Unified theoretical prediction of fully developed nucleate boiling and critical heat flux based on a dynamic microlayer model

A new dynamic microlayer model has been proposed to predict theoretically the heat flux in fully developed nucleate boiling regions including critical heat flux (CHF). In this model, the heat transfer with boiling is mainly attributed to the evaporation of the microlayers which are periodically formed while the individual bubbles are forming. Since the initial microlayer thickness becomes thinner with the increase of wall superheat, both the local evaporation and the partial dryout speed of the microlayer increase. As a result, the time-averaged heat flux during the period of individual bubble has a maximum point, the CHF, at the predicted continuous boiling curve.     

Contribution of thin-film evaporation during flow boiling inside microchannels

Flow boiling through microchannels is characterized by nucleation and growth of vapor bubbles that fill the entire channel cross-sectional area. As the bubbles nucleate and grow inside the microchannel, a thin film of liquid or a microlayer gets trapped between the bubbles and the channel walls. The heat transfer mechanism present at the channel walls during flow boiling is studied numerically. It is then compared to the heat transfer mechanisms present during nucleate pool boiling and in a moving evaporating meniscus. Increasing contact angle improved wall heat transfer in case of nucleate boiling and moving evaporating meniscus but not in the case of flow boiling inside a microchannel. It is shown that the thermal and the flow fields present inside the microchannel around a bubble are fundamentally different as compared to nucleate pool boiling or in a moving evaporating meniscus. It is explained why thin-film evaporation is the dominant heat transfer mechanism and is responsible for creating an apparent nucleate boiling effect inside a microchannel.     

High-Speed Visualization of Bubble Behaviors for Pool Boiling of R-141b

A visualization study on the behavior of bubbles has been carried out for pool boiling of R141b on a horizontal transparent heater at pressure 0.1 MPa. The behaviors of bubbles were recorded by a high-speed camera placed beneath the heater surface. The departure diameter, departure time of bubbles and nucleation site density at different heat flux were obtained. The visualization results show that bubble departure diameter and departure time decrease , while the nucleation site density increases as the heat flux increases. It is also observed that there is no liquid recruited into the microlayer in the experiment. Based on the experimental results, boiling curve for R141b was predicted by using the dynamic microlayer model. As a result, the agreement between the predictive result based on the dynamic microlayer model and the experiment data for boiling curve of R141b is good at high heat flux.     

On the transition from partial to fully developed subcooled flow boiling

The subject of the present study is to relate the boiling heat transfer process with experimentally observed bubble behaviour during subcooled flow boiling of water in a vertical heated annulus. It presents an attempt to explain the transition from partial to fully developed flow boiling with regard to bubble growth rates and to the time that individual bubbles spend attached to the heater surface.Within the partial nucleate boiling region bubbles barely change in size and shape while sliding a long distance on the heater surface. Such behaviour indicates an important contribution of the microlayer evaporation mechanism in the overall heat transfer rate. With increasing heat flux, or reducing flow rate at constant heat flux, bubble growth rates increase significantly. Bubbles grow while sliding, detach from the heater, and subsequently collapse in the bulk fluid within a distance of 1-2 diameters parallel to the heater surface. This confirms that bubble agitation becomes a leading heat transfer mode with increasing heat flux. There is however, a sharp transition between the two observed bubble behaviours that can be taken as the transition from partial to fully developed boiling. Hence, this information is used to develop a new model for the transition from partial to fully developed subcooled flow boiling.     

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.     

Investigation of heat transfer and bubble dynamics in a boiling thin liquid film flowing over a rotating disk

Nucleate boiling heat transfer and bubble dynamics in a thin liquid film on a horizontal rotating disk were studied. A series of experiments were conducted to determine the heat transfer coefficient on the disk. At low rotation and flow rates, vigorous boiling increased the heat transfer coefficients above those without boiling. Higher rotational speeds and higher flow rates increased the heat transfer coefficient and suppressed boiling by decreasing the superheat in the liquid film. The flow field on the disk, which included supercritical (thin film) flow upstream of a hydraulic jump, and subcritical (thick film) flow downstream of a hydraulic jump, affected the type of bubble growth. Three types of bubble growth were identified. Vigorous boiling with large, stationary bubbles were observed in the subcritical flow. Supercritical flow produced small bubbles that remained attached to the disk and acted as local obstacles to the flow. At low rotational rates, the hydraulic jump that separated the supercritical and subcritical regions produced hemispherical bubbles that protruded out of the water film surface and detached from the disk, allowing them to slide radially outward. A model of the velocity and temperature of the microlayer of water underneath these sliding bubbles indicated that the microlayer thickness was approximately 1/25th of that of the surrounding water film. This microlayer is believed to greatly enhance the heat transfer rate underneath the sliding bubbles.     

