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### Research Papers: Conduction

J. Heat Transfer. 2018;140(5):051301-051301-11. doi:10.1115/1.4038554.

We present a method for solving the Boltzmann transport equation (BTE) for phonons by modifying the neutron transport code Rattlesnake which provides a numerically efficient method for solving the BTE in its self-adjoint angular flux (SAAF) form. Using this approach, we have computed the reduction in thermal conductivity of uranium dioxide (UO2) due to the presence of a nanoscale xenon bubble across a range of temperatures. For these simulations, the values of group velocity and phonon mean free path in the UO2 were determined from a combination of experimental heat conduction data and first principles calculations. The same properties for the Xe under the high pressure conditions in the nanoscale bubble were computed using classical molecular dynamics (MD). We compare our approach to the other modern phonon transport calculations, and discuss the benefits of this multiscale approach for thermal conductivity in nuclear fuels under irradiation.

Commentary by Dr. Valentin Fuster

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

J. Heat Transfer. 2018;140(5):051501-051501-10. doi:10.1115/1.4038520.

We analyze the condensation of a quiescent vapor, that is in equilibrium with its liquid, induced by a stagnation point flow in the liquid. The liquid flow brings subcooled liquid from far away to the interface. The ensuing heat transfer causes the vapor to condense. A similarity formulation for the liquid and vapor flow fields and the liquid temperature field is pursued, and a perturbation solution is performed when the ratio of the product of viscosity and density of the vapor to that of the liquid is small. A two-term higher order asymptotic solution is shown to be in excellent agreement with numerical results. The reduction in the rate of condensation due to the presence of a noncondensable gas in the vapor that is insoluble in the liquid is also analyzed.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2018;140(5):051502-051502-9. doi:10.1115/1.4038481.

Most of the existing empirical correlations for wall heat transfer during flow boiling show a limited predictability stemming mainly from so-called the suppression and enhancement factors, which are introduced to describe the boiling heat transfer hypothetically by a combination of nucleate pool boiling and single-phase forced convection. There is no physical basis strongly supporting the determination of these factors. This study, to avoid such limitations, presents a distinctive approach to the modeling of wall boiling heat transfer utilizing the physical concept of wall heat flux partitioning. A new correlation of local boiling heat transfer coefficient is composed of primary heat transfer mechanisms of transient conduction and forced convection. Heat transfer areas of these mechanisms replace the suppression and enhancement factors in the new correlation and are determined empirically by dimensionless analysis. Based on an experimental database of 3187 points collected for saturated boiling of various working fluids flowing inside channels of different configurations, the new correlation is obtained and compared with existing correlations widely used. The evaluation highlights much better predictability of the present correlation. While the other correlations show relatively large scattering with over 30% deviation from the experimental data, the newly proposed correlation shows an excellent agreement with a deviation of less than 10%. The good predictability would be from the well-structured physical basis and make the new correlation promising in practical boiling heat transfer analysis.

Commentary by Dr. Valentin Fuster

### Research Papers: Forced Convection

J. Heat Transfer. 2018;140(5):051701-051701-2. doi:10.1115/1.4038553.

The heat function concept introduced by Kimura and Bejan (1983, “The Heatline Visualization of Convective Heat Transfer,” ASME J. Heat Transfer, 105(4), pp. 916–919) for two-dimensional (2D) heat transfer is being extended in this note to three dimensions. It is shown that a heat flux vector potential exists and can be used in three-dimensional (3D) heat convection problems. It is further shown that this heat flux vector potential degenerates to the heat function introduced by Kimura and Bejan (1983, “The Heatline Visualization of Convective Heat Transfer,” ASME J. Heat Transfer, 105(4), pp. 916–919) when the heat convection is two-dimensional.

Topics: Convection , Heat flux , Heat
Commentary by Dr. Valentin Fuster

### Research Papers: Heat Exchangers

J. Heat Transfer. 2018;140(5):051801-051801-8. doi:10.1115/1.4038852.

Heat exchangers are important components in many engineering applications. This paper proposes a numerical two-phase heat exchanger model with simultaneous heat transfer and pressure drop calculations. The presented model provides a modeling framework compatible with numerous different correlations for both single- and two-phase flow of pure fluids and fluid mixtures. Furthermore, it considers nonconstant fluid properties as well as longitudinal heat conduction and parasitic heat loads, which is particularly relevant in mixed refrigerant cycles for cooling of low-temperature applications. The governing equations are derived and the solution strategy is presented, followed by the model validation against analytical solutions in the corresponding limits. Finally, an exemplary heat exchanger is analyzed using both homogeneous and separated flow models, and the results are compared with experimental data from literature.

