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### PHOTOGALLERY

J. Heat Transfer. 2011;133(8):080901-080901-1. doi:10.1115/1.4003888.
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The Fifteenth Heat Transfer Photogallery was sponsored by the K-22 Heat Transfer Visualization Committee for the 2010 International Mechanical Engineering Congress and Exhibition (IMECE) held in Vancouver, British Columbia in Canada, on November 12–18, 2010. The peer-reviewed evaluation for all of the presented entries identified the 10 entries for publication in the ASME Journal of Heat Transfer August issue of 2011.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2011;133(8):080902-080902-1. doi:10.1115/1.4003889.
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Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2011;133(8):080903-080903-1. doi:10.1115/1.4003890.
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Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2011;133(8):080904-080904-1. doi:10.1115/1.4003891.
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Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2011;133(8):080905-080905-1. doi:10.1115/1.4003892.
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Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2011;133(8):080906-080906-1. doi:10.1115/1.4003893.
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Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2011;133(8):080907-080907-1. doi:10.1115/1.4003894.
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Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2011;133(8):080908-080908-1. doi:10.1115/1.4003895.
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Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2011;133(8):080909-080909-1. doi:10.1115/1.4003896.
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Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2011;133(8):080910-080910-1. doi:10.1115/1.4003897.
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Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2011;133(8):080911-080911-1. doi:10.1115/1.4003898.
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Commentary by Dr. Valentin Fuster

### Research Papers: Electronic Cooling

J. Heat Transfer. 2011;133(8):081401-081401-10. doi:10.1115/1.4003709.

A novel, integrated approach in thermal management of electronic products, based on two-phase cooling, is presented. A flat miniature heat pipe, integrated inside the laminated structure of a printed circuit board (PCB), has been developed, based on mainstream PCB multilayer technology. To accurately predict the thermal performance of this two-phase heat transport device and to establish the operational limitations, a numerical model based on control volume elements is discussed. The advantage of this modular approach, compared with, e.g., finite element models, is that the model can be expanded with additional components (e.g., multiple evaporators) very easily. Actual PCBs with several hot spots cooled by flat miniature heat pipes and their parameter effects can be analyzed very quickly, without the necessity of complex and time-consuming finite element analyses. Experimental verification has shown a good comparison with model predictions. Time evolution analyses show that the developed control volume model is well capable of describing the heat pipe transient behavior.

Topics: Heat pipes , Heat , Vapors
Commentary by Dr. Valentin Fuster

### Research Papers: Evaporation, Boiling, and Condensation

J. Heat Transfer. 2011;133(8):081501-081501-10. doi:10.1115/1.4003669.

In this paper, the experimental flow boiling heat transfer results of a minichannel are presented. A series of experiments was conducted to measure the heat transfer coefficients in a minichannel made of stainless steel (AISI 316) having an internal diameter of 1.70 mm and a uniformly heated length of 220 mm. R134a was used as a working fluid, and experiments were performed at two different system pressures corresponding to saturation temperatures of $27°C$ and $32°C$. Mass flux was varied from $50 kg/m2 s$ to $600 kg/m2 s$, and heat flux ranged from $2 kW/m2$ to $156 kW/m2$. The test section was heated directly using a dc power supply. The direct heating of the channel ensured uniform heating, which was continued until dryout was reached. The experimental results show that the heat transfer coefficient increases with imposed wall heat flux, while mass flux and vapor quality have no considerable effect. Increasing the system pressure slightly enhances the heat transfer coefficient. The heat transfer coefficient is reduced as dryout is reached. It is observed that the dryout phenomenon is accompanied with fluctuations and a larger standard deviation in outer wall temperatures.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2011;133(8):081502-081502-8. doi:10.1115/1.4003742.

