A method of correlating forced convection heat-transfer data and a comparison with fluid friction

A general method for the correlation of forced convection heat-transfer data is proposed, which consists in plotting, against the Reynolds number, a dimensionless group representing the experimentally measured data from which film heat-transfer coefficients would be calculated, namely, , or its equivalent, h/cG, multiplied by the two-thirds power of the group, . Data are cited from the literature which show that the resulting plots of heat-transfer data for flow parallel to plane surfaces and for fully turbulent flow inside tubes, coincide (when the properties are taken at the “film” temperature) with the best data on fluid friction plotted in the customary manner, as the friction factor , against the Reynolds number. For flow at right angles to tubes, however, the friction and heat-transfer factors differ, the friction factors being higher.

The equations successfully employed for representing heat-transfer data in streamline flow inside tubes have been modified for plotting with the same coordinates as used for turbulent flow ; and a quantitative allowance is suggested for the effect of free convection at low velocities by including a function of the group, . There is seen to be no relation between heat transfer and friction in the viscous region.

The method of correlation here proposed is shown to be particularly valuable in the transition region between streamline and turbulent flow in tubes, since heat-transfer factors may show “dips” analogous to those for friction. The controlling variables in this region are fully discussed in the light of the available data.     

Natural convection from isothermal flat surfaces

Local heat-transfer coefficients along a flat plate in natural convection in air were measured using Boelter-Schmidt type heat flux meters. Experiments were carried out for different temperature differences in heating and cooling, and with inclinations varying from the horizontal “facing upwards” position, through the vertical position, to the horizontal “facing downwards” position.

The results are presented in terms of local Nusselt number as a function of the local Grashof number “tangential component”. All runs were in the range accepted as that of laminar boundary layer flow. However, under certain conditions when the normal velocity component of the air is directed away from the surface, separated flow is indicated along the trailing part of the surface, well before turbulence sets in in the boundary layer. Separation starts at a certain point along the surface. This point is nearer to the leading edge the higher the temperature difference, and the larger the inclination of the surface to the vertical.

In a separation region, the flux density is uniform. In all other regions the results agreed closely with established theories of laminar boundary layer flow.

A leading adiabatic section, used in some of the experiments, did not affect the results. An appendix gives relations recommended for engineering calculations.     

Recent developments in EHD Enhanced Heat Transfer

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

Study of bubble growth in water pool boiling through synchronized,infrared thermometry and high-speed video

High-speed video and infrared thermometry were used to obtain time- and space-resolved information on bubble nucleation and heat transfer in pool boiling of water. The bubble departure diameter and frequency, growth and wait times, and nucleation site density were directly measured for a thin, electrically-heated, indium–tin-oxide surface, laid on a sapphire substrate. These data are very valuable for validation of two-phase flow and heat transfer models, including computational fluid dynamics with interface tracking methods. Here, detailed experimental bubble-growth data from individual nucleation sites were used to evaluate simple, commonly-used, but poorly-validated, bubble-growth and nucleate-boiling heat-transfer models. The agreement between the data and the models was found to be reasonably good. Also, the heat flux partitioning model, to which our data on nucleation site density, bubble departure diameter and frequency were directly fed, suggests that transient conduction following bubble departure is the dominant contribution to nucleate-boiling heat transfer.     

Convection film boiling on horizontal cylinders

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

Numerical study of bubble growth and boiling heat transfer on a microfinned surface

The bubble growth and boiling heat transfer on a microfinned surface are studied numerically by solving the conservation equations of mass, momentum and energy. The bubble shape is tracked by a sharp-interface level-set method, which is modified to include the effect of phase change and to treat the contact angle and microlayer heat flux on an immersed solid surface. The present computation demonstrates that the microfinned surface enhances boiling heat transfer significantly compared to a plain surface. The effects of fin spacing and height on the bubble growth and heat transfer are investigated to find the optimal conditions for boiling enhancement.     

Natural convection heat transfer from isothermal horizontal plates of different shapes

Experiments were carried out on natural convection heat transfer from isothermal plates facing upwards in air in the range of Gr·Pr from , Both the average and local heat transfer were determined. Plates of different shapes (square, rectangular and circular) were used and “corner” and “edge” effects were investigated. Dimensionless equations are suggested for the laminar and turbulent regions.     

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.     

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.     