Commentary by Dr. Valentin Fuster

### Research Papers: Heat and Mass Transfer

J. Heat Transfer. 2018;140(5):052001-052001-4. doi:10.1115/1.4038449.

A general expression has been obtained to estimate thermal conductivities of both stochastic and periodic structures with high-solid thermal conductivity. An air layer partially occupied by slanted circular rods of high-thermal conductivity was considered to derive the general expression. The thermal conductivity based on this general expression was compared against that obtained from detailed three-dimensional numerical calculations. A good agreement between two sets of results substantiates the validity of the general expression for evaluating the stagnant thermal conductivity of the periodic structures. Subsequently, this expression was averaged over a hemispherical solid angle to estimate the stagnant thermal conductivity for stochastic structures such as a metal foam. The resulting expression was found identical to the one obtained by Hsu et al., Krishnan et al., and Yang and Nakayama. Thus, the general expression can be used for both stochastic and periodic structures.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2018;140(5):052002-052002-14. doi:10.1115/1.4038479.

The present work establishes an improved experimentally validated analysis to predict performance and exergy-related parameters of a mechanical draft cooling tower involving wooden splash fills. Unlike earlier studies, which accounted for the effect of at most three tower inlet parameters for the exergy analysis, the present study simultaneously considers all five inlet parameters affecting the tower exergy performance. To simultaneously predict outlet air and water conditions, an optimization algorithm involving discrete functions of dry- and wet-bulb temperatures is used in conjunction with the mathematical model derived from mass and energy conservations within the control volume involving Bosnjakovic correlation. From practical point of view, five inlet parameters such as dry-bulb temperature, relative humidity, water temperature, water, and air flow rates are selected for the exergy analysis. Thereafter, the influence of all inlet parameters on the tower performance is analyzed on various important exergy-related factors. The quantitative analysis reveals that the inlet air humidity, water inlet temperature, and the inlet water mass flow rate significantly influence the air and water exergy changes. The present study also reveals that among the five inlet parameters, the water temperature, air humidity, and air mass flow rate are primarily responsible for the exergy destruction. Furthermore, it is observed that the second law efficiency is mainly governed by the inlet air flow rate. The present study is proposed to be useful for selecting the tower inlet parameters to improve exergy performance of mechanical cooling towers.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2018;140(5):052003-052003-11. doi:10.1115/1.4038540.

Electrowetting-induced microwater droplet detachment from hydrophobic surface has been studied numerically. The governing equations for transient microfluidic flow are solved by a finite volume scheme with a two-step projection method on a fixed computational domain. The free surface of the droplet is tracked by the volume-of-fluid method with the surface tension force determined by the continuum surface force (CSF) model. The static contact angle has been implemented using a wall-adhesion boundary condition at the solid–liquid interface, while the dynamic contact angle is computed assuming a fixed deflection from the static contact angle. The results of the numerical model have been validated with published experimental data and the physics of stretching, recoiling, and detachment of the droplet have been investigated. A parametric study has been performed in which the effects of droplet volume, voltage amplitude, and voltage pulse width have been examined.

Topics: Drops
Commentary by Dr. Valentin Fuster

### Research Papers: Jets, Wakes, and Impingment Cooling

J. Heat Transfer. 2018;140(5):052201-052201-8. doi:10.1115/1.4038547.

High power light emitting diodes (LEDs) being used for low and high beam in automotive lighting need active cooling of their heat sinks by radial or axial fans. But the moving elements of the fan cause abrasion, noise, and high energy consumption. Synthetic jets can replace conventional fans with their disadvantages and allow the directed cooling of LEDs. Therefore, in this paper, flow and heat transfer characteristics of impinging synthetic jets are investigated numerically and experimentally as an alternative to cooling LEDs with fans. It is shown that the impact plate brings forward the laminar-turbulent transition of the jets temporally and spatially. The impact plate itself should not be positioned in the region of the free jet's transition height. Increasing the frequency of the synthetic jet has a greater influence on the heat transfer compared to an increase in amplitude. The maximum cooling performance is achieved for all jet configurations with moderate distances between the orifice and the impact plate. In this case, the jet reaches its highest mass flow and impulse and its lowest temperature.