A mathematical model is developed to represent and predict the dropwise condensation phenomenon on nonwetting surfaces having hydrophobic or superhydrophobic (contact angle greater than 150 deg) features. The model is established by synthesizing the heat transfer through a single droplet with the drop size distribution. The single droplet heat transfer is analyzed as a combination of the vapor-liquid interfacial resistance, the resistance due to the conduction through the drop itself, the resistance from the coating layer, and the resistance due to the curvature of the drop. A population balance model is adapted to develop a drop distribution function for the small drops that grow by direct condensation. Drop size distribution for large drops that grow mainly by coalescence is obtained from a well-known empirical equation. The evidence obtained suggests that both the single droplet heat transfer and drop distribution are significantly affected by the contact angle. More specifically, the model results indicate that a high drop-contact angle leads to enhancing condensation heat transfer. Intense hydrophobicity, which produces high contact angles, causes a reduction in the size of drops on the verge of falling due to gravity, thus allowing space for more small drops. The simulation results are compared with experimental data, which were previously reported.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2011;133(8):081503-081503-8. doi:10.1115/1.4003748.

Presented are the results of experiments that investigated nucleate boiling of PF-5060 on microporous Cu surface layers at saturation and 10 K, 20 K, and 30 K subcooling. The three microporous layers, electrochemically deposited on $10×10 mm2$ Cu substrates and investigated herein, are $∼139 μm$, $171 μm$, and $220 μm$ thick. The critical heat flux increases linearly with increased subcooling, $ΔTsub$, at an average rate of 4.5%/K. For the $171 μm$ thick, Cu microporous surface, saturation boiling CHF of $27.8 W/cm2$ increases to $63.25 W/cm2$ at $ΔTsub=30 K$, while the saturation $hMNB$ of $13.5 W/cm2 K$ decreases slightly to $12.7 W/cm2 K$ at $ΔTsub=30 K$. The values of the surface superheat, $ΔTsat$, at $hMNB$ and CHF increase from 2.0 K and 2.16 K at saturation to 4.2 and 6.42 K at 30 K subcooling.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2011;133(8):081504-081504-9. doi:10.1115/1.4003759.

This article deals with the numerical modeling of the pulsating heat pipe (PHP) and is based on the film evaporation/condensation model recently applied to the single-bubble PHP (Das, 2010, “Thermally Induced Two-Phase Oscillating Flow Inside a Capillary Tube,” Int. J. Heat Mass Transfer, 53(19–20), pp. 3905–3913). The described numerical code can treat the PHP of an arbitrary number of bubbles and branches. Several phenomena that occur inside the PHP are taken into account: coalescence of liquid plugs, film junction or rupture, etc. The model reproduces some of the experimentally observed regimes of functioning of the PHP such as chaotic or intermittent oscillations of large amplitudes. Some results on the PHP heat transfer are discussed.

Commentary by Dr. Valentin Fuster

### Research Papers: Experimental Techniques

J. Heat Transfer. 2011;133(8):081601-081601-7. doi:10.1115/1.4003545.

Fiber aligned frequency domain thermoreflectance (FAFDTR) is a simple noncontact optical technique for accurately measuring the thermal conductivity of thin films and bulk samples for a wide range of materials, including electrically conducting samples. FAFDTR is a single-sided measurement that requires minimal sample preparation and no microfabrication. Like existing thermoreflectance techniques, a modulated pump laser heats the sample surface, and a probe laser monitors the resultant thermal wave via the temperature dependent reflectance of the surface. Via the use of inexpensive fiber coupled diode lasers and common mode rejection, FAFDTR addresses three challenges of existing optical methods: complexity in setup, uncertainty in pump-probe alignment, and noise in the probe laser. FAFDTR was validated for thermal conductivities spanning three orders of magnitude $(0.1–100 W/m K)$, and thin film thermal conductances greater than $10 W/m2 K$. Uncertainties of 10–15% were typical, and were dominated by uncertainties in the laser spot size. A parametric study of sensitivity for thin film samples shows that high thermal conductivity contrast between film and substrate is essential for making accurate measurements.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2011;133(8):081602-081602-6. doi:10.1115/1.4003743.

This study provides a new inverse approach based on fuzzy inference for solving the problem of estimating heat flux distribution at the metal-mold interface in the continuous casting process. Measured temperatures acquired with the thermocouples buried in the mold are used to obtain corresponding inference results with the fuzzy inference. Then according to the importance of measured information for estimating the heat flux distribution, inference results are weighted to realize estimation of heat flux distribution at the metal-mold interface. Some numerical tests are presented to discuss the validity of the present approach by using different initial guesses of heat flux distribution, the number of measuring points, and measurement errors. In comparison with the conjugate gradient method, it is concluded that the method based on fuzzy inference is of a good anti-ill-posed characteristic.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2011;133(8):081603-081603-9. doi:10.1115/1.4003757.

