Heat Transport Model Research Articles

Development of an x-ray radiography platform to study laser-direct-drive energy coupling at the National Ignition Facility.

A platform has been developed to study laser-direct-drive energy coupling at the National Ignition Facility (NIF) using a plastic sphere target irradiated in a polar-direct-drive geometry to launch a spherically converging shock wave. To diagnose this system evolution, eight NIF laser beams are directed onto a curved Cu foil to generate Heα line emission at a photon energy of 8.4keV. These x rays are collected by a 100-ps gated x-ray imager in the opposing port to produce temporally gated radiographs. The platform is capable of acquiring images during and after the laser drive launches the shock wave. A backlighter profile is fit to the radiographs, and the resulting transmission images are Abel inverted to infer radial density profiles of the shock front and to track its temporal evolution. The measurements provide experimental shock trajectories and radial density profiles that are compared to 2D radiation-hydrodynamic simulations using cross-beam energy transfer and nonlocal heat-transport models.

New Capabilities in MT3D-USGS for Simulating Unsaturated-Zone Heat Transport.

Changes in climate and land use will alter groundwater heat transport dynamics in the future. These changes will in turn affect watershed processes (e.g., nutrient cycling) as well as watershed characteristics (e.g., distribution and persistence of cold-water habitat). Thus, groundwater flow and heat transport models at watershed scales that can characterize and quantify thermal impacts of surface temperature change on groundwater system temperatures may support forecasting changes to groundwater-linked ecosystems in riparian zones, streams, and lakes. Including unsaturated zone processes has previously been shown to be important for properly determining the timing and magnitude of groundwater recharge (Hunt et al. 2008). Similarly, heat transport dynamics in the saturated-zone, as well as connected surface-water systems, can be appreciably influenced by unsaturated-zone processes; in this way the unsaturated zone forms an inextricable link between the land surface where change occurs and the groundwater system that transmits that change. This paper presents new capabilities for the existing MT3D-USGS transport simulator by adding functionality for simulating heat transport through the unsaturated zone. New simulation capabilities are verified through comparison of simulation results with those of the variably saturated heat transport simulator VS2DH under steady and transient conditions for both water and heat flow. The new capabilities are assessed using a number of conceptualizations and include evaluations of convective and conductive heat flow. These additional capabilities increase the utility for applied watershed-scale simulations, which in turn may facilitate more realistic characterizations of temperature change on thermally sensitive ecosystems, such as stream habitat.

A model for multiphase moisture and heat transport below and above the saturation point of deformable and swelling wood fibers – I: Mass transport

A thermodynamically consistent model for heat and mass transfer in deformable wood fibers is developed. The hybrid mixture theory is used to model the material as a mixture of three phases, consisting of a solid, a liquid and a gas phase. The solid phase consists of dry fibers and bound water constituents, whereas the gas phase has dry air and water vapor constituents. Emphasis is put on the mass flow and mass exchange of moisture in the material both below and above the saturation point of the solid wood fibers. Generalized forms of Fick’s, Darcy’s and Fourier’s laws are derived, and the chemical potential is used as a driving force for mass flow. Mass exchange due to sorption and evaporation/condensation processes is implemented in the model, where hysteretic properties both within and above the hygroscopic moisture range are described using Frandsen’s hysteresis model. Moisture induced swelling/shrinkage is included where the porosity of the material can vary. A large strain setting formulated for general orthotropy is adopted for the mechanical deformations. To show the performance of the resulting model, it is implemented in a finite element method framework and used to simulate the processes of heat and moisture transport dynamics of a wood sample subjected to drying from an over-hygroscopic moisture state.

A model for multiphase moisture and heat transport below and above the saturation point of deformable and swelling wood fibers-II: Hygro-mechanical response

A non-linear elastic constitutive model for a swelling/shrinking orthotropic wood matrix is proposed. The model is thermodynamically consistent, derived based on the principles of continuum mechanics and the hybrid mixture theory. Moisture induced strains are introduced considering finite deformations by assuming a multiplicative split of the deformation gradient tensor into a swelling and an elastic part. Novel definitions of the Cauchy stress tensor and the moisture-dependent elastic material tangent matrix are obtained. The model is coupled to a multi-phase transient mass and heat transport model developed in Part I of this work. In this part of the work 2-D and 3-D test examples are used to describe the ability of the model to simulate moisture-induced distortions when drying wood within the hygroscopic and also from the over-hygroscopic moisture ranges. Despite deriving the model considering wood, the obtained constitutive relations can be suitably adopted to other orthotropic porous materials displaying properties similar to that of wood.