Saturated flow boiling heat transfer of R-407C and associated bubble characteristics in a narrow annular duct

Experiments are conducted here to investigate how the channel size affects the R-407C saturated flow boiling heat transfer and associated bubble characteristics in a horizontal narrow annular duct. The gap of the duct is fixed at 1.0 and 2.0 mm in this study. The measured data indicate that the saturated flow boiling heat transfer coefficient increases with a decrease in the duct gap. Besides, raising the imposed heat flux can cause a significant increase in the boiling heat transfer coefficients. However, the effects of the refrigerant mass flux and saturated temperature on the boiling heat transfer coefficient are milder. The results from the flow visualization show that the mean diameter of the bubbles departing from the heating surface decreases noticeably at increasing R-407C mass flux. Moreover, the bubble departure frequency increases at reducing duct size and at a high imposed heat flux many bubbles generated from the cavities in the heating surface tend to merge together to form big bubbles. Meanwhile comparison of the present heat transfer data for R-407C with R-134a in the same duct and with some existing correlations is conducted. Furthermore, correlation for the present R-407C saturated flow boiling heat transfer data is proposed. Additionally, the present data for some quantitative bubble characteristics such as the mean bubble departure diameter and frequency and the active nucleation site density are also correlated.     

一种新型微热管传热性能的实验研究

对一种新型的平板式微热管一零切角曲面微热管进行了实验研究。以热阻为基础,研究不同倾角、工质、充液比下微热管的热性能。为便于分析,将热管总热阻分解为4个部分：加热热阻、蒸发段热阻、冷凝段热阻和热沉热阻。通过实验得出如下结论：微热管总热阻的主要变化因素是冷凝段热阻和蒸发段热阻;与相应的无工质平板式换热器相比,实验件主要热阻变为热沉热阻．蒸发段和冷凝段热阻所占比例较低。根据不同的充液比和倾角。微热管传热极限分别由局部干烧和核态沸腾向膜态沸腾转化引起。实验表明。这种新型的微热管具有良好的应用前景,但是对于其机理还需要更深入的研究。     

Subcooled flow boiling heat transfer and associated bubble characteristics of R-134a in a narrow annular duct

Experiments are conducted here to investigate how the channel size affects the subcooled flow boiling heat transfer and associated bubble characteristics of refrigerant R-134a in a horizontal narrow annular duct. The gap of the duct is fixed at 1.0 and 2.0 mm in this study. From the measured boiling curves, the temperature undershoot at ONB is found to be relatively significant for the subcooled flow boiling of R-134a in the duct. The R-134a subcooled flow boiling heat transfer coefficient increases with a reduction in the gap size, but decreases with an increase in the inlet liquid subcooling. Besides, raising the imposed heat flux can cause a substantial increase in the subcooled boiling heat transfer coefficient. However, the effects of the refrigerant mass flux and saturated temperature on the boiling heat transfer coefficient are small in the narrow duct. Visualization of the subcooled flow boiling processes reveals that the bubbles are suppressed to become smaller and less dense by raising the refrigerant mass flux and inlet subcooling. Moreover, raising the imposed heat flux significantly increases the bubble population, coalescence and departure frequency. The increase in the bubble departure frequency by reducing the duct size is due to the rising wall shear stress of the liquid flow, and at a high imposed heat flux many bubbles generated from the cavities on the heating surface tend to merge together to form big bubbles. Correlation for the present subcooled flow boiling heat transfer data of R-134a in the narrow annular duct is proposed. Additionally, the present data for some quantitative bubble characteristics such as the mean bubble departure diameter and frequency and the active nucleation site density are also correlated.     

Subcooled Flow Boiling Over Microstructured Plates In Rectangular Minichannels

Microstructures offer enhancements in boiling heat transfer by increasing bubble departure frequency, active nucleation site density, critical cavity size, and surface area. Integration of microstructures to surfaces alters significant surface parameters such as porosity of the microstructured plates, contact angle, and configuration of microstructures on the surface, which all affect boiling heat transfer. The goal of this study is to investigate boiling heat transfer on different microstructured plates and the effect of various microscale surface morphologies on boiling heat transfer. The microstructured surfaces were formed on aluminum alloy 2024 sheets with the use of a simple and environmentally friendly technique of random mechanical sanding (grits of #36, #60, #400, and #1,000). Distilled water was pumped using a micro gear pump to the rectangular minichannel test section at flow rates of 100, 180, and 290 ml/min, which correspond to mass fluxes of 5.46, 10.58, and 16.15 kg/m².s, respectively. It was observed that surfaces with low grit (grit #36) showed no considerable enhancement, whereas the use of higher grit counts considerably enhanced boiling heat transfer up to a critical grit count. The results were supported by the images from the performed visualization of flow boiling.     

