Study on heat transfer performance of spray cooling: model and analysis

In consideration of droplet–film impaction, film formation, film motion, bubble boiling (both wall nucleation bubbles and secondary nucleation bubbles), droplet–bubble interaction, bulk air convection and radiation, a model to predict the heat and mass transfer in spray cooling was presented in this paper. The droplet–film impaction was modeled based on an empirical correlation related with droplet Weber number. The film formation, film motion, bubble growth, and bubble motion were modeled based on dynamics fundamentals. The model was validated by the experimental results provided in this paper, and a favorable comparison was demonstrated with a deviation below 10%. The film thickness, film velocity, and non-uniform surface temperature distribution were obtained numerically, and then analyzed. A parameters sensitivity analysis was made to obtain the influence of spray angle, surface heat flux density, and spray flow rate on the surface temperature distribution, respectively. It can be concluded that the heat transfer induced by droplet–film impaction and film-surface convection is dominant in spray cooling under conditions that the heated surface is not superheated. However, the effect of boiling bubbles increases rapidly while the heated surface becomes superheated.     

Experimental investigation of vapor bubble growth during flow boiling in a microchannel

Experiments were conducted to analyze flow boiling characteristics of water in a single brass microchannel of 25 mm length, 201 μm width, and 266 μm depth. Different heat flux conditions were tested for each of two different mass flow rates over three different values of inlet fluid temperature. Temporal and spatial surface temperature profiles were analyzed to show the relative effect of axial heat conduction on temperature rise along the channel length and the effect of flow regime transition on local surface temperature oscillation. Vapor bubble growth rate increased with increasing wall superheat. The slower a bubble grew, the further it was carried downstream by the moving liquid. Bubble growth was suppressed for increased mass flux while the vapor bubble was less than the channel diameter. The pressure spike of an elongating vapor bubble was shown to suppress the growth of a neighboring bubble by more than 50% of its volume. An upstream progression of the Onset of Bubble Elongation (OBE) was observed that began at the channel exit and progressed upstream. The effects of conjugate heat transfer were observed when different flow regime transitions produced different rates of progression for the elongation sequence. Instability was observed at lower heat fluxes for this single channel experiment than for similar studies with multiple channels.     

Effects of bubble size on heat transfer enhancement by sub-millimeter bubbles for laminar natural convection along a vertical plate

Injection of sub-millimeter bubbles is considered a promising technique for enhancing natural convection heat transfer for liquids. So far, we have experimentally investigated heat transfer characteristics of laminar natural convection flows with sub-millimeter bubbles. However, the effects of the bubble size on the heat transfer have not yet been understood. The purpose of this study is to clarify the effects of the bubble size on the heat transfer enhancement for the laminar natural convection of water along a vertical heated plate with uniform heat flux. Temperature and velocity measurements, in which thermocouples and a particle tracking velocimetry technique are, respectively used, are conducted to investigate heat transfer and flow characteristics for different bubble sizes. Moreover, two-dimensional numerical simulations are performed to comprehensively understand the effects of bubble injection on the flow near the heated plate. The result shows that the ratio of the heat transfer coefficient with sub-millimeter-bubble injection to that without injection ranges from 1.3 to 2.2. The result also shows that for a constant bubble flow rate, the heat transfer coefficient ratio increases with a decrease in the mean bubble diameter. It is expected from our estimation based on both experimental data and simulation results that this increase results from an increase in the advection effect due to bubbles.     

Experimental investigation of micro-scale temperature transients in sub-cooled flow boiling on a horizontal heater

