A temperature-dependent approach involving Green-Kubo equilibrium atomic and spin dynamics (GKEASD) is reported to assess phonon and magnon thermal transport processes accounting for phonon-magnon interactions. Using body-centered cubic (BCC) iron as a case study, GKEASD successfully reproduces its characteristic temperature-dependent spin and lattice thermal conductivities. The nonelectronic thermal conductivity, i.e., the sum of phonon and magnon thermal conductivities, calculated using GKEASD for BCC Fe, agrees well with experimental measurements. Spectral energy analysis reveals that high-frequency phonon-magnon scattering rates are one order of magnitude larger than those at low frequencies due to energy scattering conservation rules and high densities of states. Higher temperatures further accentuate this phenomenon. This new framework fills existing gaps in simulating thermal transport across the ferro- to paramagnetic transition. Future application of this methodology to phonon- and magnon-dominant insulators and semiconductors will enhance understanding of emerging thermoelectric, spin caloritronic, and superconducting materials.

Received 26 September 2017DOI:https://doi.org/10.1103/PhysRevB.96.199903©2017 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasThermal conductivityPhysical Systems2-dimensional systemsCarbon-based materialsGrapheneTechniquesRaman spectroscopyCondensed Matter, Materials & Applied Physics

The measured frequencies and intensities of different first- and second-order Raman peaks of suspended graphene are used to show that optical phonons and different acoustic phonon polarizations are driven out of local equilibrium inside a submicron laser spot. The experimental results are correlated with a first-principles-based multiple temperature model to suggest a considerably lower equivalent local temperature of the flexural phonons than those of other phonon polarizations. The finding reveals weak coupling between the flexural modes with hot electrons and optical phonons. Since the ultrahigh intrinsic thermal conductivity of graphene has been largely attributed to contributions from the flexural phonons, the observed local nonequilibrium phenomena have important implications for understanding energy dissipation processes in graphene-based electronic and optoelectronic devices, as well as in Raman measurements of thermal transport in graphene and other two-dimensional materials.

A triple-scan scanning thermal microscopy (SThM) method and a zero-heat flux laser-heated SThM technique are investigated for quantitative thermal imaging of flexible graphene devices. A similar local tip-sample thermal resistance is observed on both the graphene and metal areas of the sample, and is attributed to the presence of a polymer residue layer on the sample surface and a liquid meniscus at the tip-sample junction. In addition, it is found that the tip-sample thermal resistance is insensitive to the temperature until it begins to increase as the temperature increases to 80 °C and exhibits an abrupt increase at 110 °C because of evaporation of the liquid meniscus at the tip-sample junction. Moreover, the variation in the tip-sample thermal resistance due to surface roughness is within the experimental tolerance except at areas with roughness height exceeding tens of nanometers. Because of the low thermal conductivity of the flexible polyimide substrate, the SThM measurements have found that the temperature rise in flexible graphene devices is more than one order of magnitude higher than those reported for graphene devices fabricated on a silicon substrate with comparable dimensions and power density. Unlike a graphene device on a silicon substrate where the majority of the electrical heating in the graphene device is conducted vertically through the thin silicon dioxide dielectric layer to the high-thermal conductivity silicon substrate, lateral heat spreading is important in the flexible graphene devices, as shown by the observed decrease in the average temperature rise normalized by the power density with decreasing graphene channel length from about 30 μm to 10 μm. However, it is shown by numerical heat transfer analysis that this trend is mainly caused by the size scaling of the thermal spreading resistance of the polymer substrate instead of lateral heat spreading by the graphene. In addition, thermoelectric effects are found to be negligible compared to Joule heating in the flexible graphene devices measured in this work.

