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Predicting mesoscale spectral thermal conductivity using advanced deterministic phonon transport techniques
We present a review, demonstration and simulation of phonon transport for the purposes of predicting materials performance at the mesoscale. We focus primarily on the development and implementation of a unified methodology to enable predictive heat transport. We report on the current state of the art as it pertains to deterministic phonon transport methodologies, discussing various topics concerning phonons. In application, we focus on the Self-Adjoint Angular Flux (SAAF) formulation of the Boltzmann transport equation for phonons, and develop the spatial, angular, and material property discretization required to accurately simulate the predictive physics of heat transport in dielectrics. We discuss thermal interfacial resistance and present our formulation of the diffuse mismatch model for simulating phonon interactions at internal boundaries. We have recently developed a deterministic, spectral phonon transport method for predicting effective thermal conductivity ($\kappa_{\textrm{eff}}$), using Bose-Einstein source terms coupled through an average material temperature. In this method, we introduce a closure term to the phonon transport system which acts as a redistribution function for the total energy of the system, and serves as a guide for the amount of non-equilibrium behavior occurring in the system. This method predicts thermal conductivity and equilibrium temperature distributions in homogeneous and heterogeneous materials using data generated by ab initio density functional theory methods. We employ polarization, density of states and full dispersion spectra to resolve thermal conductivity with numerous angular and spatial discretizations. Our implementation utilizes a Richardson iteration on a modified version of the phonon scattering source. The equations associated with this method are solved via a modification of traditional source iteration. We compare the performance of source iteration applied to an existing uncoupled, traditional SAAF method to our new method and comment on the iterative performance of each. We observe ballistic and diffusive phonon scattering as acoustic thickness of the domain changes, and are able to make comparisons between the accuracy and efficiency of both methods.
Boiling Heat Transfer Measurements on Highly Conductive Surfaces Using Microscale Heater and Temperature Arrays
Two systems have been developed to study boiling heat transfer on the microscale. The first system utilizes a 32 x 32 array of diodes to measure the local temperature fluctuations during boiling on a silicon wafer heated from below. The second system utilizes an array of 96 microscale heaters each maintained at constant surface temperature using electronic feedback loops. The power required to keep each heater at constant temperature is measured, enabling the local heat transfer coefficient to be determined. Both of these systems as well as some preliminary results are discussed.
Electron hopping heat transport in molecules
The realization of single-molecule thermal conductance measurements has driven the need for theoretical tools to describe conduction processes that occur over atomistic length scales. In macroscale systems, the principle that is typically used to understand thermal conductivity is Fourier’s law. At molecular length scales, however, deviations from Fourier’s law are common in part because microscale thermal transport properties typically depend on the complex interplay between multiple heat conduction mechanisms. Here, the thermal transport properties that arise from electron transfer across a thermal gradient in a molecular conduction junction are examined theoretically. We illustrate how transport in a model junction is affected by varying the electronic structure and length of the molecular bridge in the junction as well as the strength of the coupling between the bridge and its surrounding environment. Three findings are of note: First, the transport properties can vary significantly depending on the characteristics of the molecular bridge and its environment; second, the system’s thermal conductance commonly deviates from Fourier’s law; and third, in properly engineered systems, the magnitude of electron hopping thermal conductance is similar to what has been measured in single-molecule devices.
Evaluation of the Anisotropic Radiative Conductivity of a Low-Density Carbon Fiber Material from Realistic Microscale Imaging
The radiative heat transfer inside a low-density carbon fiber insulator is analyzed using a three-dimensional direct simulation model. A robust procedure is presented for the numerical calculation of the geometric configuration factor to compute the radiative energy exchange processes among the small discretized surface areas of the fibrous material. The methodology is applied to a polygonal mesh of a fibrous insulator obtained from three-dimensional microscale imaging of the real material. The anisotropic values of the radiative conductivity are calculated for that geometry. The results yield both directional and thermal dependence of the radiative conductivity.