The present study explains a steady-state method of measuring convective heat transfer coefficient on the casing of an axial flow turbine. The goal is to develop an accurate steady-state heat transfer method for the comparison of various casing surface and tip designs used for turbine performance improvements. The freestream reference temperature, especially in the tip gap region of the casing, varies monotonically from the rotor inlet to rotor exit due to work extraction in the stage. In a heat transfer problem of this nature, the definition of the freestream temperature is not as straightforward as constant freestream temperature type problems. The accurate determination of the convective heat transfer coefficient depends on the magnitude of the local freestream reference temperature varying in axial direction, from the rotor inlet to exit. The current study explains a strategy for the simultaneous determination of the steady-state heat transfer coefficient and freestream reference temperature on the smooth casing of a single stage rotating turbine facility. The heat transfer approach is also applicable to casing surfaces that have surface treatments for tip leakage control. The overall uncertainty of the method developed is between 5% and 8% of the convective heat transfer coefficient.

Commentary by Dr. Valentin Fuster

### Research Papers: Forced Convection

J. Heat Transfer. 2011;133(8):081701-081701-8. doi:10.1115/1.4003571.

A numerical method is developed with the capability to predict transient thermal boundary layer response under various flow and thermal conditions. The transient thermal boundary layer variation due to a moving compressible turbulent fluid of varying temperature was numerically studied on a two-dimensional semi-infinite flat plate. The compressible Reynolds-averaged boundary layer equations are transformed into incompressible form through the Dorodnitsyn–Howarth transformation and then solved with similarity transformations. Turbulence is modeled using a two-layer eddy viscosity model developed by Cebeci and Smith, and the turbulent Prandtl number formulation originally developed by Kays and Crawford. The governing differential equations are discretized with the Keller-box method. The numerical accuracy is validated through grid-independence studies and comparison with the steady state solution. In turbulent flow as in laminar, the transient heat transfer rates are very different from that obtained from quasi-steady analysis. It is found that the time scale for response of the turbulent boundary layer to far-field temperature changes is 40% less than for laminar flow, and the turbulent local Nusselt number is approximately 4 times that of laminar flow at the final steady state.

Commentary by Dr. Valentin Fuster

### Research Papers: Heat Exchangers

J. Heat Transfer. 2011;133(8):081801-081801-9. doi:10.1115/1.4003553.

This paper analyzes the thermal and hydraulic performance of a counterflow microchannel heat exchanger (CFMCHE) with and without nanofluid as working fluid. A 3D conjugate heat transfer simulation is carried out using a finite volume approach to evaluate the effects of inlet Reynolds number, Brownian motion, and volume fraction of nanoparticles on the pumping power, effectiveness, and performance index of CFMCHE. The accuracy of the code has been verified by comparing the results with those available in the literature. A single phase approach is used for the nanofluid modeling. The base fluid used in the analyses as a basis for comparison was pure water. Two types of nanofluids, namely, water-$Al2O3$ with a mean diameter of 47 nm and water-CuO with a mean diameter of 29 nm, each one with three different volume fractions, are utilized. In addition, two temperature dependent models for the thermal conductivity and viscosity of nanofluids that account for the fundamental role of Brownian motion are used. Calculated results demonstrate that the effectiveness and performance index of CFMCHE decrease with increasing Reynolds number. Moreover, it is observed that the relative enhancements in the pumping power become more prominent for higher values of Reynolds numbers. It was also found that the performance index and pumping power are not sensitive to volume fraction at higher and lower Reynolds numbers, respectively.

