Heat Transport Model Research Articles

Ballistic-Diffusive Heat Conduction in Thin Films by Phonon Monte Carlo Method: Gray Medium Approximation Versus Phonon Dispersion

Abstract The gray medium approximation treating all phonons with an averaged and representative mean-free-path (MFP) is an often used method in analyzing ballistic-diffusive heat conduction at nanoscale. However, whether there exists a reasonable value of the average MFP which effectively represents the entire spectrum of modal MFPs remains unclear. In this paper, phonon Monte Carlo (MC) method is employed to study the effects of the gray medium approximation on ballistic-diffusive heat conduction in silicon films by comparing with dispersion MC simulations. Four typical ways for calculating the average MFP with gray medium approximation are investigated. Three of them are based on the weighted average of the modal MFPs, and the remaining one is based on the weighted average of the reciprocals of the modal MFPs. The first three methods are found to be good at predicting effective thermal conductivity and heat flux distribution, but have difficulties in temperature profile, while the last one performs better for temperature profile than effective thermal conductivity and heat flux distribution. Therefore, none of the average MFPs can accurately characterize all the features of ballistic-diffusive heat conduction for the gray medium approximation. Phonon dispersion has to be considered for the accurate thermal analyses and modeling of ballistic-diffusive heat transport. Our work could be helpful for further understanding of phonon dispersion and more careful use of the gray medium approximation.

First-Order Comprehensive Adjoint Method for Computing Operator-Valued Response Sensitivities to Imprecisely Known Parameters, Internal Interfaces and Boundaries of Coupled Nonlinear Systems: II. Application to a Nuclear Reactor Heat Removal Benchmark

This work illustrates the application of a comprehensive first-order adjoint sensitivity analysis methodology (1st-CASAM) to a heat conduction and convection analytical benchmark problem which simulates heat removal from a nuclear reactor fuel rod. This analytical benchmark problem can be used to verify the accuracy of numerical solutions provided by software modeling heat transport and fluid flow systems. This illustrative heat transport benchmark shows that collocation methods require one adjoint computation for every collocation point while spectral expansion methods require one adjoint computation for each cardinal function appearing in the respective expansion when recursion relations cannot be developed between the corresponding adjoint functions. However, it is also shown that spectral methods are much more efficient when recursion relations provided by orthogonal polynomials make it possible to develop recursion relations for computing the corresponding adjoint functions. When recursion relations cannot be developed for the adjoint functions, the collocation method is probably more efficient than the spectral expansion method, since the sources for the corresponding adjoint systems are just Dirac delta functions (which makes the respective computation equivalent to the computation of a Green’s function), rather than the more elaborated sources involving high-order Fourier basis functions or orthogonal polynomials. For systems involving many independent variables, it is likely that a hybrid combination of spectral expansions in some independent variables and collocation in the remaining independent variables would provide the most efficient computational outcome.

Axial variability of pattern formation in Rayleigh-Bénard convection: MRI velocimetry in a low aspect ratio cylinder

Natural convection is a fundamental hydrodynamic instability and a template process for the study of pattern formation. It is also an important mode of energy transport in natural geophysical and environmental systems, as well as technological applications. In solar heating devices, pasteurization processes, industrial mixing, and pebble-bed nuclear reactors, low aspect ratio systems of greater depth than width are widely used for their favorable convection properties. Here, magnetic resonance imaging was used to quantify the axial spatial variation of flow patterns in a narrow cylinder. Fluid velocity maps were acquired in multiple transverse and longitudinal planes. It is shown that the flow patterns vary significantly as a function of the height above the heated bottom boundary. The large scale circulation varies among predicted azimuthal mode patterns. Azimuthal 180o reorientation of the upward and downward flow cells was observed over short axial distances. The complex circulation patterns observed suggest acquisition of velocity data in only one plane could lead to mischaracterization of flow patterns in low aspect ratios systems, an aspect of the current literature which is lacking quantification. A preliminary computational fluid dynamics model in STAR-CCM+, corroborated by the experimental results, provided velocity and temperature data for the full fluid column height. Together these results indicate the need for further investigation into circulation characteristics in long narrow cylinders. Enhanced understanding of these rapid axial variations in flow pattern will allow better modeling of heat and mass transport in low aspect ratio natural convection flows.

Coupling Flow, Heat, and Reactive Transport Modeling to Reproduce In Situ Redox Potential Evolution: Application to an Infiltration Pond

Redox potential (Eh) measurements are widely used as indicators of the dominant reduction-oxidation reactions occurring underground. Yet, Eh data are mostly used in qualitative terms, as actual values cannot be used to distinguish uniquely the dominant redox processes at a sampling point and should therefore be combined with a detailed geochemical characterization of water samples. In this work, we have intensively characterized the redox potential of the first meter of soil in an infiltration pond recharged with river water using a set of in situ sensors measuring every 12 min during a 1 year period. This large amount of data combined with hydrogeochemical campaigns allowed developing a reactive transport model capable of reproducing the redox potential in space and time together with the site hydrochemistry. Our results showed that redox processes were mainly driven by the amount of sedimentary organic matter in the system as well as by seasonal variation of temperature. As a subsidiary result, our work emphasizes the need to use a fully coupled model of flow, heat transport, solute transport, and the geochemical reaction network to fully reproduce the Eh observations in the topsoil.