Saturated flow boiling heat transfer and associated bubble characteristics of R-134a in a narrow annular duct

Experiments are conducted here to investigate how the channel size affects the saturated flow boiling heat transfer and associated bubble characteristics of refrigerant R-134a in a horizontal narrow annular duct. The gap of the duct is fixed at 1.0 and 2.0 mm in this study. The measured heat transfer data indicate that the saturated flow boiling heat transfer coefficient increases with a decrease in the gap of the duct. Besides, raising the imposed heat flux can cause a significant increase in the boiling heat transfer coefficients. However, the effects of the refrigerant mass flux and saturated temperature on the boiling heat transfer coefficient are milder. The results from the flow visualization show that the mean diameter of the bubbles departing from the heating surface decreases slightly at increasing R-134a mass flux. Moreover, the bubble departure frequency increases at reducing duct size mainly due to the rising shear stress of the liquid flow, and at a high imposed heat flux many bubbles generated from the cavities in the heating surface tend to merge together to form big bubbles. Correlation for the present saturated flow boiling heat transfer data of R-134a in the narrow annular duct is proposed. Additionally, data for some quantitative bubble characteristics such as the mean bubble departure diameter and frequency and the active nucleation site density are also correlated.     

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.     

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.     

Models for enhanced boiling heat transfer by unusual Marangoni effects under microgravity conditions

A new approach is suggested to enhance boiling heat transfer through introduction of unusual surface tension effects. The surface tension of aqueous solutions of alcohols with a chain length longer than four carbon atoms offers a positive gradient with temperature when the temperature exceeds a certain value. Moreover, the positive gradient near the boiling point has a very large value. This will generate a considerable driving force for bubble departure. As a result, in the nucleate boiling of these solutions, the Marangoni effect around the bubble surface will not impede the bubble detachment from the heater surface but rather will provide an additional driving force for the bubble departure. This effect combines with the buoyancy under normal gravity and acts as a main driving force of bubble departure in microgravity. Models for predictions of the bubble detachment diameters, the nucleate boiling heat transfer coefficient, and the critical heat flux are developed.     

Numerical Simulation of Bubble Growth and Heat Transfer During Flow Boiling in a Surface-Modified Microchannel

Flow boiling in a microchannel without or with surface modifications, such as fins, grooves, and cavities, has received significant attention as an effective cooling method for high-power microelectronic devices. However, a general predictive approach for the boiling process has not yet been developed because of its complexity involving the bubble dynamics coupled with boiling heat transfer in a microscale channel. In this study, direct numerical simulations for flow boiling in a surface-modified microchannel are performed by solving the conservation equations of mass, momentum, and energy in the liquid and vapor phases. The bubble surfaces are determined by a sharp-interface level-set method, which is modified to include the effect of phase change at the liquid–vapor interface and to treat the no-slip and contact-angle conditions on immersed solid surface of microstructures. This computation demonstrates that the surface-modified microchannel enhances boiling heat transfer significantly compared to a plain microchannel. The effects of various surface modifications on the bubble growth and heat transfer are investigated to find better conditions for boiling enhancement.     

Optimization of an absorber plate fin having a step-change in local thickness

Solar collectors having “tube-and-fin” absorber plates have traditionally used rectangular fins. The introduction of a “step-change” in fin thickness, so that the fin is thinner far from the tube, permits a savings in material content. Through heat transfer analysis, this paper derives an expression for the efficiency of a fin of this step-change shape, and applies it to the problem of finding the savings in material this shape permits. The results indicate that roughly a 20% reduction in fin material is possible.     

Theoretical research of critical heat flux in subcooled impingement boiling on the stagnation zone

A new mechanism model for determination of the critical heat flux (CHF) in subcooled impingement boiling on the stagnation zone is proposed in this paper. It is based on the combination of the Helmholtz instability theory of macrolayer and the model of bubble induced turbulent heat transfer in subcooled impingement boiling. A semi-theoretical and semi-empirical correlation and its nondimensional form of the CHF for subcooled jet impingement boiling on the stagnation zone are also derived. Under the circumstances of CHF, the bubble induced turbulent heat transfer coefficient gets doubled as compared to the single-phase laminar heat transfer coefficient according to the theoretical model and the experimental data. And this kind of bubble induced turbulent heat transfer enhancing effect can be considered as a fixed ratio. The theoretical analysis result for the present case is successfully verified by the experimental result obtained on the smooth heating surface. Through the discussions, it is obtained that the CHF ratio of the subcooled jet impingement boiling against the saturated jet impingement boiling is theoretically related to the surface condition of the heater and the properties and impact velocity of the working fluid.