Thermal energy is composed, by definition, of randomized carriers and is often an unwanted byproduct of human-engineered functions such as propulsion, communications, and directed forms of other types of energy. This inherent randomness greatly impedes the "orderly" management and control of heat, particularly when compared to electrical energy (e.g., power distribution lines) and optical energy (e.g., fiber optics). The thermal conductivities of common solids, for example, span only a few orders of magnitude, whereas electrical conductivities vary by 10 or more orders. Further, chemical and electrical energy can be stored and released with relative ease, whereas thermal storage materials and systems are typically bulky and inefficient. Motivated by critical aerospace needs to develop transformative thermal management strategies, particularly for high-flux, episodic heat loads within the tightly weight- and volume-constrained environment of aerospace vehicles, this paper provides an overview of prospective strategies and technologies that can address these challenges by exploiting the transient nature of the required cooling while also providing insights into the commensurate uncertainty quantification and control methods that will be essential to their eventual transition to practical applications.

Selective laser sintering (SLS) is an additive manufacturing technique for rapidly creating parts directly from a computer-aided design (CAD) model by using a laser to fuse successive layers of powder. However, better understanding of the effect of particle-level variations on the overall build quality is needed. In this work, we investigated these effects computationally by considering the role of the particle size distribution and variations in the powder bed depth to mimic the part complexity found in overhangs and protrusions. In addition, the results from these studies can be distilled to obtain better effective material properties such as laser absorptivity and laser extinction coefficient that are needed for continuum models of the process. We implement a Monte Carlo ray-tracing algorithm within the discrete element model in the open-source simulation software MFiX. Random, loose-packed, particle bed structures are generated, and effective absorptivity and extinction coefficients are calculated. Results are compared against previous computational and experimental measurements for free, monodisperse, and deep powder beds, with good agreement being obtained. Correlations along with uncertainties are developed to allow the effective absorptivity and extinction coefficient as a function of various particle and operational parameters to be accurately set in SLS macroscale models.

Selective laser sintering (SLS) is an additive manufacturing technique able to rapidly create parts directly from a CAD model using a laser to selectively fuse successive layers of powder. However, defects can arise in SLS parts due to incomplete fusion of the powder layers or thermal stresses introduced by large temperature gradients during the part build. Accurate models of the SLS process are needed to ensure that high quality parts are produced and to allow new materials and designs to be used without requiring extensive experimentation. Most existing models of the SLS process are very narrowly focused, predicting the temperature history of a single powder layer after a single laser pass or examining the impact of a few processing parameters on the properties of the produced part. A model capable of predicting a complete temperature history during an entire part build does not yet exist. Therefore, a new thermal model able to simulate multiple powder layers is proposed.A transient, three-dimensional, finite volume model is developed and implemented in ANSYS Fluent. A domain of cells representing multiple layers of an SLS build is initialized, some with the properties of air and some with the properties of powder, depending on cell location. A Gaussian heat source representing the laser is applied to the top layer of powder cells. The center of the Gaussian is varied with time along an established path to simulate the motion of the laser along the powder bed. At all times the three-dimensional heat equation is solved to produce a temperature profile of the powder bed. When the laser completes a full scan of the powder layer, the air cells directly above the powder layer are re-initialized as powder cells and re-set to an initial temperature, representing the addition of a new powder layer. The process is repeated for each new layer. Temperature history results from the model are validated against experimental data available in the literature and good agreement is obtained. As the model accounts for multiple powder layers, it can be used to simulate an entire part build and predict the impact of any of the SLS processing parameters on part quality and thus enable better control and optimization of the SLS process.

Characterization and design of fluid–thermal transport through random porous sintered beds is critical for improving the performance of two-phase heat transport devices such as heat pipes. Two-dimensional imaging techniques are quite well developed and commonly employed for microstructure and material characterization. In this study, we employ 2D image data (thin sections) for measuring critical microstructural features of commercial wicks for use in correlation-based prediction of transport properties. We employ a stochastic characterization methodology based on the two-point autocorrelation function, and compare the predicted properties such as particle and pore diameters and permeability with those from our previously published studies, in which 3D X-ray microtomography data was employed for reconstruction. Further, we implement a reconstruction technique for reconstructing a three-dimensional stochastic equivalent structure from the thin sections. These reconstructed domains are employed for predicting effective thermal conductivity, permeability and interfacial heat transfer coefficient in single-phase flow. The current computations are found to compare well with models and correlations from the literature, as well as our previous numerical studies. Finally, we propose a new parametrized model for the design of porous materials based on the nature of the two-point autocorrelation functions. Using this model, we reconstruct sample three-dimensional microstructures, and analyze the influence of various parameters on fluid–thermal properties of interest. With advances in additive manufacturing techniques, such an approach may eventually be employed to design intricate porous structures with properties tailored to specific applications.