Investigation of seepage near the interface between an embankment dam and a concrete structure: monitoring and modelling of seasonal temperature trends

Seasonal subsurface temperature monitoring, which exploits the fact that increased seepage flow may locally alter the temperature distribution, is a useful approach for leakage monitoring and evaluation within embankment dams and their foundations. At the Mactaquac Generating Station, New Brunswick, Canada, spatial and temporal variations of temperature have been monitored and modelled at the steeply inclined interface between the compacted clay till core of the embankment dam and an abutting concrete diversion sluiceway. Over a 4-year period, two seasonally recurring anomalies at different depths were observed by fibre optic distributed temperature sensing in the concrete structure close to the interface. A 3D coupled flow and heat transport model was developed in FEFLOW to simulate temperature distribution within the dam resulting from seasonal variations in air and reservoir temperature. Leakage zones near the interface were simulated in the concrete and embankment. At a depth of 13 m below the crest, the significant lag time between temperature variations in the reservoir and dam core shows that the leakage responsible for an observed temperature anomaly must be limited to enhanced flow within the concrete. At much shallower depths, where seasonal reservoir and dam core temperatures fluctuate nearly in phase, seepage paths are more challenging to determine.

Modelling Soil Water, Salt and Heat Dynamics under Partially Mulched Conditions with Drip Irrigation, Using HYDRUS-2D

Drip irrigation under mulch is a widely used technique in the arid region of northwest China. The partially mulched soil and the bare strips between mulched areas may complicate the migration of water, salt, and heat in soils, and cause lateral salt accumulation on bare soil surfaces. For investigating hydrothermal dynamics and salt distribution patterns under such circumstances, tank experiments with drip irrigation under plastic film on partially mulched soil were conducted under two intensities of drip irrigation (i.e., low (W1) and high (W2)) with the same total irrigation amount. The spatial distributions of soil water, temperature, and electrical conductivity were monitored accordingly. The two-dimensional (2D) model of soil water, salt, and heat transport under drip irrigation and partially mulched soil conditions was established using HYDRUS-2D, and kinetic adsorption during salt migration was considered. The results of the experiments showed that the uneven distribution of the hydrothermal state led to the accumulation of salt on the un-mulched soil surface. Water migrated from where the dripper was located, and heat accumulated mainly in the mulched soil. HYDRUS-2D matched reasonably well with the observed data, with an R2 higher than 0.54. Under the partially mulched conditions, lower intensity of drip irrigation (W1) show higher desalination efficiency in root zones, with less even lateral salt distribution. Scenario simulations further demonstrated that a larger total irrigation amount would result in a larger desalination zone, and drip irrigations with appropriate incremental intensity could improve salt leaching in the root zone with increased lateral migration of water.

Tuning transport mechanisms in fuel-assisted solid oxide electrolysis cells for enhanced performance and product selectivity: Thermodynamic and kinetic modeling

Fuel-assisted solid oxide electrolysis cells (FASOECs) have the capacity to generate power and valuable chemicals, simultaneously, by supplying fuels including methane, carbon monoxide, and hydrogen to a cell’s anode. Such fuels can comprise the tail gas of Fischer–Tropsch (FT) reactors and can be further exploited by FASOECs to reduce the amount of energy required to facilitate steam electrolysis. Important challenges that remain in the development of FASOECs, however, are determining the reactions that contribute to the transport phenomena of the system and how they influence the performance of these devices. To date, most numerical models of FASOECs have accounted for methane steam reforming and the water gas shift reaction in the anode, which cannot predict the onset of carbon deposition and other reactions that can occur in different regions of a cell. For the first time, a combined mass and heat transport model of an FASOEC fed with a multi-component fuel mixture is constructed to track the reaction pathways by which each component is utilized/produced and to develop strategies to enhance their performance and product selectivity. We reveal the transport regimes (and corresponding cell specifications) in which carbon deposition can be alleviated, which has been observed in previous experiments on methane-assisted solid oxide cells, and those that yield H2/CO ratios desirable for the feedstock of FT reactors. As a result of this framework, designers will have an understanding of how to select appropriate values of the design specifications and operating conditions of FASOECs, in order to augment their efficiency and product selectivity, while mitigating carbon deposition.