Commentary by Dr. Valentin Fuster

### Research Papers: Melting and Solidification

J. Heat Transfer. 2018;140(5):052301-052301-11. doi:10.1115/1.4038423.

Selective laser melting (SLM) is a widely used powder-based additive manufacturing process. However, it can be difficult to predict how process inputs affect the quality of parts produced. Computational modeling has been used to address some of these difficulties, but a challenge has been accurately capturing the behavior of the powder in a large, bed-scale model. In this work, a multiscale melting model is implemented to simulate the melting of powder particles for SLM. The approach employs a particle-scale model for powder melting to develop a melt fraction–temperature relationship for use in bed-scale simulations of SLM. Additionally, uncertainties from the particle-scale are propagated through the relationship to the bed scale, thus allowing particle-scale uncertainties to be included in the bed-scale uncertainty estimation. Relations, with uncertainty, are developed for the average melt fraction of the powder as a function of the average temperature of the powder. The utility of these melt fraction–temperature relations is established by using them to model phase change using a continuum bed-scale model of the SLM process. It is shown that the use of the developed relations captures partial melt behavior of the powder that a simple melting model cannot. Furthermore, the model accounts for both uncertainty in material properties and packing structure in the final melt fraction–temperature relationship, unlike simple melting models. The developed melt fraction–temperature relations may be used for bed-scale SLM simulations with uncertainty due to particle effects.

Commentary by Dr. Valentin Fuster

### Research Papers: Micro/Nanoscale Heat Transfer

J. Heat Transfer. 2018;140(5):052401-052401-7. doi:10.1115/1.4038359.

The basic theme of this investigation is to analyze heat and mass transport for three-dimensional (3D) stagnation-point flow of nanofluid caused by an exponentially stretched surface when water is treated as base fluid. In this study, we invoked the boundary layer phenomena and suitable similarity transformation of exponential character; as a result, our 3D nonlinear equations of momentum and energy are transmuted into nonlinear and nonhomogeneous differential equations involving ordinary derivatives. Final equations are then puzzled out by applying homotopy analysis technique. Interesting outcomes of aggressing parameters involved in this study, and effecting profiles of temperature field and velocity are explained in detail. Graphical results of involved parameters appearing in considered nanofluid are presented separately. Different aspects of skin friction coefficient as well as Nusselt number are calculated. It is worth mentioning that skin friction (as we go) along x and y-direction is maximal for Cu-water nanofluid and minimal for $AL2O3-$water nanofluid. Also, the resulting quantity of local Nusselt number came out maximum for Cu-water nanofluid whereas minimum for $TiO2-$water nanofluid.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2018;140(5):052402-052402-11. doi:10.1115/1.4038451.

We focus on the entropy generation minimization for the flow of a viscoelastic fluid through a parallel plate microchannel under the combined influences of applied pressure gradient, interfacial slip, and conjugate heat transfer. We use the simplified Phan–Thien–Tanner model (s-PTT) to represent the rheological behavior of the viscoelastic fluid. Using thermal boundary conditions of the third kind, we solve the transport equations analytically to obtain the velocity and temperature distributions in the flow field, which are further used to calculate the entropy generation rate in the analysis. In this study, the influential role of the following dimensionless parameters on entropy generation rate is examined: the viscoelastic parameter $(εDe2)$, slip coefficient $(k¯)$, channel wall thickness $(δ)$, thermal conductivity of the wall $(γ)$, Biot number $(Bi)$ and Peclet number $(Pe)$. We show that there exists a particular value of the abovementioned parameters that lead to a minimum entropy generation rate in the system. We believe the results of this analysis could be of helpful in the optimum design of microfluidic system/devices typically used in thermal management, such as micro-electronic devices, microreactors, and microheat exchangers.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2018;140(5):052403-052403-9. doi:10.1115/1.4038559.

This work presents the development and analysis of constructal microchannel network architectures for heat dissipation. The network configurations are characterized by multiple flow ramifications and changes in length and hydraulic diameter scales through each ramification level. Architectures investigated experimentally in the past years have adopted constant scaling rules throughout their ramification levels. In this study, constructal theory inspires the design of network architectures with variable scaling rules and up to three ramification levels (N). As a result, it was verified that constructal networks allowed thermal resistance reduction of 15% (N = 2) and 42% (N = 3) for a micro heat sink at a characteristic operational regime. Architecture's selection criterion using performance curves is proposed and it was also demonstrated that the bifurcated network with diameter ratio according to Hess–Murray law is not appropriate for heat dissipation purposes in miniaturized devices.

