Identification of Nucleate Boiling as the Dominant Heat Transfer Mechanism during Confined Two-Phase Jet Impingement

Thermal management of high-power electronics requires cooling strategies capable of dissipating high heat fluxes while maintaining the device at low operating temperatures. Two-phase jet impingement offers a compact cooling technology capable of meeting these requirements at a low pressure drop. Generally, confined impingement geometries are used in electronics cooling applications, where the flow is constrained between the hot surface and orifice plate. Understanding the primary heat transfer mechanisms occurring as boiling takes place on the surface during jet impingement is important, specifically under such confined conditions. In this study, heat transfer from a copper surface is experimentally characterized in both confined jet impingement and pool boiling configurations. The dielectric liquid HFE- 7100 is used as the working fluid. For the jet impingement configuration, the jet issues through a single 2 mm-diameter orifice, at jet exit velocities of 1, 3, 6, and 9 m/s, into a confinement gap with a spacing of 3 jet diameters between the orifice and heat source. Additional orifice-to-target spacings of 0.5, 1, and 10 jet diameters are tested at the lowest (Vj = 1 m/s) and highest (Vj = 9 m/s) jet velocities. By incrementing the heat flux applied to the surface and observing the steady-state response at each flux, the single-phase and two-phase heat transfer performance is characterized; all experiments were carried through to critical heat flux conditions. The jet impingement data in the fully boiling regime either directly overlap the pool boiling data, or coincide with an extension of the trend in pool boiling data beyond the pool boiling critical heat flux limit. This result confirms that nucleate boiling is the dominant heat transfer mechanism in the fully boiling regime in confined jet impingement; the convective effects of the jet play a negligible role over the wide range of parameters considered here. While the presence of the jet does not enhance the boiling heat transfer coefficient, the jet does greatly increase single-phase heat transfer performance and extends the critical heat flux limit. Critical heat flux displays a linear dependence on jet velocity while remaining insensitive to changes in the orifice-to-target spacing

A super-analogue of Kontsevich's theorem on graph homology

In this paper we will prove a super-analogue of a well-known result by Kontsevich which states that the homology of a certain complex which is generated by isomorphism classes of oriented graphs can be calculated as the Lie algebra homology of an infinite-dimensional Lie algebra of symplectic vector fields.Comment: 15 page

Essential Role of the G-Domain in Targeting of the Protein Import Receptor atToc159 to the Chloroplast Outer Membrane

Two homologous GTP-bindin proteins, atToc33 and atToc159, control access of cytosolic precursor proteins to the chloroplast, at Toc33 is a constitutive outer chloroplast membrane protein, whereas the precusor receptor atToc159 may be able to switch between a soluble and an integral membrane form. By transient expression of GFP fusion proteins, mutant analysis, and biochemical experimentation, we demonstrate that the GTP-binding domain regulates the targeting of cytosolic atToc159 to the chloroplast and mediates the switch between cytosolic and integral membrane forms. Mutant atToc159, unable to bind GTP, does not reinstate a green phenotype in an albino mutant (ppi2) lacking endogenous atToc159, remaining trapped in the cytosol. Thus, the function of atToc159 in chloroplast biogenesis is dependent on an intrinsic GTP-regulated swtich that controls localization of the receptor to the chloroplast envelope

On equivariant characteristic ideals of real classes

Let $p$ be an odd prime, $F/{\Bbb Q}$ an abelian totally real number field, $F_\infty/F$ its cyclotomic ${\Bbb Z}_p$-extension, $G_\infty = Gal (F_\infty / {\Bbb Q}),$ ${\Bbb A} = {\Bbb Z}_p [[G_\infty]].$ We give an explicit description of the equivariant characteristic ideal of $H^2_{Iw} (F_\infty, {\Bbb Z}_p(m))$ over ${\Bbb A}$ for all odd $m \in {\Bbb Z}$ by applying M. Witte's formulation of an equivariant main conjecture (or "limit theorem") due to Burns and Greither. This could shed some light on Greenberg's conjecture on the vanishing of the $\lambda$-invariant of $F_\infty/F.

Development and Validation of a Semi-Empirical Model for Two-Phase Heat Transfer from Arrays of Impinging Jets

Two-phase jet impingement is a compact cooling technology that provides high-heat-flux dissipation at manageable pressure drop, with applications in cooling power electronics and server modules. The extensive set of geometrical parameters and operating conditions that determine the heat transfer behavior of jet impingement systems provide an attractive level of design flexibility. In the present study, a semiempirical approach is developed to predict heat transfer from arrays of jets of liquid that undergoes phase change upon impingement. In the modeling approach developed, the jet array is divided into unit cells centered on each orifice that are assumed to behave identically. Based on prior experimental observations, the impingement surface in each unit cell is divided into two distinct regions: a single-phase heat transfer region directly under the jet, and a surrounding boiling heat transfer region along the periphery. Single-phase convection and boiling heat transfer correlations available in the literature are used to estimate the heat transfer coefficient distribution in each region, and the mean surface temperature of the unit cell is estimated via area-averaging. An analysis is performed to show that the model outputs are sensitive to the heat transfer coefficient correlations used as inputs, with the choice depending on the heat flux input and the expected operating regime. Experiments are performed to validate the areaaveraged thermal performance predictions. The model results are also compared against experimental data in the literature. The semi-empirical modeling approach developed in this work successfully represents the different heat transfer modes and transitions that occur during two-phase jet impingement. The location of transition to boiling predicted by the model is consistent with prior experimental observations of an inward-creeping boiling front with increasing heat flux. The predicted temperature difference between the surface and the jet inlet across all experimental comparisons has a mean absolute percentage error of 3.88%. The proposed modeling approach is demonstrated to be a practical tool in the development of two-phase jet array impingement devices, allowing for parametric exploration across the expansive design space