Surface temperature fluctuations that occur locally underneath departing bubbles in pool boiling are shown to result in local heat transfer coefficients ranging from 1 to 10 kW/cm². These estimates were reported in the literature involved both numerical and experimental approaches. Significantly higher heat fluxes are associated with flow boiling than pool boiling under similar conditions of wall superheat and liquid subcooling (e.g. at boiling inception and at critical heat flux). These enhancements are primarily caused by the convective transport, acceleration/distortion of the bubble departure process as well as the resultant potential enhancement of the local surface temperature fluctuations.In this study we measure the surface temperature fluctuations using temperature micro/nano-sensors fabricated on a silicon wafer during flow boiling on the silicon wafer which is heated from below. The silicon wafer is clamped on a constant heat flux type calorimeter consisting of a vertical copper cylinder with embedded cartridge heaters and K-type thermocouples. Micro/nano-thermocouples (thin film thermocouples or “TFT”) are fabricated on the surface of the silicon wafer. High speed data acquisition apparatus is used to record temperature data from the TFT at 1 kHz. A fluorinert was used as the test fluid (PF-5060, manufacturer: 3M Co.). The calorimeter and surface temperature measurement apparatus is housed in a test section with glass walls for visual observation. The liquid is pumped from a constant temperature bath to maintain a fixed subcooling during the experiments under steady state conditions. The transient temperature data from the FFT array during flow boiling on the silicon wafer is analyzed using fast Fourier transform (FFT). The FFT data is analyzed as a function of the wall heat flux and wall superheat. The number of temperature peaks in the FFT data is observed to increase with increase in wall heat flux and the peaks are found to cover a wider spectrum with peaks at higher frequencies with enhancement of heat flux. The surface temperature fluctuations, especially at small length and time scales, are perturbed potentially by the coupled hydrodynamic and thermal transport processes, resulting in enhanced local and global heat flux values. Boiling incipience condition and the flow boiling data are compared with correlations reported in the literature.     

A method of concurrent thermographic–photographic visualization of flow boiling in a minichannel

A method is developed to capture the distribution of surface temperature while simultaneously imaging the bubble motions in diabatic flow boiling in a horizontal minichannel. Liquid crystal thermography is used to obtain highly resolved surface temperature measurements on the uniformly heated upper surface of the channel. High-speed images of the flow field are acquired simultaneously and are overlaid with the thermal images. The local surface temperature and heat transfer coefficient can be analyzed with the knowledge of the nucleation site density and location, and bubble motion and size evolution. The horizontal channel is 1.2 mm high × 23 mm wide × 357 mm long, and the working fluids are Novec 649 and R-11. Optical access is through a machined glass plate which forms the bottom of the channel. The top surface is an electrically heated 76 μm-thick Hastelloy foil held in place by a water-cooled aluminum and glass frame. The heat loss resulting from this construction is computed using a conduction model in Fluent. The model is driven by temperature measurements on the foil, glass plate and aluminum frame. This model produces a corrected value for the local surface heat flux and enables the computation of the bulk fluid temperature and heat transfer coefficient along the channel. The streamwise evolution of the heat transfer coefficient for single-phase laminar flow is compared to theoretical values for a uniform-flux boundary condition. Examples of the use of the facility for visualizing subcooled two-phase flows are presented. These examples include measurements of the surface temperature distribution around active nucleation sites and the construction of boiling curves for locations along the test surface. Points on the curve can be associated with specific image sequences so that the role of mechanisms such as nucleation and the sliding of confined bubbles may be discerned.     

Explosive boiling of water in parallel micro-channels

The objective of this study is to visualize the flow pattern and to measure heat transfer coefficient during explosive boiling of water in parallel triangular micro-channels. Tests were performed in the range of inlet Reynolds number 25–60, mass flux 95–340 kg/m²s, and heat flux 80–330 kW/m².The flow visualization showed that the behavior of long vapor bubbles, occurring in a micro-channel at low Reynolds numbers, was not similar to annular flow with interposed intermitted slugs of liquid between two long vapor trains. This process may be regarded as explosive boiling with periodic wetting and dryout.In the presence of two-phase liquid–vapor flow in the micro-channel, there are pressure drop oscillations, which increase with increasing vapor quality.This study shows strong dependence of the heat transfer coefficient on the vapor quality. The time when liquid wets the heated surface decreases with increasing heat flux. Dryout occurs immediately after venting of the elongated bubble.     

Seed bubbles stabilize flow and heat transfer in parallel microchannels

Seed bubbles are generated on microheaters located at the microchannel upstream and driven by a pulse voltage signal, to improve flow and heat transfer performance in microchannels. The present study investigates how seed bubbles stabilize flow and heat transfer in micro-boiling systems. For the forced convection flow, when heat flux at the wall surface is continuously increased, flow instability is self-sustained in microchannels with large oscillation amplitudes and long periods. Introduction of seed bubbles in time sequence improves flow and heat transfer performance significantly. Low frequency (∼10 Hz) seed bubbles not only decrease oscillation amplitudes of pressure drops, fluid inlet and outlet temperatures and heating surface temperatures, but also shorten oscillation cycle periods. High frequency (∼100 Hz or high) seed bubbles completely suppress the flow instability and the heat transfer system displays stable parameters of pressure drops, fluid inlet and outlet temperatures and heating surface temperatures. Flow visualizations show that a quasi-stable boundary interface from spheric bubble to elongated bubble is maintained in a very narrow distance range at any time. The seed bubble technique almost does not increase the pressure drop across microsystems, which is thoroughly different from those reported in the literature. The higher the seed bubble frequency, the more decreased heating surface temperatures are. A saturation seed bubble frequency of 1000–2000 Hz can be reached, at which heat transfer enhancement attains the maximum degree, inferring a complete thermal equilibrium of vapor and liquid phases in microchannels. Benefits of the seed bubble technique are the stabilization of flow and heat transfer, decreasing heating surface temperatures and improving temperature uniformity of the heating surface.     

