Gopinath R. Warrier

Heat transfer and pressure drop in narrow rectangular channels

Recently, with the advent of more powerful electronic chips and the miniaturization of electronic circuits and other compact systems, a great demand exists for developing efficient heat removal techniques to accommodate these high heat fluxes. With this objective in mind, both single-phase forced convection and subcooled and saturated nucleate boiling experiments have been performed in small rectangular channels using FC-84 as test fluid. The test section used in these experiments consisted of five parallel channels with each channel having the following dimensions: hydraulic diameter (Dh)=0.75 mm and length to diameter ratio (L/Dh)=409.8. The experiments were performed with the channels oriented horizontally and uniform heat fluxes applied at the top and bottom surfaces. The parameters that were varied during the experiments included the mass flow rate, inlet liquid subcooling, and heat flux. In each of the experiments conducted, the temperature of both the liquid and the wall were measured at various locations along the flow direction. Based on the measured temperatures, pressure drops, and the overall energy balance across the test section, the heat transfer coefficients for both single-phase forced convection and flow boiling has been calculated. Additionally, in these experiments, the single- and two-phase pressure drop across the channels was also measured. A correlation has been developed for two-phase flow pressure drop under subcooled and saturated nucleate boiling conditions. Furthermore, two new correlations are proposed – one for subcooled flow boiling heat transfer and the other for saturated flow boiling heat transfer.

Onset of Nucleate Boiling and Active Nucleation Site Density During Subcooled Flow Boiling

The partitioning of the heat flux supplied at the wall is one of the key issues that needs to be resolved if one is to model subcooled flow boiling accurately. The first step in studying wall heat flux partitioning is to account for the various heat transfer mechanisms involved and to know the location at which the onset of nucleate boiling (ONB) occurs. Active nucleation site density data is required to account for the energy carried away by the bubbles departing from the wall. Subcooled flow boiling experiments were conducted using a flat plate copper surface and a nine-rod (zircalloy-4) bundle. The location of ONB during the experiments was determined from visual observations as well as from the thermocouple output. From the data obtained it is found that the heat flux and wall superheat required for inception are dependent on flow rate, liquid subcooling, and contact angle. The existing correlations for ONB underpredict the wall superheat at ONB in most cases. A correlation for predicting the wall superheat and wall heat flux at ONB has been developed from the data obtained in this study and that reported in the literature. Experimental data are within630 percent of that predicted from the correlation. Active nucleation site density was determined by manually counting the individual sites in pictures obtained using a CCD camera. Correlations for nucleation site density, which are independent of flow rate and liquid subcooling, but dependent on contact angle have been developed for two ranges of wall superheat—one below 15°C and another above 15°C. @DOI: 10.1115/1.1471522#

Wall Heat Flux Partitioning During Subcooled Flow Boiling: Part 1—Model Development

In this work a mechanistic model has been developed for the wall heat flux partitioning during subcooled flow boiling. The premise of the proposed model is that the entire energy from the wall is first transferred to the superheated liquid layer adjacent to the wall. A fraction of this energy is then utilized for vapor generation, while the rest of the energy is utilized for sensible heating of the bulk liquid. The contribution of each of the mechanisms for transfer of heat to the liquid—forced convection and transient conduction, as well as the energy transport associated with vapor generation has been quantified in terms of nucleation site densities, bubble departure and lift-off diameters, bubble release frequency, flow parameters like velocity, inlet subcooling, wall superheat, and fluid and surface properties including system pressure. To support the model development, subcooled flow boiling experiments were conducted at pressures of 1.03 ‐3.2 bar for a wide range of mass fluxes ~124‐926 kg/m 2 s!, heat fluxes ~2.5‐90 W/cm 2 ! and for contact angles varying from 30° to 90°. The model developed shows that the transient conduction component can become the dominant mode of heat transfer at very high superheats and, hence, velocity does not have much effect at high superheats. This is particularly true when boiling approaches fully developed nucleate boiling. Also, the model developed allows prediction of the wall superheat as a function of the applied heat flux or axial distance along the flow direction. @DOI: 10.1115/1.1842784#

