Showing papers in "Journal of Heat Transfer-transactions of The Asme in 2010"

The Classical Nature of Thermal Conduction in Nanofluids

Abstract: We show that a large set of nanofluid thermal conductivity data falls within the upper and lower Maxwell bounds for homogeneous systems. This indicates that the thermal conductivity of nanofluids is largely dependent on whether the nanoparticles stay dispersed in the base fluid, form large aggregates, or assume a percolating,fractal confguration. The experimental data, which are strikingly analogous to those in most solid composites and liquid mixtures, provide strong evidence for the classical nature of thermal conduction in nanofluids.

Airflow and Cooling in a Data Center

Abstract: This paper deals with the distribution of airflow and the resulting cooling in a data center. First, the cooling challenge is described and the concept of a raised-floor data center is introduced. In this arrangement, cooling air is supplied through perforated tiles. The flow rates of the cooling air must meet the cooling requirements of the computer servers placed next to the tiles. These airflow rates are governed primarily by the pressure distribution under the raised floor. Thus, the key to modifying the flow rates is to influence the fiow field in the under-floor plenum. Computational fluid dynamics (CFD) is used to provide insight into various factors affecting the airflow distribution and the corresponding cooling. A number of ways of controlling the airflow distribution are explored. Then attention is turned to the above-floor space, where the focus is on preventing the hot air from entering the inlets of computer serves. Different strategies for doing this are considered. The paper includes a number of comparisons of measurements with the results of CFD simulations.

Criteria for Cross-Plane Dominated Thermal Transport in Multilayer Thin Film Systems During Modulated Laser Heating

Abstract: Pump-probe transient thermoreflectance (TTR) techniques are powerful tools for measuring the thermophysical properties of thin films, such as thermal conductivity A, or thermal boundary conductance, G. This paper examines the assumption of one-dimensional heating on, A and G, determination in nanostructures using a pump-probe transient thermoreflectance technique. The traditionally used one-dimensional and axially symmetric cylindrical conduction models for thermal transport are reviewed. To test the assumptions of the thermal models, experimental data from Al films on bulk substrates (Si and glass) are taken with the TTR technique. This analysis is extended to thin film multilayer structures. The results show that at 11 MHz modulation frequency thermal transport is indeed one dimensional. Error among the various models arises due to pulse accumulation and not accounting for residual heating.

Tomography-Based Heat and Mass Transfer Characterization of Reticulate Porous Ceramics for High-Temperature Processing

Abstract: Reticulate porous ceramics employed in high-temperature processes are characterized for heat and mass transfer. The exact 3D digital geometry of their complex porous structure is obtained by computer tomography and used in direct pore-level simulations to numerically calculate their effective transport properties. Two-point correlation functions and mathematical morphology operations are applied for the geometrical characterization that includes the determination of porosity, specific surface area, representative elementary volume edge size, and mean pore size. Finite volume techniques are applied for conductive/convective heat transfer and flow characterization, which includes the determination of the thermal conductivity, interfacial heat transfer coefficient, permeability, Dupuit–Forchheimer coefficient, residence time, tortuosity, and diffusion tensor. Collision-based Monte Carlo method is applied for the radiative heat transfer characterization, which includes the determination of the extinction coefficient and scattering phase function.

Buoyancy Driven Heat Transfer of Nanofluids in a Tilted Enclosure

Abstract: Buoyancy driven heat transfer of water-based nanofluids in a differentially heated, tilted enclosure is investigated in this study. The governing equations (obtained with the Boussinesq approximation) are solved using the polynomial differential quadrature method for an inclination angle ranging from 0 deg to 90 deg, two different ratios of the nanolayer thickness to the original particle radius (0.02 and 0.1), a solid volume fraction ranging from 0% to 20%, and a Rayleigh number varying from 104 to 106. Five types of nanoparticles, Cu, Ag, CuO, Al2O3, and TiO2 are taken into consideration. The results show that the average heat transfer rate from highest to lowest is for Ag, Cu, CuO, Al2O3, and TiO2. The results also show that for the particle radius generally used in practice ( 0.1 or 0.02), the average heat transfer rate increases to 44% for Ra 104, to 53% for Ra 105, and to 54% for Ra 106 if the special case of 90 deg, which also produces the minimum heat transfer rates, is not taken into consideration. As for 90 deg, the heat transfer enhancement reaches 21% for Ra 104, 44% for Ra 105, and 138% for Ra 106. The average heat transfer rate shows an increasing trend with an increasing inclination angle, and a peak value is detected. Beyond the peak point, the foregoing trend reverses and the average heat transfer rate decreases with a further increase in the inclination angle. Maximum heat transfer takes place at 45 deg for Ra 104 and at 30 deg for Ra 105 and 106. DOI: 10.1115/1.4000744