Design of a novel carbon/carbon composite microvascular solar receiver
Solar thermal power tower systems are the primary technology being proposed for solar electricity from thermal energy. Operational limits on these towers are often driven by mechanical properties under significant thermal loads, particularly at the receiver where incoming flux is converted to thermal energy. While the solar receiver’s efficiency is largely driven by its optical properties, thermomechanical stresses on the receiver limits the operational envelope. One pathway to higher efficiency is greater allowable solar fluxes on the receiver but novel materials are required. The present study uses computational fluid dynamics to describe a parametric design space for a microvascular carbon/carbon composite solar receiver as a new material option for high flux solar receivers. Simulations are conducted for different microvascular geometries considering the role of material properties and heat transfer fluids, for the impact on thermal efficiency, and allowable strain. Results show that microscale receiver modules made of the proposed carbon/carbon composite could achieve thermal efficiencies over 90% and full-scale receivers can achieve up to 85% thermal efficiency for the design explored considering realistic strain limits, flux levels, and material properties. These values are highly dependent on the heat transfer fluid pairing, the through plane thermal conductivity of the carbon/carbon composite, the path architecture of the microscale receiver, and the incident solar flux profiles.
A First Principles Approach to Spectral Phonon Transport in Heterostructures
Understanding thermal transport across interfaces which give rise to a thermal resistance (also known as Kapitza resistance) is a critical issue affecting the development of nanotechnologies. Much modern and emergent nanotechnology consist of adjacent materials, and phonon mediated heat transfer governs thermal behavior across internal interfaces in these devices. The physics of thermal transport in solids are governed both by phenomena occurring at the atomic scale and interactions with the material's microstructure. The forecasting of fundamental quantities such as temperature, heat flux and thermal conductivity typically employs the semi-classical Boltzmann transport equation to predict the macroscopic behavior of materials in terms of the microscopic dynamics of its heat carriers. Kapitza resistance was first discovered in liquid helium experiments and has led to a fundamental research thrust in micro and nano-scale heat transport, the behavior of thermal carriers across internal interfaces. Thermal interfacial resistance (TIR) is a widely studied phenomenon, first engaged by Swartz and Pohl through their development of the acoustic and diffuse mismatch methods, then continued through myriad efforts with varying methods and approaches in an attempt to resolve carrier behavior at thermal interfaces. Many of the fundamental approaches to TIR have been at the nanoscale, and research is conducted with molecular dynamics (MD) and density functional theory (DFT) methods. The limitations of these methods is system size; atomistic methods tend to be limited to system sizes of 100,000 atoms or less. Larger length-scale methods have also been pursued, based on the principles of acoustic or diffuse mismatch, but not all include simulation of TIR using a full phonon band spectrum, or temperature dependent methods. Our approach to enabling phonon transport in layered materials draws upon our previous work of demonstrating spectrally coupled phonon transport in homogeneous and heterogeneous materials. We use a semi-analytical approach in which the Bose-Einstein (B-E) statistics set the strength of the phonon radiance in a frequency group, but the B-E statistics are informed with information from the transport system. The B-E statistics in a single frequency group feels the influence of all the groups through the spatial temperature. We also include a new field term which is an indicator of the amount of non-equilibrium behavior of the phonon spectrum---this is added to the phonon source term in all groups to ensure closure and conservation of energy, as the phonon groups in the transport system and the analytical systems are coupled. This work builds upon our previous approach by adding a phonon coupling term at an internal interface, using the principles of the DMM through transmission and reflection coefficients. In this work, the coefficients are determined through computing a common temperature at the interface, influenced by the phonon band structure of both materials, in effect, providing mixing between the two material systems and using the common temperature to set the strength of the phonon radiance at the boundaries on either side of the interface. Our approach uses material properties computed along various crystallographic orientations, and while some isotropy is built into the interface condition, the material properties weight the phonon distributions in the proper crystalline direction. Greater resolution of phonon behavior in proximity to an interface, and more accurate predictions of TIR are obtained. While it is true the assumption of diffuse mismatch can yield inconsistent results compared to experiment especially at low temperatures, this work focuses on room temperature and beyond effects, for future applications in nuclear fuel, or thermoelectric devices; a modified mismatch approach may be feasible if applied properly. Additionally, our methods focus on bridging mesoscale to engineering scale