Validation study of a Spatially-Averaged Two-Fluid Model for heat transport in gas-particle flows

We validate a multi-scale turbulence model for the thermal energy estimation in coarse-grid simulations of moderately dense gas-particle flows. The model is based on spatially-averaging the Two-Fluid Model balance equations including the thermal energy balance equation of both phases. We found, that the drift temperature is a valid measure for the heat transfer reduction due to heterogeneous particle clusters. Furthermore, we propose the dynamic estimation of the drift temperature through the application of test-filters and the solution of transport equations for the variances of the phase temperatures and the solid volume fraction. Closure models for the Reynolds stress contributions are based on single-phase Large-Eddy Simulation models, such as gradient assumptions. In this study, we consider different test-cases including Geldart type A and type B particles in moderately dense regimes with domain averaged volume fractions ranging from 0.05 to 0.25. The operating conditions include unbounded sedimentation under gravity, as well as a turbulent-sluggish fluidization. In all cases, we discuss the influence of the meso-scale particle clusters on the macro-scale temperature distributions through the individual contributions of the unresolved terms in coarse-grid simulations. Thereby, we find that the dynamic estimation of the drift temperature leads to accurate results for the influence of local heat sinks on the global temperature difference decay between the phases and that the jump-response of a fluidized bed to an elevated gas-inflow temperature is correctly captured by the proposed multi-phase turbulence model. Furthermore, the importance of the correct estimation of the hydrodynamics for a correct prediction of the thermodynamics is highlighted.

Streambed water flux characterization through a Deep-Learning-Based approach considering data worth analysis: Numerical modeling and sandbox experiments

• An approach named CNN-DWA is proposed for estimating streambed water fluxes. • High-utility data are chosen through data worth analysis for CNN model training. • A few chosen data points provide similar information content to entire dataset. • CNN-DWA achieves more accurate flux estimations than the previously used IES. Quantifying streambed water fluxes (SWFs) is a prerequisite for studying the transport and fate of contaminants in the hyporheic zone. One approach, the heat tracing technique combined with analytical or numerical heat transport models has been widely used to quantify SWFs. However, both analytical and numerical methods are limited. For example, analytical methods are built upon rarely met assumptions, while the inversion performance of numerical methods can be impeded by uncertainties from different sources. To overcome these limitations, we introduce a new approach that combines convolutional neural networks (CNNs) with the Bayesian data worth analysis (DWA) framework for estimating SWFs. In this approach, a synthetic dataset is first generated through numerical simulations of groundwater flow and heat transport in streambeds. Then high-utility temperatures are chosen from the synthetic dataset through Bayesian DWA and further used to train the CNN model. We assess the capability of Bayesian DWA in improving the SWF estimation accuracy of CNN models through both numerical and sandbox experimental cases. Results show that the CNN model trained on temperatures with higher utility generally gives more accurate SWF estimations; use of a few high-utility temperature measurements can provide near similar constraint on the CNN model training and SWF estimation as compared to the full time series. Furthermore, a comparison to the iterative ensemble smoother algorithm shows the proposed inversion approach can estimate the flux field in the sandbox more accurately. The proposed CNN-based inversion approach considering DWA (CNN-DWA) would be beneficial more broadly for other hydrological problems.

Modelling Debris-Covered Glacier Ablation Using the Simultaneous Heat and Water Transport Model. Part 1: Model Development and Application to North Changri Nup