Infrared Radiative Properties of Heavily Doped Silicon at Room Temperature

Abstract: This paper describes an experimental investigation on the infrared radiative properties of heavily doped Si at room temperature. Lightly doped Si wafers were ion-implanted with either boron or phosphorus atoms, with dosages corresponding to as-implanted peak doping concentrations of 10 20 and 10 21 cm -3 ; the peak doping concentrations after annealing are 3.1 × 10 19 and 2.8 × 10 20 cm -3 , respectively. Rapid thermal annealing was performed to activate the implanted dopants. A Fourier-transform infrared spectrometer was employed to measure the transmittance and reflectance of the samples in the wavelength range from 2 μm to 20 μm. Accurate carrier mobility and ionization models were identified after carefully reviewing the available literature, and then incorporated into the Drude model to predict the dielectric function of doped Si. The radiative properties of doped Si samples were calculated by treating the doped region as multilayer thin films of different doping concentrations on a thick lightly doped Si substrate. The measured spectral transmittance and reflectance agree well with the model predictions. The knowledge gained from this study will aid future design and fabrication of doped Si microstructures as wavelength selective emitters and absorbers in the midinfrared region.

Experimental Investigation of an Ultrathin Manifold Microchannel Heat Sink for Liquid-Cooled Chips

Abstract: We report an experimental investigation of a novel, high performance ultrathin manifold microchannel heat sink. The heat sink consists of impinging liquid slot-jets on a structured surface fed with liquid coolant by an overlying two-dimensional manifold. We developed a fabrication and packaging procedure to manufacture prototypes by means of standard microprocessing. A closed fluid loop for precise hydrodynamic and thermal characterization of six different test vehicles was built. We studied the influence of the number of manifold systems, the width of the heat transfer microchannels, the volumetric flow rate, and the pumping power on the hydrodynamic and thermal performance of the heat sink. A design with 12.5 manifold systems and 25 μm wide microchannels as the heat transfer structure provided the optimum choice of design parameters. For a volumetric flow rate of 1.3 l/min we demonstrated a total thermal resistance between the maximum heater temperature and fluid inlet temperature of 0.09 cm 2 K/W with a pressure drop of 0.22 bar on a 2 ×2 cm 2 chip. This allows for cooling power densities of more than 700 W/cm 2 for a maximum temperature difference between the chip and the fluid inlet of 65 K. The total height of the heat sink did not exceed 2 mm, and includes a 500 μm thick thermal test chip structured by 300 μm deep microchannels for heat transfer. Furthermore, we discuss the influence of elevated fluid inlet temperatures, allowing possible reuse of the thermal energy, and demonstrate an enhancement of the heat sink cooling efficiency of more than 40% for a temperature rise of 50 K.

Experimental and Numerical Investigation of Heat Transfer Characteristics of Inline and Staggered Arrays of Impinging Jets

Abstract: A combined experimental and numerical investigation of the heat transfer characteristics within an array of impinging jets has been conducted. The experiments were carried out in a perspex model using a transient liquid crystal method. Local jet temperatures were measured at several positions on the impingement plate to account for an exact evaluation of the heat transfer coefficient. The effects of the variation in different impingement patterns, jet-to-plate spacing, crossflow schemes, and jet Reynolds number on the distribution of the local Nusselt number and the related pressure loss were investigated experimentally. In addition to the measurements, a numerical investigation was conducted. The motivation was to evaluate whether computational fluid dynamics (CFD) can be used as an engineering design tool in the optimization of multijet impingement configurations. This required, as a first step, a validation of the numerical results. For the present configuration, this was achieved assessing the degree of accuracy to which the measured heat transfer rates could be computed. The overall agreement was very good and even local heat transfer coefficients were predicted at high accuracy. The numerical investigation showed that state-of-the-art CFD codes can be used as suitable means in the thermal design process of such configurations.