Ultra-High Temperature Thermal Conductivity Measurements of a Reactive Magnesium Manganese Oxide Porous Bed Using a Transient Hot Wire Method
Pelletized magnesium manganese oxide shows promise for high temperature thermochemical energy storage. It can be thermally reduced in the temperature range between 1250 °C and 1500 °C and re-oxidized with air at typical gas-turbine inlet pressures (1–25 bar) in the temperature range between 600 °C and 1500 °C. The combined thermal and chemical volumetric energy density is approximately 2300 MJ/m3. The rate at which a thermochemical storage module can be charged is limited by heat transfer inside the solid packed bed. Hence, the effective thermal conductivity of packed beds of magnesium-manganese oxide pellets is a crucial parameter for engineering Mg-Mn-O redox storage devices. We have measured the effective thermal conductivity of a packed bed of 3.66 ± 0.516 mm sized magnesium manganese oxide (Mn to Mg molar ratio of 1:1) pellets in the temperature range of 300–1400 °C. Since the material is electrically conductive at temperatures above 600 °C, the sheathed transient hot wire method is used for measurements. Raw data is analyzed using the Blackwell solution to extract the bed thermal conductivity. The effective thermal conductivity standard deviation is less than 10% for a minimum of three repeat measurements at each temperature. Experimental results show an increase in the effective thermal conductivity with temperature from 0.50 W/m °C around 300 °C to 1.81 W/m °C close to 1400 °C. We propose a dual porosity model to express the effective thermal conductivity as a function of temperature. This model also considers the effect of radiation within the bed, as this is the dominant heat transfer mode at high temperatures. The proposed model accounts for microscale pellet porosity, macroscale bed porosity, pellet size, solid thermal conductivity (phonon transport), and radiation (photon transport). The coefficient of determination between the proposed model and the experimental results is greater than 0.90.
Microscale Imaging of Thermal Conductivity Suppression at Grain Boundaries
Abstract Grain‐boundary engineering is an effective strategy to tune the thermal conductivity of materials, leading to improved performance in thermoelectric, thermal‐barrier coatings, and thermal management applications. Despite the central importance to thermal transport, a clear understanding of how grain boundaries modulate the microscale heat flow is missing, owing to the scarcity of local investigations. Here, thermal imaging of individual grain boundaries is demonstrated in thermoelectric SnTe via spatially resolved frequency‐domain thermoreflectance. Measurements with microscale resolution reveal local suppressions in thermal conductivity at grain boundaries. Also, the grain‐boundary thermal resistance – extracted by employing a Gibbs excess approach – is found to be correlated with the grain‐boundary misorientation angle. Extracting thermal properties, including thermal boundary resistances, from microscale imaging can provide comprehensive understanding of how microstructure affects heat transport, crucially impacting the materials design of high‐performance thermal‐management and energy‐conversion devices.
Gas-Phase Temperature Mapping of Evaporating Microdroplets
Evaporation is a ubiquitous and complex phenomenon of importance to many natural and industrial systems. Evaporation occurs when molecules near the free interface overcome intermolecular attractions with the bulk liquid. As molecules escape the liquid phase, heat is removed, causing evaporative cooling. The influence of evaporative cooling on inducing a temperature difference with the surrounding atmosphere as well as within the liquid is poorly understood. Here, we develop a technique to overcome past difficulties encountered during the study of heterogeneous droplet evaporation by coupling a piezo-driven droplet generation mechanism to a controlled micro-thermocouple to probe microdroplet evaporation. The technique allowed us to probe the gas-phase temperature distribution using a micro-thermocouple (50 μm) in the vicinity of the liquid–vapor interface with high spatial (±10 μm) and temporal (±100 ms) resolution. We experimentally map the temperature gradient formed surrounding sessile water droplets having varying curvature dictated by the apparent advancing contact angle (100° ≲ θ ≲ 165°). The experiments were carried out at temperatures below and above ambient for a range of fixed droplet radii (130 μm ≲ R ≲ 330 μm). Our results provide a primary validation of the centuries-old theoretical framework underpinning heterogeneous droplet evaporation mediated by the working fluid, substrate, and gas thermophysical properties, droplet apparent contact angle, and droplet size. We show that microscale droplets residing on low-thermal-conductivity substrates such as glass absorb up to 8× more heat from the surrounding gas compared to droplets residing on high-thermal-conductivity substrates such as copper. Finally, our work not only develops an experimental understanding of the heat transfer mechanisms governing droplet evaporation but also presents a powerful platform for the study and characterization of liquid–vapor transport at curved interfaces wetting and nonwetting advanced functional surfaces.
