated wall temperature oscillation is stronger for a longer period and a larger amplitude of the mass flux oscillation. And for a larger amplitude of the mass flux oscillation, stronger temporal oscillations in the bubble characteristics are noted. The effects of the mass flux oscillation on the size of the departing bubble and active nucleation site density dominate over the bubble departure frequency, causing the heated wall temperature to decrease and heat transfer coefficient to increase at reducing mass flux in the flow boiling, opposing to that in the single-phase flow. But they are only mildly affected by the period of the mass flux oscillation. However, a short time lag in the wall temperature oscillation is also noted. Finally, a flow regime map is provided to delineate the boundaries separating different boiling regimes for the R-134a flow boiling in the annular duct.     

Enhancement of Heat Transfer in a Laminar Hydromagnetic Flow of a Liquid Metal Past a Thermally Conducting and Oscillating Infinite Flat Plate

The combined effects of conjugation and magnetic field on the heat transfer enhancement in a laminar liquid metal flow past a thermally conducting and sinusoidally oscillating infinite flat plate are investigated. The wall materials used are compatible with the liquid metals and are assumed to be of finite thickness. Analytical solutions are obtained for the velocity and the temperature distributions. The combined effects of thermal conductivity, the thickness of the plate, and the transverse magnetic field on the net heat flux transported are analyzed in detail and it is found that such effects are same as those on the transverse temperature gradient at any frequency. Due to oscillation, the heat flux is enhanced by O(10³). The optimum value of wall thickness and the corresponding boundary layer thickness for which the maximum heat flux is obtained are reported. The heat flux transported can be increased by choosing a wall of low thermal conductivity. A maximum increase of 52.03% in heat flux can be achieved by optimizing the wall thickness. These information may be useful while designing magnetohydrodynamic liquid metal heat transfer systems. All the results obtained are in good agreement with the results reported earlier.     

On the profile of the liquid wedge underneath a growing vapour bubble and the reversal of the wall heat flux

Combining mass and energy balances, a differential equation for the profile of a liquid wedge underneath a vapour bubble that is growing on a solid surface is derived. It connects the spatial and temporal changes of the film (wedge) thickness with the spatial temperature changes and velocity of liquid at the interface. Specifying particular conditions, the equation reduces to those from the literature. The paper brings further an illustrative explanation of why the wall heat flux in the wedge region may reverse its direction.