Interfacial heat transfer during subcooled flow boiling

Abstract In order to develop a mechanistic model for the subcooled flow boiling process, the key issues which must be addressed are wall heat flux partitioning and interfacial (condensation) heat transfer. The sink term in the two-fluid models for void fraction prediction is provided by the condensation rate at the vapor–liquid interface. Low pressure subcooled flow boiling experiments, using water, were performed using a vertical flat plate heater to investigate the bubble collapse process. A high-speed CCD camera was used to record the bubble collapse in the bulk subcooled liquid. Based on the analyses of these digitized images, bubble collapse rates and the associated heat transfer rate were determined. The experimental data were in turn used to correlate the bubble collapse rate and the interfacial heat transfer rate. These correlations are functions of bubble Reynolds number, liquid Prandtl number, Jacob number, and Fourier number. The correlations account for both the effect of forced convection heat transfer and thickening of the thermal boundary layer as the vapor bubble condenses which in turn makes the condensation heat transfer time dependent. Comparison of the measured experimental data with those predicted from the correlations show that predictions are well within ±25% of the experimentally measured values. These correlations have also been compared with those available in the literature.

Heat Transfer and Wall Heat Flux Partitioning During Subcooled Flow Nucleate Boiling—A Review

In this paper we provide a review of heat transfer and wall heat flux partitioning models/correlations applicable to subcooled forced flow nucleate boiling. Details of both empirical and mechanistic models that have been proposed in the literature are provided. A comparison of the experimental data with predictions from selected models is also included.

Wall heat flux partitioning during subcooled flow boiling : Part II-model validation

A mechanistic model for wall heat flux partitioning during subcooled flow boiling proposed in Part I of this two-part paper, is validated in this part. As the first step of the validation process, the developed model was applied to experimental data obtained as part of this study

Natural Convection From Horizontal Cylinders at Near-Critical Pressures—Part II: Numerical Simulations

A numerical investigation of laminar natural convection heat transfer from small horizontal cylinders at near-critical pressures has been carried out. Carbon dioxide is the test fluid. The parameters varied are: pressure (P), (ii) bulk fluid temperature (Tb), (iii) wall temperature (Tw), and (iv) wire diameter (D). The results of the numerical simulations agree reasonably well with available experimental data. The results obtained are as follows: (i) At both subcritical and supercritical pressures, h is strongly dependent on Tb and Tw. (ii) For Tw Pc), the behavior of h as a function of Tw is similar; h increases with increase in Tw. (iii) For P > Pc and large Tw (Tw > Tpc), natural convection heat transfer occurring on the cylinder is similar that observed during film boiling on a cylinder. The heat transfer coefficient decreases as Tw increases. (iv) For subcritical pressures, the dependence of h on D is h ∝ D−0.5 in the range 25.4 ≤ D ≤ 100 μm. For larger values of D (500–5000 μm), h ∝ D−0.24. (v) For supercritical pressures, the dependence of h on D is h ∝ D−0.47 in the range 25.4 ≤ D ≤ 100 μm. For larger values of D (500–5000 μm), h ∝ D−0.27. (vi) For a given P, the maximum heat transfer coefficient is obtained for conditions where Tb < Tpc and Tw ≥ Tpc. Analysis of the temperature and flow field shows that this peak in h occurs when k, Cp, and Pr in the fluid peak close to the heated surface.