Effectiveness of street trees in reducing air temperature and outdoor heat exposure in Las Vegas
Urban greening and especially tree planting strategies are being widely planned and implemented to mitigate urban overheating and thermal stress in many urban areas. However, the effectiveness of these strategies depends on multiple factors, including urban morphology, environmental conditions, and tree characteristics. This study investigates the effects of street tree planting strategies on air temperature and outdoor heat exposure in Las Vegas by combining an urbanized mesoscale climate model coupled to a multi-layer street tree model (Weather Research and Forecasting-BEP-Tree; Δ x = 900 m) with a microscale pedestrian heat exposure model (Temperatures of Urban Facets for Pedestrian; Δ x = 1 m). A series of simulations are conducted for July and August 2022. Large city-wide increases of a drought tolerant tree species cool air temperature mainly during the nighttime (up to 1.5 °C), with daytime effects being limited due to leaves shedding sensible instead of latent heat as stomata close in response to high vapor pressure deficits. Increased evaporative cooling is achieved with a different tree species (double at night, and reaching 0.4 °C during the day), but water requirements increase threefold. Despite their relatively small effect on air temperature during the day, trees provide significant shade by intercepting solar radiation, reducing mean radiant temperature (up to 16 °C) and enhancing outdoor thermal comfort, a major benefit of street trees in hot arid climates. The nighttime cooling of trees and the daytime reduction of radiant loading show potential to reduce the heat-related health impacts. Our results highlight the need to evaluate the effects of street trees on a case-by-case basis.
Micro-Textured Black Silicon Wick for Silicon Heat Pipe Array
Planar, semiconductor heat arrays have been previously proposed and developed; however, this design makes use of a novel, microscale black silicon wick structure that provides increased capillary pumping pressure of the internal working fluid, resulting in increased effective thermal conductivity of the device, and also enables operation of the device in any orientation with respect to the gravity vector. In a heat pipe, the efficiency of thermal transfer from the case to the working fluid is directly proportional to the surface area of the wick in contact with the fluid. Also, the primary failure mechanism for heat pipes operating within the temperature range of interest is inadequate capillary pressure for the return of fluid from the condenser to the wick. This is also what makes the operation of heat pipes orientation-sensitive. Thus, the two primary requirements for a good wick design are a large surface area and high capillary pressure. Surface area can be maximized through nanomachined surface roughening. Capillary pressure is largely driven by the working fluid and wick structure. The proposed nanostructure wick has characteristic dimensions on the order of tens of microns, which promotes menisci of very small radii. This results in the possibility of enormous pumping potential due to the inverse proportionality with radius. Wetting, which also enhances capillary pumping, can be maximized through growth of an oxide layer or material deposition (e.g. TiO2) to create a superhydrophilic surface.