A heat and mass transport model of clay pot evaporative coolers for vegetable storage

Clay pot coolers are low-cost technologies that can prolong vegetable shelf-life by providing a cool and humid storage environment through evaporative cooling. A predictive performance model of these systems is not available for investigating the impact of design modifications on device performance. This study proposes transport models for pot-in-pot and pot-in-dish coolers that have been validated with experimental data from 17 field trials from Mali and Rwanda with maximum errors of less than 6% observed. Results show that the pot-in-pot and pot-in-dish devices consume 1.96 and 2.85 L/day of water, respectively. A parametric study was conducted to evaluate how the refrigeration efficiency and daily water consumption are affected by the size of the device, local wind speed, and the mass of vegetables stored in the cooler. Increasing local wind speeds provides a net positive impact on refrigeration efficiency despite the increased convective heating. In addition, the quantity of vegetable mass showed a negligible impact on daily water consumption. Insights from the model suggest that water consumption is more efficient for larger devices.

Erratum: Impact de la reconstruction d’une rivière sur l’écoulement des eaux souterraines via la filtration sur berge évalué par un modèle tridimensionnel en régime transitoire de l’écoulement et du transport de chaleur

The original version of this article unfortunately contained mistakes.

Laser heating numerical simulation of titanium-containing optothermal fiber converter and vein wall during endovasal laser coagulation

Subject of Research. The paper presents numerical methods that first studied laser heating of titanium-containing optothermal fiber converter and vein wall, as well as the effect of thermal damage of the vein wall during endovasal laser coagulation with different average power of 980 nm semiconductor laser and the traction speed of the converter inside the vein. Method. Models and conditions for numerical simulation of optical and thermal physical processes were formulated, occurring during endovasal laser coagulation of veins using titanium-containing optothermal fiber converter. The Monte Carlo method was used in optical modeling. The initial-edge task for a non-linear model of radiation-conductive heat transport with moving sources of radiation was analyzed at thermal simulation by the method of finite dispositions. The effect of vein wall thermal damage was assessed as a result of solving the Arrhenius equation. Main Results. The titanium-containing optothermal fiber converter can be used for endovasal laser coagulation of veins by radiation of 980 nm laser with average power up to 20 W. Laser radiation is almost completely absorbed by the converter. With the simultaneous start of laser radiation and the beginning of traction, the temperature of the vein wall does not immediately reach the maximum value; the waiting time can reach units and even tens of seconds. The temperature inside converter exceeds 250 °C. The optimal combinations of average laser power and titanium-containing converter traction speed are defined for uniform coagulation of the vein wall. Practical Relevance. The results can be used in the development of laser methods and devices for endovasal laser coagulation of veins.

Validation of heat transport modeling using directly driven beryllium spheres

Recent experiments involving directly driven beryllium spheres are reported. Plasma conditions are measured using Thomson scattering with the probe beam pointed 200, 300, and 400 μm from the surface of the sphere. Laser coupling is assessed using calorimeters that collect scattered light placed at various locations within the target chamber. Laser intensities of 1014 W/cm2 and 2.5×1014 W/cm2 are chosen to minimize unmodeled laser-plasma interactions (LPIs) that lead to laser-target decoupling. Two-dimensional simulations are compared to the interpreted data using the radiation-hydrodynamics code Lasnex. Heat transport is simulated using flux-limited Spitzer–Harm with both high (f = 0.15) and low (f = 0.03) flux limiters and the Schurtz–Nicolai-Busquet (SNB) model. At 1014 W/cm2, all three heat transport models agree well with the measurement, demonstrating that the heat flux is local at low intensities near the measurement locations. At 2.5×1014 W/cm2, the SNB and high flux model roughly match the plasma conditions but predict 2% uncoupled light compared to 10% measured. The use of drive multipliers to match the measured coupled light does not alter the agreement between measured and simulated plasma conditions, suggesting that decoupling due to LPI is unlikely to alter this agreement. The low flux model cannot match the plasma conditions and results in 19% scattered light. The use of a resonant absorption model can be used to bring the simulated scattered light into agreement, but the simulated plasma conditions are still in disagreement with the measurement. For this reason, the low flux model is rejected.