Experimental Study of the Gas Entrapment Process in Closed-End Microchannels

Earlier studies have shown that for cavities present on any heater surface to become active nucleation sites during boiling, they should entrap gas. The liquid penetrates the cavity due to the capillary and surface forces, but the exact physical mechanisms have not been fully quantified. The physical mechanisms of the gas entrapment process in closed-end microchannels, representing nucleation sites, are investigated in this study. Aside from the fluid properties, the width, length and depth of the cavities, as well as the static contact angle of the test liquid with the solid are considered as main parameters that influence the gas entrapment process. Test pieces consisted of micromachined silicon dices with glass bonded on top. Widths of 50, 30, 15 and 5μm were chosen based on size distribution probability. The mouth angle was 90° in all cases. Test pieces were held horizontally under a microscope equipped with a CCD camera. A drop of liquid was placed at the entrance of the microchannel and capillary and surface forces drive the liquid into the microchannel. Experiments show two main filling behaviors: (1) A uniform meniscus forms at the entrance and moves inwards, (2) Two menisci: one at the entrance and the other at the closed end of the microchannel. In some cases droplet formation at the walls was observed. A single meniscus typically forms for higher contact angles, while two menisci form for lower contact angles. In all cases, after a sufficient time interval (hours to days) the microchannel was completely flooded. In general, for a given depth, wider microchannels take longer to fill. Surface cleanliness and fabrication process also play a role in modifying the contact angle and hence the time taken to fill the microchannel. A comparison of the interface advancement in the microchannel with a simple mass diffusion model shows reasonable agreement.Copyright

WALL HEAT FLUX PARTITIONING DURING SUBCOOLED FLOW BOILING AT LOW PRESSURES

In this work a mechanistic model for nucleate boiling heat flux as a function of wall superheat has been developed. The premise of the proposed model is that the entire energy from the wall is first transferred to the superheated liquid layer adjacent to the wall. A fraction of this energy is then utilized for vapor generation. Contribution of each of the heat transfer mechanisms - forced convection, transient conduction, and vapor generation, has been quantified in terms of nucleation site densities, bubble departure and lift off diameters, bubble release frequency, flow parameters like velocity, inlet subcooling, wall superheat, and fluid and surface properties including system pressures. To support the model development, subcooled flow boiling experiments were conducted at pressures of 1.03 to 3.2 bar for a wide range of mass fluxes (124 to 926 kg/m 2 s), heat fluxes (2.5 to 90 W/cm 2 ) and for contact angles varying from 30 o to 90 o . Model validation has been carried out with low-pressure data obtained from present work and the wall heat flux predictions are within ± 30% of experimental values. Application of the model to high-pressure data available in literature also showed good agreement, signifying that the model can be extended to all pressures.

Flow and Heat Transfer in Liquid Films Flowing Over Highly Curved Surfaces

Large-scale evaporative cooling is one of the leading sources of fresh water consumption. Dry cooling based on existing heat exchangers, however, has found limited usage due to the high cost and large foot prints/weights. Development of alternative low-cost light-weight heat exchangers for dry cooling is therefore urgently needed. One promising design for such alternative heat exchangers is what we call Direct-contact Liquid-on-String Heat Exchangers (DILSHE). DILSHE consists of a vertically aligned array of inexpensive polymer strings. A nonvolatile liquid flows over the strings, forming thin liquid films. Large surface areas provided by these films enable efficient heat transfer to counter-flowing cooling air. Physics-based design and optimization of DILSHE requires rigorous understanding of flow and heat transfer phenomena of falling liquid films on highly curved surfaces. Formation of travelling beads through the Rayleigh-Plateau or Kapitza instability can enhance heat transfer across liquid-gas interfaces. We have developed a numerical model for liquid-gas flows and heat transfer in the drop-like regime, where the Rayleigh-Plateau instability dominates and the shape of travelling beads is governed mainly by the influence of surface tension. We solve the Young-Laplace equation to obtain the liquid bead shape, which was then used to construct a finite element model. The time-dependent Navier-Stokes equation and the energy equation were then solved to obtain velocity and temperature distributions in the liquid and the surrounding counter-flowing air. The temporal and spatial variations in the temperature of travelling beads are analyzed to evaluate the effective heat transfer coefficients, which are key input parameters for an overall heat exchange model to quantify the heat transfer characteristic of DILSHE. The present work helps build foundation for systematic design of new generations of heat exchangers for dry cooling.© 2015 ASME