Modelling ablation of glacier ice under a layer of mineral debris is increasingly important, because the extent of supraglacial debris is expanding worldwide due to glacier recession. Physically based models have been developed, but the uncertainty in predictions is not yet well constrained. A new one-dimensional model of debris-covered ice ablation that is based on the Simultaneous Heat and Water transfer model is introduced here. SHAW-Glacier is a physically based, vertically integrated, fully coupled, water and energy balance model, which includes the advection of heat by rainwater and lateral flow. SHAW-Glacier was applied to North Changri Nup, a high elevation alpine glacier in the monsoon-dominated Central Himalaya. Simulations were compared with observed debris temperature profiles, snow depth, and ablation stake measurements for debris 0.03–0.41 m thick, in a 2500 m2 study area. Prediction uncertainty was estimated in a Monte Carlo analysis. SHAW-Glacier simulated the characteristic pattern of decreasing ablation with increasing debris thickness. However, the observations of ablation did not follow the characteristic pattern; annual ablation was highest where the debris was thickest. Recursive partitioning revealed a substantial, non-linear sensitivity to the snow threshold air temperature, suggesting a sensitivity to the duration of snow cover. Photographs showed patches of snow persisting through the ablation season, and the observational data were consistent with uneven persistence of snow patches. The analyses indicate that patchy snow cover in the ablation season can overwhelm the sensitivity of sub-debris ablation to debris thickness. Patchy snow cover may be an unquantified source of uncertainty in predictions of sub-debris ablation.

The development of a high-resolution Eulerian radiation-hydrodynamics simulation capability for laser-driven Hohlraums

Hohlraums are hollow cylindrical cavities with high-Z material walls used to convert laser energy into uniform x-ray radiation drives for inertial confinement fusion capsule implosions and high energy density physics experiments. Credible computational modeling of hohlraums requires detailed modeling and coupling of laser physics, hydrodynamics, radiation transport, heat transport, and atomic physics. We report on improvements to Los Alamos National Laboratory's xRAGE radiation-hydrodynamics code in order to enable hohlraum modeling. xRAGE's Eulerian hydrodynamics and adaptive mesh refinement make it uniquely well suited to study the impacts of multiscale features in hohlraums. In order to provide confidence in this new modeling capability, we demonstrate xRAGE's ability to produce reasonable agreement with data from several benchmark hohlraum experiments. We also use xRAGE to perform integrated simulations of a recent layered high density carbon capsule implosion on the National Ignition Facility in order to evaluate the potential impacts of the capsule support tent, mixed cell conductivity methodologies, plasma transport, and cross-beam energy transfer (XBT). We find that XBT, seeded by plasma flows in the laser entrance hole (LEH), causes a slight decrease in energy coupling to the capsule and that all of these impact the symmetry of the x-ray drive such that they have an appreciable impact on the capsule implosion shape.

Numerical investigation of impact of crystal diameter fluctuations on intrinsic point defects distribution in Si crystal grown by Czochralski method

Intrinsic point defects distribution is primarily controlled by the crystal pulling rate and temperature gradient directly at growth interface in silicon crystals grown using the Czochralski (Cz) method. The fluctuation in crystal diameter during the Cz process is one of the primary features associated with the temporal variation in growth process parameters, such as the pulling rate and heater power in the growth system, and which is expected to affect the thermal stress, defects, and dopant incorporation in a growing crystal. In this study, we numerically investigated the effect of temporal variation in crystal diameter on the intrinsic point defects distribution in a silicon crystal grown using the Cz method. The point defect dynamics in the crystal were numerically evaluated within a two-dimensional axisymmetric unsteady global heat and mass transport model for dynamically pulled silicon crystals, considering the shape of the crystal and diameter variation. Unsteady numerical simulations showed that the distribution of intrinsic point defects near crystal side surface in a growing silicon crystal significantly depends on the temporal variation in the crystal diameter.

Multi-scale modelling of nanoparticle delivery and heat transport in vascularised tumours.

We focus on modelling of cancer hyperthermia driven by the application of the magnetic field to iron oxide nanoparticles. We assume that the particles are interacting with the tumour environment by extravasating from the vessels into the interstitial space. We start from Darcy's and Stokes' problems in the interstitial and fluid vessels compartments. Advection-diffusion of nanoparticles takes place in both compartments (as well as uptake in the tumour interstitium), and a heat source proportional to the concentration of nanoparticles drives heat diffusion and convection in the system. The system under consideration is intrinsically multi-scale. The distance between adjacent vessels (the micro-scale) is much smaller than the average tumour size (the macro-scale). We then apply the asymptotic homogenisation technique to retain the influence of the micro-structure on the tissue scale distribution of heat and particles. We derive a new system of homogenised partial differential equations (PDEs) describing blood transport, delivery of nanoparticles and heat transport. The new model comprises a double Darcy's law, coupled with two double advection-diffusion-reaction systems of PDEs describing fluid, particles and heat transport and mass, drug and heat exchange. The role of the micro-structure is encoded in the coefficients of the model, which are to be computed solving appropriate periodic problems. We show that the heat distribution is impaired by increasing vessels' tortuosity and that regularization of the micro-vessels can produce a significant increase (1-2 degrees) in the maximum temperature. We quantify the impact of modifying the properties of the magnetic field depending on the vessels' tortuosity.