Commentary by Dr. Valentin Fuster

### Research Papers: Heat Transfer Enhancement

J. Heat Transfer. 2011;133(8):081901-081901-10. doi:10.1115/1.4003668.

Heat transfer enhancement using corrugated ribbed passages is one of the common enhancement techniques inside heat exchangers. The present study investigated numerically the effect of the corrugation rib angle of attack on the fluid flow and heat transfer characteristics inside the corrugated ribbed passage. The commercial computational fluid dynamics code PHOENICS 2006 was used to perform the numerical analysis by solving the Navier–Stokes and energy equations. The experimental part of this study was used only to validate the numerical model, and a good agreement between the experimental results and the model was obtained. The flow field characteristics and heat transfer enhancement were numerically investigated for different corrugated rib angles of attack as follows: 90 deg, 105 deg, 120 deg, 135 deg, and 150 deg. The corrugation rib angle of attack has a great effect on the reversed flow zone, the flow reattachments, and the enhancement of the heat transfer coefficient through the duct. The recommended rib angle of attack, which gives the optimum thermohydraulic performance, is found to be between 135 deg and 150 deg. The value of the maximum thermohydraulic performance is about 3.6 for the 150 deg rib angle of attack at a Reynolds number equal to 10,000.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2011;133(8):081902-081902-7. doi:10.1115/1.4003710.

Constructal design is a method that conducts the designer toward flow (e.g., heat flux) architectures that have greater global performance. This numerical work uses this method to seek for the best geometry of a complex assembly of fins, i.e., an assembly where there is a cavity between the two branches of the T-Y-assembly of fins and two additional extended surfaces. The global thermal resistance of the assembly is minimized four times by geometric optimization subject to the following constraints: the total volume, the volume of fin material, the volume of the cavity, and the volume of the two additional extended surfaces. Larger amount of fin material improves the performance of the assembly of fins. The three times optimized global thermal resistance of the complex assembly of fins performs 32% better than the best T-Y-configuration under the same thermal and geometric conditions. The three times minimized global thermal resistance of the complex assembly of fins was correlated by power laws as a function of its corresponding optimal configurations.

Commentary by Dr. Valentin Fuster

### Research Papers: Micro/Nanoscale Heat Transfer

J. Heat Transfer. 2011;133(8):082401-082401-6. doi:10.1115/1.4003533.

Two mechanisms that enhance heat dissipation at solid-liquid interfaces are investigated from the atomistic point of view using nonequilibrium molecular dynamics simulation. The mechanisms include surface functionalization, where –OH terminated headgroups and self-assembled monolayers (SAMs) with different chain lengths are used to recondition and modify the hydrophilicity of silica surface, and vibrational matching between crystalline silica and liquid water, where three-dimensional nanopillars are grown at the interface in the direction of the heat flux with different lengths to rectify the vibrational frequencies of surface atoms. The heat dissipation is measured in terms of the thermal conductance of the solid-liquid interface and is obtained by imposing a one-dimensional heat flux along the simulation domain. A comparison with reported numerical and experimental thermal conductance measurements for similar interfaces indicates that the thermal conductance is enhanced by 1.8–3.2 times when the silica surface is reconditioned with hydrophilic groups. The enhancement is further promoted by SAMs, which results in a 20% higher thermal conductance compared with that of the fully hydroxylated silica surface. Likewise, the presence of nanopillars enhances the interface thermal conductance by 2.6 times compared with a bare surface (without nanopillars). Moreover, for different nanopillar densities, the conductance increases linearly with the length of the pillar and saturates at around 4.26 nm. Changes in the vibrational spectrum of surface atoms and water confinement effects are found to be responsible for the increase in conductance. The modification of surface vibrational states provides a tunable path to enhance heat dissipation, which can also be easily applied to other fluids and interfaces.