Simulations of lithium ion batteries on a cell level are usually performed with volume averaging methods that employ effective transport properties. Bruggeman's model, which is widely used to determine these effective properties, is solely based on the volume fraction of these porous electrodes. However, other factors like the topology and microstructure of electrodes also play a crucial role in determining effective properties. In this paper, a general derivation of the effective thermal conductivity of multiphase materials, which can be correlated with these factors, is derived using the volume averaging technique. For demonstration, three-dimensional microstructures of various porous materials are reconstructed from scanned images. These images are used to generate fully-resolved finite volume meshes representing the various constituents. The resulting mesh is then employed for numerical analysis of thermal transport, results from which are used for correlating the effective thermal conductivity with various parameters describing the microstructure. It is shown that commonly used power law exponents in the Bruggeman model for effective thermal conductivity must be re-calibrated to fit the effective thermal conductivity computed from these detailed simulations.

Raman spectroscopy is typically used to characterize graphene in experiments and also to measure properties like thermal conductivity and optical phonon lifetime. The laser-irradiation processes underlying this measurement technique include coupling between photons, electrons and phonons. Recent experimental studies have shown that e-ph scattering limits the performance of graphene-based electronic devices due to the difference in their timescales of relaxation resulting in various bottleneck effects. Furthermore, recently published thermal conductivity measurements on graphene are sensitive to the laser spot size which strengthens the possibility of non-equilibrium between various phonon groups. These studies point to the need to study the spatially-resolved non-equilibrium between various energy carriers in graphene. In this work, we demonstrate non-equilibrium in the e-ph interactions in graphene by solving the linearized electron and phonon Boltzmann transport equations (BTE) iteratively under steady state conditions. We start by assuming that all the electrons equilibrate rapidly to an elevated temperature under laser-irradiation and they gradually relax by phonon emission and reach a steady state. The-electron and phonon BTEs are coupled because the e-ph scattering rate depends on the phonon population while the rate of phonon generation depends on the e-ph scattering rate. We used density-functional theory/density-functional perturbation theory (DFT/DFPT) to calculate the electronic eigen states, phonon frequencies and the e-ph coupling matrix elements. (1)We calculated the rate of energy loss from the hot electrons in terms of the phonon generation rate (PGR) which serve as an input for solving the BTE. Likewise, ph-ph relaxation times are calculated from the anharmonic lattice dynamics (LD)/FGR. Through our work, we obtained the spatially resolved temperature profiles of all the relevant energy carriers throughout the entire domain; these are impossible to obtain through experiments.

Heat pipes offer passive transport of heat over long distances without incurring a significant drop in temperature. Topological and microstructural details of the wick material embedded in a heat pipe help determine its thermal performance. A good understanding of pore-scale transport phenomena is crucial to enhancing heat pipe performance. In this study, pore-scale analysis of thin-film evaporation through sintered copper wicks is performed. X-ray microtomography is employed to generate geometrically faithful, feature-preserving meshes. Commercial sintered wicks with particle sizes in the range of 45–60μm, 106–150μm and 250–355μm and with approximately 61% porosity are considered. The capillary pressure, characteristic pore radius, percentage thin film area and evaporative mass and heat fluxes are computed using a volume of fluid (VOF) approach. Two different solution strategies are employed to stabilize the numerical solution and to improve convergence. After verifying that these strategies yield the correct solution, the VOF model is used to obtain static meniscus shapes in the pore space of the sintered wick samples. The meniscus shape is then held fixed and steady-state, thin-film evaporation analysis is performed. Liquid–vapor phase change heat transfer is modeled using a modified Schrage equation. Based on the present analysis, the best performing sample (particle size range) is identified along with the optimum contact angle.