Entropy Generation Analysis for Nanofluid Flow in Microchannels

Abstract: Employing a validated computer simulation model, entropy generation is analyzed in trapezoidal microchannels for steady laminar flow of pure water and CuO-water nanofluids. Focusing on microchannel heat sink applications, local and volumetric entropy rates caused by frictional and thermal effects are computed for different coolants, inlet temperatures, Reynolds numbers, and channel aspect ratios. It was found that there exists an optimal Reynolds number range to operate the system due to the characteristics of the two different entropy sources, both related to the inlet Reynolds number. Microchannels with high aspect ratios have a lower suitable operational Reynolds number range. The employment of nanofluids can further minimize entropy generation because of their superior thermal properties. Heat transfer induced entropy generation is dominant for typical microheating systems while frictional entropy generation becomes more and more important with the increase in fluid inlet velocity/Reynolds number.

Monte Carlo Study of Phonon Heat Conduction in Silicon Thin Films Including Contributions of Optical Phonons

Abstract: The Monte Carlo method has found prolific use in the solution of the Boltzmann transport equation for phonons for the prediction of nonequilibrium heat conduction in crystalline thin films. This paper contributes to the state-of-the-art by performing a systematic study of the role of the various phonon modes on thermal conductivity predictions, in particular, optical phonons. A procedure to calculate three-phonon scattering time-scales with the inclusion of optical phonons is described and implemented. The roles of various phonon modes are assessed. It is found that transverse acoustic (TA) phonons are the primary carriers of energy at low temperatures. At high temperatures T200 K, longitudinal acoustic (LA) phonons carry more energy than TA phonons. When optical phonons are included, there is a significant change in the amount of energy carried by various phonons modes, especially at room temperature, where optical modes are found to carry about 25% of the energy at steady state in silicon thin films. Most importantly, it is found that inclusion of optical phonons results in better match with experimental observations for silicon thin-film thermal conductivity. The inclusion of optical phonons is found to decrease the thermal conductivity at intermediate temperatures (50‐200 K) and to increase it at high temperature 200 K, especially when the film is thin. The effect of number of stochastic samples, the dimensionality of the computational domain (two-dimensional versus three-dimensional), and the lateral (in-plane) dimension of the film on the statistical accuracy and computational efficiency is systematically studied and elucidated for all temperatures. DOI: 10.1115/1.4000447

Thermal Characterization of Interlayer Microfluidic Cooling of Three-Dimensional Integrated Circuits With Nonuniform Heat Flux

Abstract: It is now widely recognized that the three-dimensional (3D) system integration is a key enabling technology to achieve the performance needs of future microprocessor integrated circuits (ICs). To provide modular thermal management in 3D-stacked ICs, the interlayer microfluidic cooling scheme is adopted and analyzed in this study focusing on a single cooling layer performance. The effects of cooling mode (single-phase versus phase-change) and stack/layer geometry on thermal management performance are quantitatively analyzed, and implications on the through-silicon-via scaling and electrical interconnect congestion are discussed. Also, the thermal and hydraulic performance of several two-phase refrigerants is discussed in comparison with single-phase cooling. The results show that the large internal pressure and the pumping pressure drop are significant limiting factors, along with significant mass flow rate maldistribution due to the presence of hot-spots. Nevertheless, two-phase cooling using R123 and R245ca refrigerants yields superior performance to single-phase cooling for the hot-spot fluxes approaching ∼300 W/cm 2 . In general, a hybrid cooling scheme with a dedicated approach to the hot-spot thermal management should greatly improve the two-phase cooling system performance and reliability by enabling a cooling-load-matched thermal design and by suppressing the mass flow rate maldistribution within the cooling layer.