Analysis of pool boiling heat transfer: effect of bubbles sliding on the heating surface

Pool boiling on surfaces where sliding bubble mechanism plays an important role has been studied. The heat transfer phenomenon for such cases has been analysed. The model considers different mechanisms such as latent heat transfer due to microlayer evaporation, transient conduction due to thermal boundary layer reformation, natural convection and heat transfer due to the sliding bubbles. Both microlayer evaporation and transient conduction take place during the sliding of bubbles, which occurs in geometries such as inclined surfaces and horizontal tubes. The model has been validated against experimental results from literature for water, refrigerant R134a and propane. The model was found to agree well for these fluids over a wide range of pressures. The model shows the importance of the contributions of the different mechanisms for different fluids, wall superheats and pressures.     

Physical mechanisms of heat transfer during single bubble nucleate boiling of FC-72 under saturation conditions. II: Theoretical analysis

This paper is the second part of a two-part study concerning the dynamics of heat transfer during the nucleation process of FC-72 liquid. The experimental findings on the nature of different heat transfer mechanisms involved in the nucleation process were discussed in part I. In this paper, the experimental results are compared with the existing boiling models. The boiling models based on dominance of a single mechanism of heat transfer did not match the experimental results. However, the Rohsenow model was found to closely predict the heat transfer through the microconvection mechanism that is primarily active outside the bubble/surface contact area. An existing transient conduction model was modified to predict the surface heat transfer during the rewetting process (i.e. transient conduction mechanism). This model takes into account the gradual rewetting of the surface during the transient conduction process rather than a simple sudden surface coverage assumption commonly used in the boiling literature. The initial superheat energy of the microlayer (i.e. microlayer sensible energy) was accurately calculated and found to significantly contribute in microlayer evaporation. This even exceeded the direct wall heat transfer to microlayer at high surface superheat temperatures. A composite model was introduced that closely matches our experimental results. It incorporates models for three mechanisms of heat transfer including microlayer evaporation, transient conduction, microconvection, as well as their influence area and activation time. The significance of this development is that, for the first time, all submodels of the composite correlation were independently verified using experimental results.     

Bubble growth rates in pure and binary systems: Combined effect of relaxation and evaporation microlayers

Pohlhausen's equation has been used to determine the initial thickness of the evaporating microlayer beneath a hemispherical vapour bubble on a superheated horizontal wall. Microlayer thickness is proportional to the square root of the distance to the nucleation site during early bubble growth, while a linear relationship exists during advanced growth.A (heat and mass) diffusion-type solution is derived for advanced bubble growth, which accounts for the interaction of the mutually dependent contributions due to the relaxation microlayer (around the bubble dome) and the evaporation microlayer. The entire bubble behaviour during adherence is determined by a combination of this asymptotic solution and the Rayleigh solution, which governs early growth. Also, expressions are derived for both the radius of the dry area and the radius of the maximum contact area between bubble and wall.At low concentrations of the more volatile component in binary systems, the dominating influence of mass diffusion is demonstrated by the following effects: (i) asymptotic bubble growth is slowed down substantially; (ii) the formation of dry areas beneath bubbles is prevented, even at subatmospheric pressures; (iii) the lower part of the bubble is contracted; (iv) the evaporation microlayer contribution to bubble growth is negligible at atmospheric and at elevated pressures.     