Heat transfer enhancement for laminar natural convection along a vertical plate due to sub-millimeter-bubble injection

Sub-millimeter-bubble injection is one of the most promising techniques for enhancing heat transfer for the laminar natural convection of liquids. However, flow and heat transfer characteristics for laminar natural convection of water with sub-millimeter bubbles have not yet been fully understood. The purpose of this study is to experimentally clarify the effects of sub-millimeter-bubble injection on the laminar natural convection of water along a heated vertical plate. The use of thermocouples and a particle tracking velocimetry (PTV) technique are applied to temperature and velocity measurements, respectively. The temperature measurement shows that the ratio of the heat transfer coefficient with sub-millimeter-bubble injection to that without injection increases with an increase in the bubble flow rate or a decrease in the wall heat flux and that the ratio ranges from 1.35 to 1.85. Moreover, it is concluded from simultaneous measurement of temperature and velocity that the heat transfer enhancement is directly affected by flow modification due to bubbles rising near the heated vertical plate.     

Transformational-zone method of calculation of complex heat exchange during flow of optically active medium inside tube of diffuse grey surface

The paper presents analytical and experimental investigations of influence of radiative heat transfer on complex heat exchange during flow of optically active gas inside a pipe of diffusegrey properties. It was assumed that the pipe is heated from the outside by a constant heat flux and gas flowing inside is both absorbing and emitting and of small optical density. The influence of length and radiative properties of the pipe surface and of the gas temperature distribution on the wall and in the gas were analysed. The influence of radiative energy transfer on overall heat transfer coefficient was estimated. Mathematical model of radiative convective heat exchange in a system of one-dimensional temperature field, based on zone division method of Hottel and surface transformation, was verified numerically and experimentally. The results of numerical calculations were compared with experimental results obtained during carbone dioxide (CO₂) flow inside electrically heated ceramic tube. The set of nonlinear differential equations was solved by Runge-Kutta method with Hamming modification and with the use of separable-kernel method.     

Flow and heat transfer of an electrically conducting fluid of second grade in a porous medium over a stretching sheet subject to a transverse magnetic field

An analysis is performed for flow and heat transfer of a steady laminar boundary layer flow of an electrically conducting fluid of second grade in a porous medium subject to a transverse uniform magnetic field past a semi-infinite stretching sheet with power-law surface temperature or power-law surface heat flux. The effects of viscous dissipation, internal heat generation of absorption and work done due to deformation are considered in the energy equation. The variations of surface temperature gradient for the prescribed surface temperature case (PST) and surface temperature for the prescribed heat flux case (PHF) with various parameters are tabulated. The asymptotic expansions of the solutions for large Prandtl number are also given for the two heating conditions. It is shown that, when the Eckert number is large enough, the heat flow may transfer from the fluid to the wall rather than from the wall to the fluid when Eckert number is small. A physical explanation is given for this phenomenon.     

A visual flow study of mixed convection in the entry region of a vertical internally heated annulus

The velocity distribution in laminar upward flow of water (Pr 7.25) in the entry of a vertical internally heated annulus (radius ratio 4:1) has been determined by visual observation. Photographic measurements have been made of the motion of hydrogen bubble clusters, which were generated by a carefully controlled process of electrolysis, to assess the effects of free convection effects on the forced flow.For heat fluxes up to 2500 W/m² and at a Reynolds number of approximately 450, local heat transfer coefficients have been obtained in a length of about 23 equivalent diameters. Heat transfer rate in the immediate entry was found to be insensitive to change in heat flux over the range of variables considered. As the distance downstream increased, the heat transfer rate was found to be dependent on the heat flux.     