Laser-induced heating of polydimethylsiloxane-magnetite nanocomposites for hyperthermic inhibition of triple-negative breast cancer cell proliferation.

This paper presents the results of an experimental and computational study of the effects of laser-induced heating provided by magnetite nanocomposite structures that are being developed for the localized hyperthermic treatment of triple-negative breast cancer. Magnetite nanoparticle-reinforced polydimethylsiloxane (PDMS) nanocomposites were fabricated with weight percentages of 1%, 5%, and 10% magnetite nanoparticles. The nanocomposites were exposed to incident Near Infrared (NIR) laser beams with well-controlled powers. The laser-induced heating is explored in: (i) heating liquid media (deionized water and cell growth media [Leibovitz L15+]) to characterize the photothermal properties of the nanocomposites, (ii) in vitro experiments that explore the effects of localized heating on triple-negative breast cancer cells, and (iii) experiments in which the laser beams penetrate through chicken tissue to heat up nanocomposite samples embedded at different depths beneath the chicken skin. The resulting plasmonic laser-induced heating is explained using composite theories and heat transport models. The results show that the laser/nanocomposite interactions decrease the viability of triple-negative breast cancer cells (MDA-MB-231) at temperatures in the hyperthermia domain between 41 and 44°C. Laser irradiation did not cause any observed physical damage to the chicken tissue. The potential in vivo performance of the PDMS nanocomposites was also investigated using computational finite element models of the effects of laser/magnetite nanocomposite interactions on the temperatures and thermal doses experienced by tissues that surround the nanocomposite devices. The implications of the results are then discussed for the development of implantable nanocomposite devices for localized treatment of triple-negative breast cancer tissue via hyperthermia.

Is natural convection within an aquifer a critical phenomenon in deep borehole heat exchangers' efficiency?

• Impacts of natural convecton on CBHE’s thermal efficiency is studied. • Various cases of CBHE depth, inflow rate and aquifers permeability are considered. • Inflow rate has a more significant effect on thermal yield when permeability is high. • Shorter CBHE's thermal performance shows more sensitivity to aquifers permeability. Deep borehole heat exchangers (BHEs) can be utilised effectively for geothermal (heat) extraction from up to a few kilometres below the subsurface using the conventional closed U-loop or coaxial configurations. These systems take advantage of the high enthalpy energy in the deeper ground without relying on fracture flow extraction/injection, hence avoiding the complexity and uncertainty of hydraulic fracturing to enhance the permeability of deep aquifers. Despite the recent theoretical advancement in deep BHE systems, recent studies mainly assume conductive heat transfer in the ground, neglecting the effects of groundwater and heat convection (natural or forced) on the system’s thermal capacity. This simplified assumption could result in underestimating geothermal extraction efficiency given the extensive fluctuations in groundwater thermo-physical properties, particularly at high temperatures. Therefore, the ultimate goal of this study is to investigate the extent to which the thermal performance of deep coaxial borehole heat exchangers (CBHEs) is affected by natural convection in deep aquifers. This is achieved by developing a novel numerical approach for reliable quantification of thermal yield, accounting for conduction and the commonly overlooked thermo-induced convection in aquifers - using a tested 3D finite element heat and mass transport model. Considering groundwater parameters’ temperature dependency, the resultant buoyancy in groundwater and the effects of gravity, parametric studies are undertaken for various ranges of permeability, carrier fluid velocity and CBHEs depth. The overall validity of the model is tested against published experimental data. It is concluded that higher carrier fluid inflow rates for a given CBHE depth can lead to up to 43% higher CBHEs thermal efficiency when the aquifer’s permeability is high (k = 10 −10 m 2 ). Furthermore, the results indicate that a higher aquifer permeability, hence a substantial thermo-induced heat exchange in the aquifer, has a more pronounced effect on CBHEs thermal yield than carrier fluid inflow rate in shorter CBHEs (63% vs 17% increase), which contradicts the behaviour of longer CBHEs in which the thermo-induced convective heat transfer in aquifers with higher permeability, i.e., k = 10 −10 m 2 and carrier fluid inflow rate could have a similar effect on the system’s efficiency (45% vs 43% increase). In general, it is concluded that an accurate evaluation of how system parameters such as the inflow rate and CBHE’s depth could contribute to CBHE’s thermal yield requires a good understanding of the impacts of aquifer’s characteristics, i.e., temperatures, permeability and depth on thermo-induced heat exchange in the aquifer, which is facilitated using the proposed numerical model.