Thermal Wave Based on the Thermomass Model

Abstract: In times comparable to the characteristic time of the energy carriers, Fourier's law of heat conduction breaks down and heat may propagate as waves. Based on the concept of thermomass, which is defined as the equivalent mass of phonon gas in dielectrics, according to the Einstein's mass-energy relation, the phonon gas in the dielectrics is described as a weighty, compressible fluid. Newton mechanics has been applied to establish the equation of state and the equation of motion for the phonon gas as in fluid mechanics, because the drift velocity of a phonon gas is normally much less than the speed of light. The propagation velocity of the thermal wave in the phonon gas is derived directly from the equation of state for the phonon gas, rather than from the relaxation time in the Cattaneo―Vernotte (CV) model (Cattaneo, C., 1948, "Sulla Conduzione Del Calore," Atti Semin. Mat. Fis. Univ. Modena, 3, pp. 83―101; Vernotte, P., 1958, "Paradoxes in the Continuous Theory of the Heat Equation, " C. R. Acad. Bulg. Sci., 246, pp. 3154―3155). The equation of motion for the phonon gas gives rise to the thermomass model, which depicts the general relation between the temperature gradient and heat flux. The linearized conservation equations for the phonon gas lead to a damped thermal wave equation, which is similar to the CV-wave equation, but with different characteristic time. The lagging time in the resulting thermal wave equation is related to the wave velocity in the phonon gas, which is approximately two orders of magnitude larger than the relaxation time adopted in the CV-wave model for the lattices. A numerical example for fast transient heat conduction in a silicon film is presented to show that the temperature peaks resulting from the thermomass model are much higher than those resulting from the CV-wave model. Due to the slower thermal wave velocity in the phonon gas, by as much as one order of magnitude, the damage due to temperature overshooting may be more severe than that expected from the CV-wave model.

Near-Field Radiation Calculated With an Improved Dielectric Function Model for Doped Silicon

Abstract: This paper describes a theoretical investigation of near-field radiative heat transfer between doped silicon surfaces separated by a vacuum gap. An improved dielectric function model for heavily doped silicon is employed. The effects of doping level, polarization, and vacuum gap width on the spectral and total radiative transfer are studied based on the fluctuational electrodynamics. It is observed that increasing the doping concentration does not necessarily enhance the energy transfer in the near-field. The energy streamline method is used to model the lateral shift of the energy pathway, which is the trace of the Poynting vectors in the vacuum gap. The local density of states near the emitter is calculated with and without the receiver. The results from this study can help improve the understanding of near-field radiation for applications such as thermophotovoltaic energy conversion, nanoscale thermal imaging, and nanothermal manufacturing.

The Effect of Local Thermal Nonequilibrium on the Onset of Convection in a Nanofluid

Abstract: The onset of convection in a horizontal layer of a nanofluid is studied analytically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis, and allows for local thermal noneguilibrium (LTNE) between the particle and fluid phases. The analysis reveals that in some circumstances, the effect of LTNE can be significant, but for a typical dilute nanofluid (with large Lewis number and with small particle-to-fluid heat capacity ratio), the effect is small.

Effects of Variable Viscosity and Thermal Conductivity of CuO-Water Nanofluid on Heat Transfer Enhancement in Natural Convection: Mathematical Model and Simulation

Abstract: Heat transfer enhancement in horizontal annuli using variable thermal conductivity and variable viscosity of CuO-water nanofluid is investigated numerically. The base case of simulation used thermal conductivity and viscosity data that consider temperature property dependence and nanoparticle size. It was observed that for Ra≥ 10 4 , the average Nusselt number was deteriorated by increasing the volume fraction of nanoparticles. However, for Ra =10 3 , the average Nusselt number enhancement depends on aspect ratio of the annulus as well as volume fraction of nanoparticles. Also, for Ra = 10 3 , the average Nusselt number was less sensitive to volume fraction of nanoparticles at high aspect ratio and the average Nusselt number increased by increasing the volume fraction of nanoaprticles for aspect ratios ≤0.4. For Ra≥ 10 4 , the Nusselt number was deteriorated everywhere around the cylinder surface especially at high aspect ratio. However, this reduction is only restricted to certain regions around the cylinder surface for Ra = 10 3 . For Ra ≥ 10 4 , the Maxwell―Garnett and the Chon et al. conductivity models demonstrated similar results. But, there was a deviation in the prediction at Ra = 10 3 and this deviation becomes more significant at high volume fraction of nanoparticles. The Nguyen et al. data and the Brinkman model give completely different predictions,for Ra≥10 4 , where the difference in prediction of the Nusselt number reached 50%. However, this difference was less than 10% at Ra =10 3 .