Studies on heat transfer and flow characteristics in subcooled flow boiling—Part 1. Boiling characteristics

Measurement of wall temperature profile and photographic observation are performed for R-113 subcooled boiling flow in a channel with heat fluxes up to the CHF. The incipient boiling superheats measured are little affected by mass velocity and liquid subcooling. Hysteresis in boiling observed by increasing and decreasing heat flux seems to be ascribed to variation in size of active nucleation cavities on the wall. Increasing heat flux up to the CHF, the bubble density on the heated surface increases and remarkably large coalescent bubbles appear periodically near the heating section outlet.     

Enhancement of pool boiling heat transfer in a horizontal water layer through surface roughness and screen coverage

An experimental investigation was carried out to study the augmentation of heat transfer in saturated pool boiling of a liquid water layer on a heated horizontal stainless steel plate by roughing the surface and/or covering it with a single layer of stainless steel screen. The results were presented in terms of the boiling curves. Effects of various parameters – the surface roughness, liquid level and size of the stainless steel mesh on the boiling heat transfer were examined in detail. The measured data clearly indicated that a lowering of the liquid level from 60 to 5?mm in water depth causes heat transfer reduction. Roughing the surface was found to sig- nificantly enhance the heat transfer. Use a layer of metal screen to cover the heated surface was shown to substantially augment the heat transfer especially for a shallow water layer if the mesh size is comparable with the bubble departure diameter. Covering the rough surface with the metal mesh, however, reduced the heat transfer.     

Large area impingement spray cooling from multiple normal and inclined spray nozzles

An inclined spray chamber with four multiple nozzles to cool a 1 kW 6U electronic test card has been designed and tested in this study. The multiple inclined sprays can cover the same heated surface area as that with the multiple normal sprays but halve the volume of the spray chamber. The spray cooling system used R134a as a working fluid in a modified refrigeration cycle. It is observed that increasing mass flow rate and pressure drop across the nozzles improved the heat transfer coefficient with a maximum enhancement of 117 %, and reduced the maximum temperature difference at the heated surface from 13.8 to 8.4 °C in the inclined spray chamber with a heat flux of 5.25 W/cm², while the heat transfer coefficient of the normal spray increased with a maximum enhancement of 215 % and the maximum temperature difference decreased from 10.8 to 5.4 °C under similar operating conditions. We conclude that the multiple inclined sprays could produce a higher heat transfer coefficient but with an increase in non-uniformity of the surface temperature compared with the multiple normal sprays.     

Natural convection with evaporation in a vertical cylindrical cavity under the effect of temperature-dependent surface tension

The effect of surface tension on laminar natural convection in a vertical cylindrical cavity filled with a weak evaporating liquid has been analyzed numerically. The cylindrical enclosure is insulated at the bottom, heated by a constant heat flux from the side, and cooled by a non-uniform evaporative heat flux from the top free surface having temperature-dependent surface tension. Governing equations with corresponding boundary conditions formulated in dimensionless stream function, vorticity, and temperature have been solved by finite difference method of the second-order accuracy. The influence of Rayleigh number, Marangoni number, and aspect ratio on the liquid flow and heat transfer has been studied. Obtained results have revealed that the heat transfer rate at free surface decreases with Marangoni number and increases with Rayleigh number, while the average temperature inside the cavity has an opposite behavior; namely, it growths with Marangoni number and reduces with Rayleigh number.     

Magnetothermal force on heated or cooled pipe flow

The effects of the magnetothermal force on the flows of heat and fluid through a pipe are investigated numerically when the pipe wall is either heated or cooled at constant heat flux. The flow is laminar and a paramagnetic fluid is presumed as the working fluid. Because the magnetic susceptibility of a paramagnetic fluid depends on the inverse of its temperature, the magnetothermal force is induced by coupling of the temperature field and magnetic induction. First, the effects are discussed using the case of a magnetic field induced by a single-turn concentrically placed electric coil. It is found that the effects of the magnetothermal force differ according to whether the pipe is cooled or heated. When cooled, the heat and fluid flows are affected behind the coil; the flow is repelled from the wall to the center and the thermal boundary layer thickens. By decomposing the force into the radial and axial directions in the heated and cooled cases, it is clarified that the axial force changes from positive to negative depending on the coil location in the heated case. Therefore, it can be concluded that the effects are not simply oppositional in the heated and cooled cases. In relation to the heat transfer, only when the coil is placed at the threshold of the heating/cooling zone do the effects on the local heat transfer become the opposite of each other. At other coil locations, the suppression of heat transfer is dominant ahead of the coil in the heated case, as indicated in previous work by our group. However, in the cooled case, this effect occurs behind the coil. For a more practical case, a solenoid coil is employed in the simulation. It is then found that the effect on the heat transfer becomes remarkable at the solenoid edges, especially for the heat-transfer suppression in both the heated and cooled cases.     