Effect of Photoperiod and Temperature on the Development of Sorghum

Three varieties of Sorghum bicolor (L.) Moench, (i.e., ‘Early Hegari,’ ‘80-Day Milo,’ and ‘Wheatland’) were grown in controlled environment chambers and subjected to all combinations of 10-, 12-, and 14-hour photoperiods, 27 and 32 C day temperatures, and 16 and 21 C night temperatures. Days to floral initiation were determined for each variety under each treatment combination. In addition, days to anthesis and days in the floral period (from initiation to anthesis) were determined for the treatment combinations involving 21 C night temperatures. Ten-hour days hastened floral initiation and anthesis of each variety at all temperature combinations. Fourteen-hour days delayed development, but with some temperature regimes the delay was not significant, compared to the shorter days. The rate of development for the varieties under 12-hour days was highly dependent upon day and night temperatures, since floral initiation ranged from as early as that obtained with 10-hour days to later than that obtained with 14-hour days. The response to day temperature during the floral period was small, but statistically significant. The time to anthesis followed a pattern similar to that for the time to floral initiation

Design, fabrication, and characterization of a compact hierarchical manifold microchannel heat sink array for two-phase cooling

High-heat-flux removal is critical for the nextgeneration electronic devices to reliably operate within their temperature limits. A large portion of the thermal resistance in a traditional chip package is caused by thermal resistances at interfaces between the device, heat spreaders, and the heat sink; embedding the heat sink directly into the heat-generating device can eliminate these interface resistances and drastically reduce the overall thermal resistance. Microfluidic cooling within the embedded heat sink improves the heat dissipation, with two-phase operation offering the potential for dissipation of very high heat fluxes while maintaining moderate chip temperatures. To enable multichip stacking and other heterogeneous packaging approaches, it is important to densely integrate all fluid flow paths into the device; volumetric heat dissipation emerges as a performance metric in this new heat sinking paradigm. In this paper, a compact hierarchical manifold microchannel design is presented that utilizes an integrated multilevel manifold distributor to feed coolant to an array of microchannel heat sinks. The flow features in the manifold layers and microchannels are fabricated in silicon wafers using deep reactive-ion etching. The heat source is simulated via Joule heating using thin-film platinum heaters. The on-chip spatial temperature measurements are made using four-wire resistance temperature detectors. The individual manifold layers and the microchannel-bearing wafers are diced and bonded into a sealed stack via thermocompression bonding using gold layers at the mating surfaces. Thermal and hydrodynamic testing is performed by pumping the dielectric fluid HFE-7100 through the device at a known flow rate

Characterization of Hierarchical Manifold Microchannel Heat Sink Arrays under Simultaneous Background and Hotspot Heating Conditions

A hierarchical manifold microchannel heat sink array is fabricated and experimentally characterized for uniform heat flux dissipation over a footprint area of 5 mm x 5 mm. A 3 x 3 array of heat sinks is fabricated into the silicon substrate containing the heaters for direct intrachip cooling, eliminating the thermal resistances typically associated with the attachment of a separate heat sink. The heat sinks are fed in parallel using a hierarchical manifold distributor that delivers flow to each of the heat sinks. Each heat sink contains a bank of high-aspect-ratio microchannels; five different channel geometries with nominal widths of 15 lm and 33 micrometers and nominal depths between 150 micrometers and 470 micrometers are tested. The thermal and hydraulic performance of each heat sink array geometry is evaluated using HFE-7100 as the working fluid, for mass fluxes ranging from 600 kg/m2 s to 2100 kg/m2 s at a constant inlet temperature of 59 degree C. To simulate heat generation from electronics devices, a uniform background heat flux is generated with thin-film serpentine heaters fabricated on the silicon substrate opposite the channels; temperature sensors placed across the substrate provide spatially resolved surface temperature measurements. Experiments are also conducted with simultaneous background and hotspot heat generation; the hotspot heat flux is produced by a discrete 200 micrometers x 200 micrometers hotspot heater. Heat fluxes up to 1020 W/cm2 are dissipated under uniform heating conditions at chip temperatures less than 69 degree C above the fluid inlet and at pressure drops less than 120 kPa. Heat sinks with wider channels yield higher wetted-area heat transfer coefficients, but not necessarily the lowest thermal resistance; for a fixed channel depth, samples with narrower channels have increased total wetted areas owing to the smaller fin pitches. During simultaneous background and hotspot heating conditions, background heat fluxes up to 900 W/cm2 and hotspot fluxes up to 2700 W/cm2 are dissipated. The hotspot temperature increases linearly with hotspot heat flux; at hotspot heat fluxes of 2700 W/cm2, the hotspot experiences a temperature rise of 16 degree C above the average chip temperature