Flow Boiling Heat Transfer on Micro Pin Fins Entrenched in a Microchannel

Abstract: Flow boiling of 1-methoxyheptafluoropropane (HFE 7000) in 222 μm hydraulic diameter channels containing a single row of 24 inline 100 μm pin fins was studied for mass fluxes from 350 kg/m2 s to 827 kg/m2 s and wall heat fluxes from 10 W/cm2 to 110 W/cm2. Flow visualization revealed the existence of isolated bubbles, bubbles interacting, multiple flow, and annular flow. The observed flow patterns were mapped as a function of the boiling number and the normalized axial distance. The local heat transfer coefficient during subcooled boiling was measured and found to be considerably higher than the corresponding single-phase flow. Furthermore, a thermal performance evaluation comparison with a plain microchannel revealed that the presence of pin fins considerably enhanced the heat transfer coefficient.

On the Mechanism of Pool Boiling Critical Heat Flux Enhancement in Nanofluids

Abstract: The pool boiling characteristics of water-based nanofluids with alumina and titania nanoparticles of 0.01 vol % were investigated on a thermally heated disk heater at saturated temperature and atmospheric pressure. The results confirmed the findings of previous studies that nanofluids can significantly enhance the critical heat flux (CHF), resulting in a large increase in the wall superheat. It was found that some nanoparticles deposit on the heater surface during nucleate boiling, and the surface modification due to the deposition results in the same magnitude of CHF enhancement in pure water as for nanofluids. Subsequent to the boiling experiments, the interfacial properties of the heater surfaces were examined using dynamic wetting of an evaporating water droplet. As the surface temperature increased, the evaporating meniscus on the clean surface suddenly receded toward the liquid due to the evaporation recoil force on the liquid-vapor interface, but the nanoparticle-fouled surface exhibited stable wetting of the liquid meniscus even at a remarkably higher wall superheat. The heat flux gain attainable due to the improved wetting of the evaporating meniscus on the fouled surface showed good agreement with the CHF enhancement during nanofluid boiling. It is supposed that the nanoparticle layer increases the stability of the evaporating microlayer underneath a bubble growing on a heated surface and thus the irreversible growth of a hot/dry spot is inhibited even at a high wall superheat, resulting in the CHF enhancement observed when boiling nanofluids.

Design and Test of Carbon Nanotube Biwick Structure for High-Heat-Flux Phase Change Heat Transfer

Abstract: With the increase in power consumption in compact electronic devices, passive heat transfer cooling technologies with high-heat-flux characteristics are highly desired in microelectronic industries. Carbon nanotube (CNT) clusters have high thermal conductivity, nanopore size, and large porosity and can be used as wick structure in a heat pipe heatspreader to provide high capillary force for high-heat-flux thermal management. This paper reports investigations of high-heat-flux cooling of the CNT biwick structure, associated with the development of a reliable thermometer and high performance heater. The thermometer/heater is a 100-nm-thick and 600 μm wide Z-shaped platinum wire resistor, fabricated on a thermally oxidized silicon substrate of a CNT sample to heat a 2 ×2 mm 2 wick area. As a heater, it provides a direct heating effect without a thermal interface and is capable of high-temperature operation over 800°C. As a thermometer, reliable temperature measurement is achieved by calibrating the resistance variation versus temperature after the annealing process is applied. The thermally oxidized layer on the silicon substrate is around 1-μm-thick and pinhole-free, which ensures the platinum thermometer/heater from the severe CNT growth environments without any electrical leakage. For high-heat-flux cooling, the CNT biwick structure is composed of 250 μm tall and 100 μm wide stripelike CNT clusters with 50 μm stripe-spacers. Using 1 ×1 cm 2 CNT biwick samples, experiments are completed in both open and saturated environments. Experimental results demonstrate 600 W/cm 2 heat transfer capacity and good thermal and mass transport characteristics in the nanolevel porous media.

Combined Effects of Joule Heating and Viscous Dissipation on Magnetohydrodynamic Flow Past a Permeable, Stretching Surface With Free Convection and Radiative Heat Transfer

Abstract: The combined effects of Joule heating and viscous dissipation on the momentum and thermal transport are studied for the Magnetohydrodynamic (MHD) flow over a stretching sheet. Effects of free convection, thermal radiation, and surface suction/blowing on the flow and heat transfer characteristics are also examined. Results demonstrate that the reduction in heat transfer due to Joule and viscous heating is more pronounced at a higher Prandtl number. The Eckert number changes appreciably the velocity profile as the buoyancy effect becomes significant, while the Eckert number has an unimpressive effect on the velocity when the free convection is week. Increasing the radiation parameter will increase the temperature profile noticeably, and thus reduce the heat transfer rate accordingly. The heat transfer is enhanced markedly by imposing surface fluid suction, while the opposite trend is observed for blowing.