In-situ Imaging of Pyrolyzing Aerospace Materials
Tracking morphological changes of materials during heating is crucial to understand its response in fire protection, biofuel production, thermal protection systems (TPS) for hypersonic flight. As materials are heated, they undergo physical and chemical changes due to water loss, stretching or shrinking, pyrolysis and chemical reactions in the ambient environment. The effects of these changes can have a profound impact on the material’s performance, indicated by changes in on the porosity and volume. While materials such as wood shrink as they pyrolyze and lose mass, others swell due to their inherent characteristics when exposed to heat [1]. This study focuses on experiments conducted at the Advanced Light Source (ALS) beamline 8.3.2, where in situ micro-computed tomography (µ-CT) is performed on materials as they are being pyrolyzed. Through in situ µ-CT, the change in total volume and porosity can be obtained in real-time, allowing for better understanding of the underlying thermophysical and chemical processes as a function of temperature. This study also focuses on the implementation of the Porous Microstructure Analysis software (PuMA) [2] to obtain thermal conductivity, permeability, and other properties of the material from the 3D tomographies. The information gained from these tomographies will supplement microscale model development of material morphological change and will aid macroscale modeling for high-temperature applications. For this study, Room Temperature Vulcanizing silicone (RTV) [3-5] is heated from room temperature to 1000°C using an infrared lamp heating system, and tomographies are continuously collected as the sample is heated. The tomographies are then segmented to obtain solid and void phases, from which estimates of pore size, porosity and total volume are extracted as a function of temperature. PuMA is deployed on the segmented tomographies to obtain thermal conductivity, permeability, and other properties as a function of temperature. Preliminary results show that RTV first intumesces (swells) as pyrolysis begins, due to build-up of pyrolysis gases in closed pores, and then shrinks significantly as more open pores are formed and the pyrolysis gases outgas. Pore network visualization of the tomographies using OpenPNM [6] showed the increase in pore connectivity with increase in temperature. Future work will focus on using PuMA to obtain macroscopic properties of RTV as a function of temperature.
Non-Contact Mass Density and Thermal Conductivity Measurements of Organic Thin Films Using Frequency–Domain Thermoreflectance
Thin-film organic materials are broadly used to study amorphous stabilization of active pharmaceuticals, control explosive detonation phenomena, and introduce insulation in novel thermal barriers. Their synthesis, however, introduces defects and thickness variations that warrant careful characterization of local thermophysical properties such as thermal conductivity and mass density. In this study, wide bandwidth (200 Hz to 20 MHz) frequency–domain thermoreflectance (FDTR) is demonstrated to simultaneously extract the thermal conductivity and mass density of 1 μm physical vapor-deposited indomethacin films on Si and SiO 2 substrates, as well as 10 and 100 μm films on Si. By assuming a bulk specific heat capacity, mass densities are determined with FDTR measurements of volumetric heat capacity and are in good agreement with the literature, as well as models based upon a dependence on porosity and the kinetic theory for phonons. Lastly, it is found that for broad-band FDTR measurements, insulating substrates provide improved fidelity for the extraction of thermal conductivity and volumetric heat capacity in organic thin films. Overall, this work demonstrates the potential for FDTR as a non-contact method to determine microscale mass density variations across the surface and thickness of organic thin films.
Temperature-Following Thermal Barrier Coatings for High Efficiency Engines (Final Report)
HRL Laboratories and General Motors (GM), pursued this effort to increase the efficiency of internal combustion engines (ICEs) by developing and implementing temperature-following thermal barrier coatings (TBCs) to decrease heat loss from the combustion chamber. HRL developed microsphere TBCs based on hollow high-temperature alloy spheres with average diameter of 50 μm and wall thickness ~1 μm (microspheres) that achieve unprecedented low thermal conductivity and heat capacity (10X lower than the state of the art) while offering exceptional environmental and mechanical resistance.> In current ICEs, approximately 29% of the fuel’s energy is lost to the cooling system and about 22% goes into moving the car. By limiting heat losses from the combustion chamber with insulating coatings, fuel energy can be redirected into additional piston work and into the exhaust stream. The additional energy that goes into the exhaust stream can be turned into useful work through the use of an exhaust energy recovery device, such as turbocompounding and/or through driving a turbocharger to increase the power density of the engine allowing downsizing. Insulating coatings for piston crowns have been pursued in the past, but previous materials—typically ceramics—exhibited low thermal conductivity but retained high heat capacity. Such materials reduce heat losses but stabilize at a high surface temperature. The high surface temperature heats the incoming gases, which lowers volumetric efficiency and increases propensity for knock, resulting in degraded engine performance. This program developed an innovative new material that combines low thermal conductivity with low heat capacity. These unique properties allow it to follow rapid changes in gas temperature during each combustion cycle. A metallic microsphere TBC has been demonstrated that exhibits increased surface temperature during the combustion period, resulting in reduced heat transfer losses, while still returning to a low surface temperature during the gas exchange period. A 10X lower thermal conductivity and heat capacity than state-of-the-art thermal barrier coatings has been demonstrated. These unprecedented thermal properties are achieved through the coating architecture, which consists of closed pores on the microscale and exhibits a total porosity of 90% to 95%. By selecting a high-temperature nickel alloy as the coating material, the ductility and strength of metals can be harnessed to achieve much better durability and damage tolerance than brittle ceramic coatings can achieve.