Bubble growth and transient heat transfer at the onset of boiling

An experimental study was conducted to investigate transient local heat transfer around a bubble at onset of boiling on a thin glass heating plate immersed in saturated n-hexane at low pressure. Eight rapid response Cu-Ni thermocouples consisting of a vacuum deposited thin film were used to measure the temperature change of the heating surface. Simultaneous high-speed video photographs were also obtained. The surface temperatures near a nucleation site decreased rapidly owing to the evaporation of a thin layer (microlayer) of liquid formed beneath the bubble in the early period and the rate of bubble growth increased with increasing incipient boiling superheat (ΔT_IB). The thickness of the microlayer decreased markedly with increasing ΔT_IB. © 1998 Scripta Technica, Heat Trans Jpn Res, 26(7): 484–492, 1997     

Bubble growth rates in nucleate boiling of water at subatmospheric pressures

The growth rate of vapour bubbles has been investigated experimentally up to departure in water boiling at pressures varying from 26·7 to 2·0 kPa (the corresponding Jakob number increasing from 108 to 2689).Comparison of the data with existing theory shows the substantial influence of liquid inertia during initial growth, in agreement with previous results of Stewart and Cole [1]on water boiling at 4·9 kPa, the Jakob number varying from 955 to 1112. As an extreme case, at a pressure of 2·0 kPa, large “Rayleigh” bubbles are observed during the entire adherence time. During advanced growth, bubble behaviour is gradually governed by heat diffusion, especially at relatively high (subatmospheric) pressures.Experimental bubble growth in the investigated pressure range is in quantitative agreement with the van Stralen, Sohal, Cole and Sluyter theory [10]. This model combines the Rayleigh solution with a diffusion-type solution, which accounts for the contributions to bubble growth due to both the relaxation microlayer (around the bubble dome) and the evaporation microlayer (beneath the bubble).Finally, a curious bubble cycle is observed at the lowest investigated pressures, which is attributed to the combined action of a high-velocity liquid jet (originating in the wake following a large primary bubble) and a succeeding secondary vapour column (generated at the adjacent dry spot at the heating wall beneath the primary bubble).     

Physical mechanisms of heat transfer during single bubble nucleate boiling of FC-72 under saturation conditions-I. Experimental investigation

This paper is the first of a two-part study concerning the dynamics of heat transfer during nucleation process of saturated FC-72 liquid. Experimental results discussed in this paper provide new physical insight on the nature of heat transfer events at the nucleation site during the nucleate boiling process. The thermal field underneath a bubble during the boiling of FC-72 was measured with a spatial resolution of 22--40 μm. The time period of activation, area of influence, and magnitude of three different mechanisms of heat transfer active at the nucleation site were determined. These mechanisms consisted of: (1) microlayer evaporation following the rapid bubble expansion, (2) transient conduction due to rewetting of the surface during bubble departure, and (3) microconvection in the region external to the bubble/surface contact area. The area of influence of the transient conduction mechanism was found to be limited to the bubble/surface contact area, with most of the heat transfer occurring prior to the bubble detachment from the surface. The microconvection heat transfer mechanism was localized primarily outside the contact area and was found to be steady in nature. All three mechanisms of heat transfer were found to make significant contributions to the total surface heat transfer. The second part of this study provides the theoretical analysis of the results.     

Bubble Dynamics and Heat Transfer During Pool Boiling on Wettability Patterned Surfaces

Surfaces with spatial wettability patterns have been proven to enhance heat transfer coefficient and critical heat flux in pool boiling. To understand the physical mechanism behind this phenomenon and obtain the correlation among some critical parameters (bubble departure frequency, bubble size, nucleation site density, surface tension), pool boiling experiments were conducted. A Pyrex glass with a layer of indium-tin-oxide was used as the substrate. Hydrophobic patterns will serve as nucleation sites. Experiments were conducted in deionized water under atmospheric pressure at a relatively low heat flux. The processes of nucleation, growth, and departure of individual bubbles were visualized by using a high speed camera through the bottom of the heater surface. It has been found that the patterned surface performed the best in heat transfer for subcooled pool boiling when compared with hydrophilic and hydrophobic surfaces. The nucleation site density of the biphilic surface was much higher, when compared with that of the homogeneous surface. The individual bubbles always nucleate on the edge of the hydrophobic and hydrophilic area, and then move onto the hydrophobic pattern. Most of the individual bubbles detach from the wettability patterned surface in the diameter range from 300 µm to 450 µm (around 77.3%). The bubble departure periods scatter in the range from 80 ms to 1500 ms.     