Optimization under uncertainty (OUU) is a powerful methodology used in design and optimization to produce robust, reliable designs. Such an optimization methodology, employed when the input quantities of interest are uncertain, yields output uncertainties that help the designer choose appropriate values for input parameters to produce safe designs. Apart from providing basic statistical information, such as mean and standard deviation in the output quantities, uncertainty-based optimization produces auxiliary information, such as local and global sensitivities. The designer may thus decide the input parameter(s) to which the output quantity of interest is most sensitive, and thereby design better experiments based on just the most sensitive input parameter(s). Another critical output of such a methodology is the solution to the inverse problem, i.e., finding the allowable uncertainty (range) in the input parameter(s), given an acceptable uncertainty (range) in the output quantities of interest. We apply optimization under uncertainty to the problem of heat transfer in fin heat sinks with uncertainties in geometry and operating conditions. The analysis methodology is implemented using DAKOTA, an open-source design and analysis kit. A response surface is first generated which captures the dependence of the quantity of interest on inputs. This response surface is then used to perform both deterministic and probabilistic optimization of the heat sink, and the results of the two approaches are compared.

Conventional microchannel heat sinks provide good heat dissipation capability but are associated with high pressure drop and corresponding pumping power. The use of a manifold system that distributes the flow into the microchannels through multiple, alternating inlet and outlet pairs is investigated here. This manifold arrangement greatly reduces the pressure drop incurred due to the smaller flow paths, while simultaneously increasing the heat transfer coefficient by tripping the thermal boundary layers. A three-dimensional numerical model is developed and validated, to study the effect of various geometric parameters on the performance of the manifold microchannel heat sink. Apart from a deterministic analysis, a probabilistic optimization study is also performed. In the presence of uncertainties in the geometric and operating parameters of the system, this probabilistic optimization approach yields an optimal design that is also robust and reliable. Uncertainty-based optimization also yields auxiliary information regarding local and global sensitivities and helps identify the input parameters to which outputs are most sensitive. This information can be used to design improved experiments targeted at the most sensitive inputs. Optimization under uncertainty also provides a quantitative estimate of the allowable uncertainty in input parameters for an acceptable uncertainty in the relevant output parameters. The optimal geometric design parameters with uncertainties that maximize heat transfer coefficient while minimizing pressure drop for fixed input conditions are identified for a manifold microchannel heat sink. A comparison between the deterministic and probabilistic optimization results is also presented.

This work examines the impact of defects on the resonant response of single-wall carbon nanotube (CNT) resonators using classical molecular dynamics (MD) simulations. The work demonstrates that the presence of defects in CNTs leads to appreciable resonant mode splitting. A dimensionless parameter has been introduced to quantify this phenomenon. It is observed that increasing the degree of asymmetry in the system generally increases the magnitude of splitting. Given the centrality of single-peak Lorentzian frequency responses in the current device design paradigm, which is utilized in applications such as resonant mass sensing, the non-Lorentzian response characteristics of imperfect devices could present both opportunities and challenges in the future design and development of resonant nanosystems.

Nongray phonon transport solvers based on the Boltzmann transport equation (BTE) are being increasingly employed to simulate submicron thermal transport in semiconductors and dielectrics. Typical sequential solution schemes encounter numerical difficulties because of the large spread in scattering rates. For frequency bands with very low Knudsen numbers, strong coupling between other BTE bands result in slow convergence of sequential solution procedures. This is due to the explicit treatment of the scattering kernel. In this paper, we present a hybrid BTE-Fourier model which addresses this issue. By establishing a phonon group cutoff Knc, phonon bands with low Knudsen numbers are solved using a modified Fourier equation which includes a scattering term as well as corrections to account for boundary temperature slip. Phonon bands with high Knudsen numbers are solved using the BTE. A low-memory iterative solution procedure employing a block-coupled solution of the modified Fourier equations and a sequential solution of BTEs is developed. The hybrid solver is shown to produce solutions well within 1% of an all-BTE solver (using Knc = 0.1), but with far less computational effort. Speedup factors between 2 and 200 are obtained for a range of steady-state heat transfer problems. The hybrid solver enables efficient and accurate simulation of thermal transport in semiconductors and dielectrics across the range of length scales from submicron to the macroscale.