Optimal discrete distribution of heat flux elements for in-tube laminar forced convection

A new technique is proposed to enhance the heat transfer from a discretely heated pipe to a developing laminar fluid flow. Unlike the common heating situation where the fluid is continuously heated along the pipe wall with uniform heat flux, the proposed technique consists in heating the fluid with stepwise distributed heat flux, namely by placing insulated segments between the heated segments. Applying this technique, the effective length of the thermal entrance region is enlarged and as a result, the average heat transfer is invigorated. In order to maximize the heating performance, an optimal placement of the insulated segments between the heated segments is calculated according to constructal design. This serves to describe the optimal stepwise distribution of the heat flux. Owing that the total heat load is considered fixed, the maximization of the heating performance translates into the minimization of the peak temperature (‘hot spot’) of the pipe wall. The analytical results demonstrate that the optimal location of the insulated segments along with the reduction of the peak temperature strongly depend on the Graetz number. It is also shown that for intermediate values of the Graetz number, the peak temperatures are remarkably reduced in response to the optimal placement of the insulated/heated segments.     

Single bubble growth in saturated pool boiling of binary mixtures

Nucleate pool boiling experiments for binary mixtures, which are consisted of R11 and R113, were performed with constant wall temperature condition. Results for binary mixtures were also compared with pure fluids. A microscale heater array and Wheatstone bridge circuits were used to maintain the constant temperature of the heating surface and to obtain heat flow rate measurements with high temporal and spatial resolutions. Bubble growth images were captured using a high-speed CCD camera synchronized with the heat flow rate measurements.The departure time for binary mixtures was longer than that for pure fluids, and binary mixtures had a higher onset of nucleate boiling (ONB) temperature than pure fluids. In the asymptotic growth region, the bubble growth rate was proportional to a value between t^1/6 and t^1/4. The bubble growth behavior was analyzed to permit comparisons with binary mixtures and pure fluids at the same scale using dimensionless parameters. There was no discernible difference in the bubble growth behavior between binary mixtures and pure fluids for a given ONB temperature. And the departure radius and time were well predicted within a ±30% error.The minimum heat transfer coefficient of binary mixtures occurred near the maximum |y−x| value, and the average required heat flux during bubble growth did not depend on the mass fraction of R11 as more volatile component in binary mixtures. Finally, the results showed that for binary mixtures, a higher ONB temperature had the greatest effect on reducing the heat transfer coefficient.     

Experimental investigation of flow boiling characteristics in a cross-linked microchannel heat sink

This paper experimentally investigates flow boiling characteristics in a cross-linked microchannel heat sink at low mass fluxes and high heat fluxes. The heat sink consists of 45 straight microchannels each with a hydraulic diameter of 248 μm and heated length of 16 mm. Three cross-links, of width 500 μm, are introduced in the present microchannel heat sink to achieve better temperature uniformity and to avoid flow mal-distribution. Flow visualization, flow instability, two-phase pressure drop, and two-phase heat transfer measurements are conducted using the dielectric coolant FC-72 over a range of heat flux from 7.2 to 104.2 kW/m², mass flux from 99 to 290 kg/m² s, and exit quality from 0.01 to 0.71. Thermochromic liquid crystals are used in the present study as full-field surface temperature sensors to map the temperature distribution on the heat sink surface. Flow visualization studies indicate that the observed flow regime is primarily slug. Visual observations of flow patterns in the cross-links demonstrate that bubbles nucleate and grow rapidly on the surface of the cross-links and in the tangential direction at the microchannels’ entrance due to the effect of circulations generated in those regions. The two-phase pressure drop strongly increases with the exit quality, at x_e,o < 0.3, and the two-phase frictional pressure drop increases by a factor of 1.6–2 compared to the straight microchannel heat sink. The flow boiling heat transfer coefficient increases with increasing exit quality at a constant mass flux, which is caused by the dominance of the nucleation boiling mechanism in the cross-link region.