Evaporation of the microlayer in hemispherical bubble growth in nucleate boiling of liquid metals

In this paper, a thermal analysis is used to estimate the extent of evaporation of the microlayer in hemispherical bubble growth, in nucleate boiling of liquid metals on heated surfaces. As the bubble grows, evaporation of the microlayer produces a dry patch at its center, whose size depends on the thermal and physical properties of the system, the roughness of the heating surface, and the boiling pressure. It was found that the area of this patch relative to that of the microlayer (or bubble base) is typically very small for liquid metals, and can be neglected in most theoretical analyses of bubble growth. It was further found that the loss of liquid from the microlayer due to evaporation into the bubble is at most a few percent, in a typical case.Since both the calculational model and mathematical analysis involve a number of simplifying assumptions, the numerical results of this pioneering study should be considered approximate.     

Surface wettability control by nanocoating: The effects on pool boiling heat transfer and nucleation mechanism

Experiments were performed to highlight the influence of surface wettability on nucleate boiling heat transfer. Nanocoating techniques were used to vary the water contact angle from 20° to 110° by modifying nanoscale surface topography and chemistry. The bubble growth was recorded by a high speed video camera to enable a better understanding of the surface wettability effects on nucleation mechanism. For hydrophilic (wetted) surfaces, it was found that a greater surface wettability increases the vapour bubble departure radius and reduces the bubble emission frequency. Moreover, lower superheat is required for the initial growth of bubbles on hydrophobic (unwetted) surfaces. However, the bubble in contact with the hydrophobic surface cannot detach from the wall and have a curvature radius increasing with time. At higher heat flux, the bubble spreads over the surface and coalesces with bubbles formed at other sites, causing a large area of the surface to become vapour blanketed. The best heat transfer coefficient is obtained with the surface which had a water contact angle close to either 0° or 90°. A new approach of nucleation mechanism is established to clarify the nexus between the surface wettability and the nucleate boiling heat transfer.     

Bubble growth,departure and the following flow pattern evolution during flow boiling in a mini-tube

In the present study, the bubble growth, departure and the following flow pattern evolution during flow boiling in the mini-tube were visualized and quantitatively investigated, along with the simultaneous measurement of the local heat transfer coefficient around a specified nucleation site. Liquid nitrogen was employed as the working fluid and the test section was a segment of vertically upward quartz glass tube with the inner diameter range of 1.3–1.5 mm, which was coated by a layer of transparent ITO film as the heater on the outer surface. The growth rates of bubbles had similar and constant growth rate in two periods of time, i.e., before and after the bubbles departing from the nucleation site, which indicated the bubble growth was primarily governed by the inertial force. The bubble departure diameter and bubble period were investigated and the corresponding correlation was obtained based on the experimental data, which showed that the tube size of the mini-tube had no notable effect on the bubble departure and the trend of the bubble departure was similar to that in macro-tubes. Whereas the following flow pattern evolution was apparently confined due to the size effect, which presented desirable heat transfer performance in mini-tubes. The heat transfer coefficients for different flow patterns along the mini-tube were obtained in terms of bubbly, slug, annular flow and the flow regimes of flow reversal and post dryout. It was found that the dominant heat transfer mechanism was the liquid film evaporation which offered desirable heat transfer capability. The heat transfer performance would be deteriorated in the post dryout regime, while flow reversal could somewhat enhance the heat transfer upstream of the nucleation site. Boiling curves around the specified nucleation site were recorded and analyzed based on the recorded flow patterns.     

Pool boiling heat transfer on the microheater surface with and without nanoparticles by pulse heating

We study the pool boiling heat transfer on the microheater surface with and without nanoparticles by pulse heating. Nanofluids are the mixture of de-ionized water and Al₂O₃ particles with 0.1%, 0.2%, 0.5% and 1.0% weight concentrations. The microheater is a platinum surface by 50 × 20 μm. Three types of bubble dynamics were identified. The first type of bubble dynamics is for the boiling in pure water, referring to a sharp microheater temperature increase once a new pulse cycle begins, followed by a continuous temperature increase during the pulse duration stage. Large bubble is observed on the microheater surface and it does not disappear during the pulse off stage. The second type of bubble dynamics is for the nanofluids with 0.1% and 0.2% weight concentrations. The microheater surface temperature has a sharp increase at the start of a new pulse cycle, followed by a slight decrease during the pulse duration stage. Miniature bubble has oscillation movement along the microheater length direction, and it disappears during the pulse off stage. The third type of bubble dynamics occurs at the nanofluid weight concentration of 0.5% and 1.0%. The bubble behavior is similar to that in pure water, but the microheater temperatures are much lower than that in pure water. A structural disjoining pressure causes the smaller contact area between the dry vapor and the heater surface, decreasing the surface tension effect and resulting in the easy departure of miniature bubbles for the 0.1% and 0.2% nanofluid weight concentrations. For the 0.5% weight concentration of nanofluids, coalescence of nanoparticles to form larger particles is responsible for the large bubble formation on the heater surface. The microlayer evaporation heat transfer and the heat transfer mechanisms during the bubble departure process account for the higher heat transfer coefficients for the 0.1% and 0.2% nanofluid weight concentrations. The shortened dry area between the bubble and the heater surface, and the additional thin nanofluid liquid film evaporation heat transfer, account for the higher heat transfer coefficient for the 0.5% nanofluid weight concentration, compared with the pure water runs.     