Commentary by Dr. Valentin Fuster

### Research Papers: Natural and Mixed Convection

J. Heat Transfer. 2018;140(5):052501-052501-12. doi:10.1115/1.4038478.

Natural convection heat transfer from a vertical hollow cylinder suspended in air has been analyzed numerically by varying the Rayleigh number (Ra) in the laminar (104 ≤ Ra ≤ 108) regime. The simulations have been carried out by changing the ratio of length to pipe diameter (L/D) in the range of 0.05 $≤$ L/D$≤20$. Full conservation equations have been solved numerically for a vertical hollow cylinder suspended in air using algebraic multigrid solver of fluent 13.0. The flow and the temperature field around the vertical hollow cylinder have been observed through velocity vectors and temperature contours for small and large L/D. It has been found that the average Nusselt number (Nu) for vertical hollow cylinder suspended in air increases with the increase in Rayleigh number (Ra) and the Nu for both the inner and the outer surface also increases with Ra. However, with the increase in L/D, average Nu for the outer surface increases almost linearly, whereas the average Nu for the inner surface decreases and attains asymptotic value at higher L/D for low Ra. In this study, the effect of parameters like L/D and Ra on Nu is analyzed, and a correlation for average Nusselt number has been developed for the laminar regime. These correlations are accurate to the level of $±6%.$

Commentary by Dr. Valentin Fuster

### Research Papers: Porous Media

J. Heat Transfer. 2018;140(5):052601-052601-8. doi:10.1115/1.4038555.

We present lattice Boltzmann (LB) simulations for the mass transfer coefficient from bulk flows to pore surfaces in chemically reactive flows for both ordered and disordered porous structures. The ordered porous structure under consideration consists of cylinders in a staggered arrangement and in a line arrangement, while the disordered one is composed of randomly placed cylinders. Results show that the ordered porous structure of staggered cylinders exhibits a larger mass transfer coefficient than ordered porous structure of inline cylinders does. It is also found that in the disordered porous structures, the Sherwood number (Sh) increases linearly with Reynolds number (Re) at the creeping flow regime; the Sh and Re exhibit a one-half power law dependence at the inertial flow regime. Meanwhile, for Schmidt number (Sc) between 1 and 10, the Sh is proportional to Sc0.8; for Sc between 10 and 100, the Sh is proportional to Sc0.3.

Commentary by Dr. Valentin Fuster

### Research Papers: Radiative Heat Transfer

J. Heat Transfer. 2018;140(5):052701-052701-10. doi:10.1115/1.4038548.

This paper presents a methodology for the application of the weighted-sum-of-gray-gases (WSGG) model to systems where the medium is bounded by nongray surfaces. The method relies on the assumption that each gray gas absorption coefficient is randomly spread across the entire wavenumber spectrum. It follows that, in the spectral integration of the radiative transfer equation (RTE), the local emission term can be computed by the joint probability of emission from the subsections of the spectrum related to each gray gas coefficient and from each wall emissivity band. One advantage of the proposed methodology is that it allows the use without any modification of WSGG correlations that are available in the literature. The study presents a few test cases considering a one-dimensional (1D), nonuniform medium slab composed of H2O and CO2, bounded by nongray surfaces. The accuracy of the methodology is assessed by direct comparison with line-by-line (LBL) calculations.