Transient Axisymmetric Flows of Casson Fluids with Generalized Cattaneo’s Law over a Vertical Cylinder

Unsteady axial symmetric flows of an incompressible and electrically conducting Casson fluid over a vertical cylinder with time-variable temperature under the influence of an external transversely magnetic field are studied. The thermal transport is described by a generalized mathematical model based on the time-fractional differential equation of Cattaneo’s law with the Caputo derivative. In this way, our model is able to highlight the effect of the temperature gradient history on heat transport and fluid motion. The generalized mathematical model of thermal transport can be particularized to obtain the classical Cattaneo’s law and the classical Fourier’s law. The comparison of the three models could offer the optimal model of heat transport. The problem solution has been determined in the general case when cylinder surface temperature is described by a function f(t); therefore, the obtained solutions can be used to study different convective flows over a cylinder. In the particular case of surface temperature varying exponentially in time, it is found that fractional models lead to a small temperature rise according to the Cattaneo model.

Analysis of a kinetic model for electron heat transport in inertial confinement fusion plasmas

To determine the electron heat flux density on macroscopic scales, the most widely used approach is to solve a diffusion equation through a multi-group technique. This method is, however, restricted to transport induced by temperature gradients without accounting for other sources of fast electrons because the electric field induced by the charge separation is indirectly treated. In addition, significant discrepancies are reported in the underlying distribution function when compared to complete kinetic calculations. These limitations motivate the research for alternative reduced kinetic models. The physical content of one of them is here deepened, its precision is improved, and the benefit of its usage compared to other models is discussed.

Corrigendum: Quasilinear turbulent particle and heat transport modeling with a neural-network-based approach founded on gyrokinetic calculations and experimental data (2021 Nucl. Fusion 61 116041)

Corrigendum: Quasilinear turbulent particle and heat transport modeling with a neural-network-based approach founded on gyrokinetic calculations and experimental data (2021 Nucl. Fusion 61 116041)

A Validated Model, Scalability, and Plant Growth Results for an Agrivoltaic Greenhouse

We developed an agrivoltaic greenhouse (a ‘test cell’) that partially trapped waste heat from two photovoltaic (PV) panels. These panels served as parts of the roof of the enclosure to extend the growing season. Relative humidity, internal air temperature, incident solar radiation, wind speed, and wind direction were measured for one year. A locally 1-D transient heat and moisture transport model, as well as a shadowing model, was developed and validated with experimental data. The models were used to investigate the effects of altering various parameters of the greenhouse in a scalability study. The design kept test cell air temperatures generally above ambient throughout the year, with the test cell temperature below freezing for 36% less of the year than ambient. Plant growth experiments showed that kale, Brassica oleraceae, a shade-tolerant plant, can be grown within the test cell throughout the winter. The simulations showed that enlarging the greenhouse will increase cell air temperatures but that powering an electric load from the PV panels will reduce cell air temperatures.

Tuning quantum heat transport in magnetic nanostructures by spin-phonon interaction

The introduction of spin degree of freedom has not only made the electronic transport properties colorful, but also highly attracted people's attention to the spin-related quantum heat transport, with the rapid progress of spin caloritronics in recent year. Against this background, the modeling and tuning of quantum heat transport in magnetic nanostructures has become an emerging and attractive topic. In particular, the spin-phonon interaction has played a crucial role in the novel transport behaviors of heat and spin. In this perspective article, we give an insight into the current theoretical and experimental progresses and discuss the further research perspectives of spin-phonon interaction-related heat transfer.