Numerical Analysis of Convective Heat Transfer From an Elliptic Pin Fin Heat Sink With and Without Metal Foam Insert

Abstract: A numerical analysis of forced convective heat transfer from an elliptical pin fin heat sink with and without metal foam inserts is conducted using three-dimensional conjugate heat transfer model. The pin fin heat sink model consists of six elliptical pin rows with 3 mm major diameter, 2 mm minor diameter, and 20 mm height. The Darcy‐Brinkman‐ Forchheimer and classical Navier‐Stokes equations, together with corresponding energy equations are used in the numerical analysis of flow field and heat transfer in the heat sink with and without metal foam inserts, respectively. A finite volume code with point implicit Gauss‐Seidel solver in conjunction with algebraic multigrid method is used to solve the governing equations. The code is validated by comparing the numerical results with available experimental results for a pin fin heat sink without porous metal foam insert. Different metallic foams with various porosities and permeabilities are used in the numerical analysis. The effects of air flow Reynolds number and metal foam porosity and permeability on the overall Nusselt number, pressure drop, and the efficiency of heat sink are investigated. The results indicate that structural properties of metal foam insert can significantly influence on both flow and heat transfer in a pin fin heat sink. The Nusselt number is shown to increase more than 400% in some cases with a decrease in porosity and an increase in Reynolds number. However, the pressure drop increases with decreasing permeability and increasing Reynolds number. DOI: 10.1115/1.4000951

Critical Heat Flux (CHF) of Subcooled Flow Boiling of Alumina Nanofluids in a Horizontal Microchannel

Abstract: This work investigates subcooled flow boiling of aqueous based alumina nanofluids in 510 μm single microchannels with a focus on the effect of nanoparticles on the critical heat flux. The surface temperature distribution along the pipe, the inlet and outlet pressures and temperatures are measured simultaneously for different concentrations of alumina nanofluids and de-ionized water. To minimize the effect of nanoparticle depositions, all nanofluid experiments are performed on fresh microchannels. The experiment shows an increase of ∼51% in the critical heat flux under very low nanoparticle concentrations (0.1 vol %). Different burnout characteristics are observed between water and nanofluids, as well as different pressure and temperature fluctuations and flow pattern development during the stable boiling period. Detailed observations of the boiling surface show that nanoparticle deposition and a subsequent modification of the boiling surface are common features associated with nanofluids, which should be responsible for the different boiling behaviors of nanofluids.

Harvesting nanoscale thermal radiation using pyroelectric materials

Abstract: Pyroelectric energy conversion offers a way to convert waste heat directly into electricity. It makes use of the pyroelectric effect to create a flow of charge to or from the surface of a material as a result of heating or cooling. However, existing pyroelectric energy converter can only operate at low frequency due to relatively small convective heat transfer rate between the pyroelectric materials and the working fluid. On the other hand, energy transfer by thermal radiation between two semi-infinite solids is nearly instantaneous and can be enhanced by several orders of magnitude from the conventional Stefan-Boltzmann law as the gap separating them becomes smaller than the Wien's displacement wavelength. This paper explores a novel way to harvest waste heat by combining pyroelectric energy conversion and nanoscale thermal radiation. A new device was investigated numerically by accurately modeling nanoscale radiative heat transfer between a pyroelectric element and hot and cold plates. Silica absorbing layers on top of every surface were used to further increase the net radiative heat fluxes. Temperature oscillations with time and performances of the pyroelectric converter were predicted at various frequencies. The device using 60/40 P(VDF-TrFE) achieved 0.2% efficiency and 0.84 mW/cm2 electrical power output for the cold and hot sources at 273 and 388 K, respectively. Better performances could be achieved with 0.9PMN-PT namely efficiency of 1.3% and power output of 6.5 mW/cm2 between the cold and hot sources at 283 and 383 K, respectively. These results are compared with alternative technologies and suggestions are made to further improve the device.