Commentary by Dr. Valentin Fuster

### Research Papers: Thermal Systems

J. Heat Transfer. 2018;140(5):052801-052801-10. doi:10.1115/1.4038713.

In this study, we calculate the steady-state temperature rise that results from laser heating of multilayer thin films using the heat diffusion equation. For time- and frequency-domain thermoreflectance (TDTR and FDTR) that rely on modulated laser sources, we decouple the modulated and steady-state temperature profiles to understand the conditions needed to achieve a single temperature approximation throughout the experimental volume, allowing for the estimation of spatially invariant thermal parameters within this volume. We consider low thermal conductivity materials, including amorphous silicon dioxide (a-SiO2), polymers, and disordered C60, to demonstrate that often-used analytical expressions fail to capture this temperature rise under realistic experimental conditions, such as when a thin-film metal transducer is used or when pump and probe spot sizes are significantly different. To validate these findings and demonstrate a practical approach to simultaneously calculate the steady-state temperature and extract thermal parameters in TDTR, we present an iterative algorithm for obtaining the steady-state temperature rise and measure the thermal conductivity and thermal boundary conductance of a-SiO2 with a 65-nm gold thin film transducer. Furthermore, we discuss methods of heat dissipation to include the use of conductive substrates as well as the use of bidirectional heat flow geometries. Finally, we quantify the influence of the optical penetration depth (OPD) on the steady-state temperature rise to reveal that only when the OPD approaches the characteristic length of the temperature decay does it alter the temperature profile relative to the surface heating condition.

Commentary by Dr. Valentin Fuster

### Technical Brief

J. Heat Transfer. 2018;140(5):054501-054501-7. doi:10.1115/1.4038477.

Nonequilibrium molecular dynamics (MD) simulations have been performed to understand the evaporation of a liquid droplet in the presence of a solid nanoparticle. The influence of solid–liquid interaction strength (εsl) on the evaporation properties was addressed. The system consists of a solid nanoparticle (platinum) engulfed in a droplet (argon) in Argon vapor environment. After the equilibration of this nanoparticle embedded droplet with its vapor, the boundary of this system is heated continuously to evaporate the droplet. It is observed that the addition of a nanoparticle to the droplet resulted in a slower evaporation rate when compared to that of a pure droplet. It was found that the evaporation rate of the droplet is decreased with increasing solid–liquid interaction strength (εsl) and those liquid atoms around the solid nanoparticle with higher εsl are able to delay evaporation even at higher temperature owing to its decreased interfacial resistance. In order to analyze further on the vibrational coupling of the solid and liquid atoms, the vibrational density of states (VDOS) of the solid atoms is studied. It is observed that the DOS of the solid atoms exhibited a higher population in the lower frequency range with the highest peak observed for a lower value of εsl. For low values of εsl, we observe a decrease in the overlap between the VDOS of the solid atom and the interfacial liquid atoms. It is observed that for higher values of εsl, the particle is able to retain a structured layer of liquid even at high temperature and also a higher heat input is necessitated to break the interaction strength of the liquid molecules around the solid nanoparticle, which makes it possible in delaying the complete evaporation of the droplet.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2018;140(5):054502-054502-4. doi:10.1115/1.4038425.

This paper presents a novel adaptive thermal management technique to improve the efficiency of solid-state power amplifier (SSPA) for geo-synchronous satellites. The thermal management for space segment is very important as it determines the reliability of the satellite. The microwave power amplifiers (MPAs), either traveling wave tube amplifiers (TWTAs) or SSPAs, are the maximum power consuming and heat dissipative elements in the satellite and their power efficiency determines weight, volume, cost, and reliability of the satellite. So, it is necessary to improve the efficiency of the SSPA. A novel technique is presented, which improves the efficiency of the SSPA and hence, saving of costly DC power generation on-board and reduction of the heat dissipation.

Commentary by Dr. Valentin Fuster
J. Heat Transfer. 2018;140(5):054503-054503-5. doi:10.1115/1.4038480.

A phase change heat transfer from liquid to gas is studied in nanoscopic framework using molecular dynamics. Water on structured Si substrate is observed from molecular viewpoint after employing heat flux at a constant rate. Initially, we observe that water settles down on the substrate occupying the free space within the notch to obtain its static shape maintaining intramolecular configuration based on attractive and repulsive forces in neighboring hydroxyl bonds. Upon applying heat flux, we observe that the molecular vibration increases which repels neighbors to make the packing loose. Molecular dilution initiated at the notch and then proceeds to the rest domain. Progressive loosening of the molecules leads to the formation of vapor bubbles which increase in size with time. The rate of growth of this bubble is studied as a function of surface geometry parameters such as notch height, notch width, notch type, and notch spacing. Present simulations enrich the knowledge of surface characteristics on boiling heat transfer from fundamental principle in the molecular domain.

Commentary by Dr. Valentin Fuster

### Discussion

J. Heat Transfer. 2018;140(5):055501-055501-2. doi:10.1115/1.4038832.

This discussion concerns some doubtful results included in this paper.

Commentary by Dr. Valentin Fuster