Local Thermal Conductivity Patterning in Rotating Lattice Crystals of Anisotropic Sb 2 S 3
The ability to control material heat transport properties over space and time can drive advanced functionalities in thermal management for electronics and system-on-chip, and enable thermal circuits. Despite the technological relevance, there are limited demonstrations of local thermal property control. Rotating lattice single (RLS) crystals—formed via laser-induced crystallization of an amorphous substrate—offer a novel avenue for local crystal engineering, unlocking opportunities for microscale property patterning. Here, thermal conductivity (𝜅) imaging is applied to RLS crystals of Sb2S3 to resolve microscale 𝜅 variations across patterned regions. Amorphous areas exhibit 𝜅 as low as 0.6 Wm −1 K −1 , while crystalline regions display periodic 𝜅 variations from 0.7 to over 2.5 Wm −1 K −1 . These variations correspond to changes in crystal orientation, revealing marked 𝜅 anisotropy. The crystal out-of-plane direction (c axis)—featuring van der Waals bonds—shows amorphous-like transport, whereas in-plane directions (a, b axes) exhibit 3.5x and 1.7x larger 𝜅, respectively. First-principles calculations, in excellent agreement with experiments, suggest that the in-plane anisotropy originates from expressed Sb lone pairs, which impart a corrugation along the b axis affecting bond stiffness and 𝜅. These findings demonstrate microscale control of thermal properties via laser-processed metastructures, with significant implications for next-generation thermal management.
Morphological-informed Thermal Property Prediction in the Engineering Domain
Using first-principle, atomic scale methods to predict thermal carrier (electron and phonon) behavior at nanoscale yields highly resolved thermal properties. Density functional theory simulations can model myriad effects on the transport of phonons and electrons (e.g., phonon and electron coupling, electron correlation, defect presence, carrier scattering), and yield thermal properties for small geometric domains such as thermal and electrical conductivity, or heat capacity. While these thermal properties are accurate in atomistic and nanoscopic systems, they must be scaled up to the microstructural domain to be a useful predictor for experimental basis, as the microscale is where myriad changes and physical phenomenon occur within a material (e.g., grain boundaries, precipitate aggregations, interfaces, defect clusters). My talk will discuss the necessity of thermal property predictions for nuclear fuels applications and more. Additionally I will discuss the necessity in developing multi-physics, multi-scale methods for future applications in predictions for not only nuclear fuels, but other materials applications.
Autonomous Fracture Conductivity Using Expandable Proppants in Enhanced Geothermal Systems
Summary Early thermal breakthrough in enhanced geothermal systems (EGS) due to the presence of preferential flow channels is a major challenge that endangers efficient and economic heat extraction in such systems. Previous studies mainly focused on adjusting circulation rates of the working fluid, which still leaves significant amounts of untapped heat behind. Currently, there is a lack of technologies for altering flow distribution within the fracture network to achieve uniform heat sweeping in the reservoir. This work presents a novel concept for making proppants to autonomously control fracture conductivity based on the surrounding temperature. Here, proppants with negative thermal expansion coefficients have demonstrated the capability for appropriate fracture conductivity adjustment as a function of temperature to achieve uniform flow across the fracture network. Particle-particle interactions governing such functions are explicitly modeled, and then the Lattice Boltzmann methods (LBM) is used to determine the potential impact of closure stress and temperature changes on the permeability of the proposed proppant packs. Microscale analyses are further used to determine the required material properties to achieve a certain improvement in the permeability of the proppant pack. Our analyses show an enhancement in permeability and the associated fracture conductivity by half of their initial values. Field-scale analysis further confirms the effectiveness of the proposed concept as 31.4% more heat can be extracted from EGS over 50 years of production when the proposed proppants are used. Such novel proppants may effectively delay thermal breakthrough, sweep heat from larger rock volumes, and elongate the life span of the EGS project.