Three-Dimensional Magnetic Fluid Boundary Layer Flow Over a Linearly Stretching Sheet

Abstract: The three-dimensional laminar and steady boundary layer flow of an electrically nonconducting and incompressible magnetic fluid, with low Curie temperature and moderate saturation magnetization, over an elastic stretching sheet, is numerically studied. The fluid is subject to the magnetic field generated by an infinitely long, straight wire, carrying an electric current. The magnetic fluid far from the surface is at rest and at temperature greater of that of the sheet. It is also assumed that the magnetization of the fluid varies with the magnetic field strength H and the temperature T. The numerical solution of the coupled and nonlinear system of ordinary differential equations, resulting after the introduction of appropriate nondimensional variables, with its boundary conditions, describing the problem under consideration, is obtained by an efficient numerical technique based on the common finite difference method. Numerical calculations are carried out for the case of a representative water-based magnetic fluid and for specific values of the dimensionless parameters entering into the problem, and the obtained results are presented graphically for these values of the parameters. The analysis of these results showed that there is an interaction between the motions of the fluid, which are induced by the stretching surface and by the action of the magnetic field, and the flow field is noticeably affected by the variations in the magnetic interaction parameter β. The important results of the present analysis are summarized in Sec. 6.

3D Integrated Water Cooling of a Composite Multilayer Stack of Chips

Abstract: New generation supercomputers with three dimensional stacked chip architectures pose a major challenge with respect to the removal of dissipated heat, which can reach currently as high as 250 W/cm 2 in multilayer chip stacks of less than 0.3 cm 3 volume. Interlayer integrated water cooling is a very promising approach for such high heat flux removal due to much larger thermal capacity and conductivity of water compared with air, the traditional cooling fluid. In the current work, a multiscale conjugate heat transfer model is developed for integrated water cooling of chip layers and validated with experimental measurements on an especially designed thermal test vehicle that simulates a four tier chip stack with a footprint of 1 cm 2 . The cooling heat transfer structure, which consists of microchannels with cylindrical pin-fins, is conceived in such a way that it can be directly integrated with the device layout in multilayer chips. Every composite layer is cooled by water flow in microchannels (height of 100 μm), which are arranged in two port water inlet-outlet configuration. The total power removed in the stack is 390 W at a temperature gradient budget of 60 K from liquid inlet to maximal junction temperature, corresponding to about 1.3 kW/cm 3 volumetric heat flow. The computational cost and complexity of detailed computational fluid dynamics (CFD) modeling of heat transfer in stacked chips with integrated cooling can be prohibitive. Therefore, the heat transfer structure is modeled using a porous medium approach, where the model parameters of heat transfer and hydrodynamic resistance are derived from averaging the results of the detailed 3D-CFD simulations of a single streamwise row of fins. The modeling results indicate that an isotropic porous medium model does not.accurately predict the measured temperature fields. The variation of material properties due to temperature gradients is found to be large; therefore, variable properties are used in the model. It is also shown that the modeling of the heat transfer in the cooling sublayers requires the implementation of a porous medium approach with a local thermal nonequilibrium, as well as orthotropic heat conduction and hydrodynamic resistance. The improved model reproduces the temperatures measured in the stack within 10%. The model is used to predict the behavior of multilayer stacks mimicking the change of heat fluxes resulting from variations in the computational load of the chips during their operation.

Experimental Investigation of Single-Phase Microjet Array Heat Transfer

Abstract: The heat transfer performance of two microjet arrays was investigated using degassed deionized water and air. The inline jet arrays had diameters of 54 μm and 112 μm, a spacing of 250 μm, a standoff of 200 μm (S/d=2.2 and 4.6, H/d=1.8 and 3.7), and jet-to-heater area ratios from 0.036 to 0.16. Average heat transfer coefficients with deionized water were obtained for 150≤Re d ≤3300 and ranged from 80,000 W/m 2 K to 414,000 W/m 2 K. A heat flux of 1110 W/cm 2 was attained with 23°C inlet water and an average surface temperature of 50°C. The Reynolds number range for the same arrays with air was 300≤Re d ≤4900 with average heat transfer coefficients of 2500 W/m 2 K to 15,000 W/m 2 K. The effect of the Mach number on the area-averaged Nusselt number was found to be negligible. The data were compared with available correlations for submerged jet array heat transfer.

On the Condition for Thermal Rectification Using Bulk Materials

Abstract: In conduction, thermal rectification occurs when a material or structure transfers heat asymmetrically. In this work, it is shown that, in the bulk, a necessary condition for thermal rectification is that the thermal conductivity of the material or structure be a function of both space and temperature, and that this function be nonseparable. Practically, this can be achieved using a composite structure consisting of many materials although it could also be achieved with a properly developed single material.