Passive phase-change thermal spreaders, such as vapor chambers have been widely employed to spread the heat from small-scale high-flux heat sources to larger areas. In this paper, a numerical model for ultrathin vapor chambers has been developed, which is suitable for reliable prediction of the operation at high heat fluxes and small scales. The effects of boiling in the wick structure on the thermal performance are modeled, and the model predictions are compared with experiments on custom-fabricated vapor chamber devices. The working fluid for the vapor chamber is water and a condenser side temperature range of 293 K-333 K is considered. The model predictions agree reasonably well with experimental measurements and reveal the input parameters to which thermal resistance and vapor chamber capillary limit are most sensitive. The vapor space in the ultrathin devices offers significant thermal and flow resistances when the vapor core thickness is in the range of 0.2 mm-0.4 mm. The performance of a 1-mm-thick vapor chamber is optimized by studying the variation of thermal resistance and total flow pressure drop as functions of the wick and vapor core thicknesses. The wick thickness is varied from 0.05 to 0.25 mm. Based on the minimization of a performance cost function comprising the device thermal resistance and flow pressure drop, it is concluded that the thinnest wick structures (0.05 mm) are optimal for applications with heat fluxes below 50 W/cm2 , while a moderate wick thickness of 0.1 mm performs best at higher heat flux inputs 50 (>;W/cm2).

Passive phase-change thermal spreaders such as vapor chambers have been widely employed to spread the heat from small-scale high-flux heat sources to larger areas. In the present work, a numerical model for ultra-thin vapor chambers has been developed which is suitable for reliable predictions of the operation at high heat fluxes and small scales. The effects of boiling in the wick structure on the thermal performance are modeled and the model predictions are compared with experiments on custom-fabricated devices. The model predictions agree reasonably well with experimental measurements and reveal the input parameters to which thermal resistance and vapor chamber capillary limit are most sensitive.

Droplet motion is important in discrete microfluidic operations as well as in emerging site-specific cooling techniques based on electrowetting. The present work reports on carefully characterized experiments that map the shape, advancing and receding contact angles, and contact area of droplets sliding under gravitational actuation as a function of droplet size and velocity. A pseudo-Lagrangian methodology based on the Volume Of Fluid - Continuous Surface Force (VOF-CSF) model is developed to simulate droplet motion down an incline. The model is benchmarked against 2D stationary reference-frame simulations. The terminal velocity of droplets on an incline is predicted and is in good agreement with in-house experimental measurements. The effect of using different contact angle models on the terminal velocity predictions is investigated. The numerical solution is highly sensitive to the contact angle boundary condition. The internal fluid motion in moving droplets is also explained.

The temperature and frequency dependence of the flexural mode quality factors (Q) of doubly clamped single wall carbon nanotube resonators are calculated using classical molecular dynamics simulations. The validity of the various methods available in the literature for calculating Q based on the temporal response of the system during ring-down is discussed and the discrepancies associated with the methods are explained. A new approach based on band-pass filtering is proposed for calculating Q, which reveals classical temperature dependence (Q ∼ T−1) in contrast to the previously reported results (Q ∼ T−β, 0 < β < 1). It is shown that the Q estimated from the temporal response is in good agreement with the Q estimated from frequency response. This work also demonstrates that the proposed method is particularly advantageous when multiple modes are simultaneously excited within the linear regime.

The thermal and hydrodynamic performance of passive two-phase cooling devices such as heat pipes and vapor chambers is limited by the capabilities of the capillary wick structures employed. The desired characteristics of wick microstructures are high permeability, high wicking capability and large extended meniscus area that sustains thin-film evaporation. Choices of scale and porosity of wick structures lead to tradeoffs between the desired characteristics. In the present work, models are developed to predict the capillary pressure, permeability and thin-film evaporation rates of various micropillared geometries. Novel wicking geometries such as conical and pyramidal pillars on a surface are proposed which provide high permeability, good thermal contact with the substrate and large thin-film evaporation rates. A comparison between three different micropillared geometries — cylindrical, conical and pyramidal — is presented and compared to the performance of conventional sintered particle wicks. The present work demonstrates a basis for reverse-engineering wick microstructures that can provide superior performance in phase-change cooling devices.