Commentary by Dr. Valentin Fuster

### Research Papers: Natural and Mixed Convection

J. Heat Transfer. 2011;133(8):082501-082501-6. doi:10.1115/1.4003749.

An experimental study is undertaken to investigate the flow structure and heat transfer in a stagnation flow chemical vapor deposition (CVD) reactor at atmospheric pressure. It is critical to develop models that predict flow patterns in such a reactor to achieve uniform deposition across the substrate. Free convection can negatively affect the gas flow as cold inlet gas impinges on the heated substrate, leading to vortices and disturbances in the normal flow path. This experimental research will be used to understand the buoyancy-induced and momentum driven flow structure encountered in an impinging jet CVD reactor. Investigations are conducted for various operating and design parameters. A modified stagnation flow reactor is built where the height between the inlet and substrate is reduced when compared with a prototypical stagnation flow reactor. By operating such a reactor at certain Reynolds and Grashof numbers, it is feasible to sustain smooth and vortex free flow at atmospheric pressure. The modified stagnation flow reactor is compared with other stagnation flow geometries with either a varied inlet length or varied heights between the inlet and substrate. Comparisons are made to understand the impact of such geometric changes on the flow structure and the thermal boundary layer. In addition, heat transfer correlations are obtained for the substrate temperature. Overall, the results obtained provide guidelines for curbing the effects of buoyancy and for improving the flow field to obtain greater film uniformity when operating a stagnation flow CVD reactor at atmospheric pressure.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2011;133(8):082502-082502-9. doi:10.1115/1.4003758.

Particle image velocimetry and thermal measurements using thermocouples are used to measure the buoyant flow of a simplified full-scale model of an engine compartment. The engine block surface temperature and exhaust heaters are kept at about 100 and $600°C$, respectively. Thermal measurements include enclosure surface temperature, temperature difference on the enclosure wall at midplane, engine block temperatures, and air temperatures under the hood. The highest surface temperatures were concentrated near the top of the enclosure around the exhaust heaters. This effect was due primarily to radiation from the exhaust heaters. Highest measured air temperature was about $300°C$ immediately above the right exhaust heater. The measured dominant flow structures are two larger counter rotating vortices over the top right side of the engine block and two counter rotating vortices over the top left side. These flow structures weaken considerably during the first 35 min of the transient cool down of the engine block and the exhaust heaters. Colder ambient air is sucked into the engine compartment at the vents near the bottom of the compartment with some exiting as hot air through the top slots. The time scale of the fluid exchange at the vents is in the order of seconds, indicating that this process is occurring very slowly.

Commentary by Dr. Valentin Fuster

### Research Papers: Radiative Heat Transfer

J. Heat Transfer. 2011;133(8):082701-082701-7. doi:10.1115/1.4003724.

Direct numerical solution of the radiation transfer equation is often easier than implementation of its differential approximations with their cumbersome boundary conditions. Nevertheless, these approximations are still used, for example, in theoretical analysis. The existing approach to obtain a differential approximation based on expansion in series of the spherical harmonics is revised and expansion in series of the eigenfunctions of the scattering integral is proposed. A system of eigenfunctions is obtained for an arbitrary phase function, and explicit differential approximations are built up to the third Chapman–Enskog order. The results are tested by its application to the problem of a layer. The third-order Chapman–Enskog approximation is found to match the boundary conditions better than the first-order one and gives considerably more accurate value for the heat flow. The accuracy of the both first- and third-order heat flows generally increases with the optical thickness. In addition, the third-order heat flow tends to the rigorous limit value when the optical thickness tends to zero.

Commentary by Dr. Valentin Fuster

### Research Papers: Thermal Systems

J. Heat Transfer. 2011;133(8):082801-082801-12. doi:10.1115/1.4003747.

This study presents the development of an analytical model to predict steady-state heat transfer in double U-tube geothermal boreholes equipped with two independent circuits. Such boreholes can be used for heat extraction in one circuit, combined with a heat pump, for example, and simultaneous thermal recharging in the other circuit. The model accounts for a thermal interaction among pipes, and it predicts the fluid temperature profiles in both circuits along the borehole depth, including the exit fluid temperature. Different circuit configurations are assessed under typical borehole operating conditions. For a typical borehole geometry, results show that double U-tube boreholes with two independent circuits connected to a relatively low temperature heat source are superior to single U-tube and regular (one circuit) double U-tube boreholes. The axial variation in fluid temperature and the heat exchange among pipes show that most of the heat transfer occurs in the downward legs. Furthermore, in some cases, the fluid in the heat extraction leg gets cooled as it flows upward, which is contrary to the desired effect.

Commentary by Dr. Valentin Fuster

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