Convection and evaporation of microlayer underneath bubbles under microgravity

The multidimensional heat transfer and fluid flow in the microlayer region below a vapor bubble formed during boiling in microgravity are investigated by numerically solving the Navier–Stokes equations with the energy equation. The flow is driven by Marangoni flow due to the surface tension gradient along the bubble surface that results from the temperature gradient. The model also includes condensation and evaporation at the bubble surface. The flow field and heat transfer are calculated for microlayer thicknesses from 0.01 mm to 10 mm to investigate the effect of microlayer thickness. The results show that the velocities are small and have only a small effect on the temperature distribution as compared to the solution for pure conduction in the liquid. Natural convection is shown to have a negligible effect on heat transfer. For less than ideal evaporative heat transfer at the bubble interface, Marangoni convection caused the heat transfer to increase several percent. The flow in the microlayer is shown to agree with the lubrication analogy only for thin, relatively flat interfaces. © 2000 Scripta Technica, Heat Trans Asian Res, 30(1): 1–10, 2001     

Scale effects on flow boiling heat transfer in microchannels: A fundamental perspective

Flow boiling in microchannels has received considerable attention from researchers worldwide in the last decade. A scaling analysis is presented to identify the relative effects of different forces on the boiling process at microscale. Based on this scaling analysis, the flow pattern transitions and stability for flow boiling of water and FC-77 are evaluated. From the insight gained through the careful visualization and thermal measurements by previous investigators, similarities between heat transfer around a nucleating bubble in pool boiling and in the elongated bubble/slug flow pattern in flow boiling are brought out. The roles of microlayer evaporation and transient conduction/microconvection are discussed. Furthermore, it is pointed out that the convective contribution cannot be ruled out on the basis of experimental data which shows no dependence of heat transfer coefficient on mass flow rate, since the low liquid flow rate during flow boiling in microchannels at low qualities leads to laminar flow, where heat transfer coefficient is essentially independent of the mass flow rate. Specific suggestions for future research to enhance the boiling heat transfer in microchannels are also provided.     

Boiling of binary mixtures—study of individual bubbles

Experiments are reported in which individual bubbles of vapour are grown at a plane wall in initially stagnant isothermal liquid. Such tests had already been done and satisfactorily analysed and understood for pure liquids, but here the liquids are binary mixtures of hexane and octane of varying composition.The chief result is that ciné observations of the general behaviour of such bubbles (rate of growth, change of shape, time and size at departure) presents no new problems; it is identical to behaviour in pure liquids, provided one change of parameter is made. That change is to substitute the correct temperature for the evaporating binary interface in place of the saturation temperature for the pure liquid. That interface temperature was determined by reference to recent analytic solutions for evaporation of semi-infinite binary liquid by diffusion of heat and mass.Detailed rapid thermometric observations were also made, of the temperatures at the wall below the bubble and inside the bubble. They showed some aspects which differ markedly from pure liquids (though not such as to affect general behaviour). Those aspects were explained by detailed analysis of diffusion of heat and mass in a thin layer of liquid (microlayer) left beneath the growing bubble.Implications for boiling heat transfer are also considered and it is shown that this analysis of individual bubbles does not, of itself, explain the known reduction in heat transfer coefficient between pure and binary liquids. Several existing methods of explaining that reduction are examined and shown to have a common basis close to that determined by our analysis of single bubbles. But on extending from that basis in a simple way, to predict boiling heat transfer rates, they fail, except where an additional pressure-dependent multiplier is introduced, on purely empirical grounds.