Thermal, spalling, and mechanical behaviour of various types of cementitious composites exposed to fire: Experimental and numerical analysis

Nowadays, new types of cementitious composites are increasingly being used for the construction of structural members. This poses a problem regarding the structural fire safety design as the thermal behaviour and mechanical properties at high temperatures of these materials are usually not known. The main aim of this paper is to investigate and present the thermal behaviour, propensity to spalling, and residual strength of various types of cementitious composites exposed to fire. Namely, the following materials are investigated: ordinary normal-weight concrete with or without fibres, light-weight aggregate (LWA) concrete with or without fibres, recycled aggregate concrete with or without fibres, LWA concrete with open structure, and two novel cementitious composites – LWA concrete containing crushed textile and foam plastic, and concrete containing mineral wool insulation shreds. Additional aim of this investigation is to resolve whether widely-used simple transport and material models are suitable for numerical simulations of thermal behaviour of unusual cementitious composites. For the purposes of the investigation, experimental program was proposed and executed, and numerical simulations were performed. The experimental program consisted of fire test of wall-panel specimens and cube specimens in a vertical furnace and of measurement of physical and mechanical properties of the investigated materials. The numerical simulations consisted of finite element analysis of temperature evolutions in the wall-panel specimens. The paper summarizes the results and conclusions of the experimental and numerical investigations. Within the paper, compressive strengths and residual compressive strengths of the investigated materials are presented and discussed. Moreover, experimentally measured thermal behaviour is analysed and compared with the thermal behaviour predicted by numerical simulations. In addition to this, spalling behaviour and surface damage of the specimens made of the investigated materials are presented and discussed. The main conclusion of this paper is that widely-used simple heat transport and material models are suitable for numerical simulations of thermal behaviour of various cementitious composites. Additional important conclusion is that concrete containing mineral wool shreds performs very well when subjected to fire.

Multi-fidelity approach to Bayesian parameter estimation in subsurface heat and fluid transport models

The increased use of the urban subsurface for competing purposes, such as anthropogenic infrastructures and geothermal energy applications, leads to an urgent need for large-scale sophisticated modelling approaches for coupled mass and heat transfer. However, such models are subject to large uncertainties in model parameters, the physical model itself and in available measured data, which is often rare. Thus, the robustness and reliability of the computer model and its outcomes largely depend on successful parameter estimation and model calibration, which are hampered by the computational burden of large-scale coupled models.To tackle this problem, we develop a novel Bayesian approach for parameter estimation, which allows us to account for different sources of uncertainty, is capable of dealing with sparse field data and makes optimal use of the output data from expensive numerical model runs. This is achieved by combining output data from different models that represent the same physical problem, but at different levels of fidelity, e.g. reflected by different spatial resolution. By applying this new approach to a 1D analytical heat transfer model and a large-scale semi-3D numerical model while using synthetic data, we show that the accuracy and precision of parameter estimation by this multi-fidelity framework by far exceeds the standard single-fidelity results. The consideration of different error terms in the Bayesian framework also allows assessment of the model bias and the discrepancy between the different fidelity levels. These are emulated by Gaussian Process models, which facilitate re-iteration of the parameter estimation without additional model runs.

A non-local heat transport model in solids with discontinuities via Lagrangian particle method

A new Lagrangian non-local diffusion model, designed as a meshless particle simulation method, is proposed to predict the thermal response of solids involving discontinuous. The main idea is to understand the heat transfer process of solids via a Lagrangian treatment of a particle-discretized system, which provides a more general physical representation of the heat transfer process of solids. In contrast to the traditional differential model, the proposed mathematical model is expressed via an integral form, which can easily handle the case involving discontinuities. The spatial convergence studies show that the proposed model converges to its associated non-local solution while increasing the number of particles in a fixed cut-off radius; and it can reach the local exact solution when the cut-off radius is close to zero. The numerical examples not only verify that the proposed diffusion model converges to the continuum heat conduction model, but also show the capability of its application to heat transfer problems involving discontinuities. In particular, the computational performance of the proposed non-local thermal model is also demonstrated its computational performance in the case with practical crack propagation in a two-dimensional plate. In addition, the specific comparison between the proposed method and the well-developed peridynamics approach for heat conduction problems is carefully described with rigor via mathematical proofs and numerical results. Specifically, the proposed model is shown to be a variation of the corresponding peridynamic-type thermal diffusion model. This model not only has a formulation consistent with that of peridynamics in solid mechanics but also shows a better performance in the case with sharp corners than that of the peridynamic diffusion in [1].

Modeling Groundwater Inflow to the New Crater Lake at Kīlauea Volcano, Hawai'i.

During the 2018 eruption of Kīlauea Volcano, Hawai'i, scientists relied heavily on a conceptual model of explosive eruptions triggered when lava-lake levels drop below the water table. Numerical modeling of multiphase groundwater flow and heat transport revealed that, contrary to expectations, liquid water inflow to the drained magma conduit would likely be delayed by months to years, owing to the inability of liquid water to transit a zone of very hot rock. The summit of Kīlauea subsequently experienced an ∼2-month period of consistent repeated collapses, and the crater now extends below the equilibrium position of the water table. Liquid water first emerged into the deepened crater in late July 2019. The timing of first appearance of liquid water (about 14 months postcollapse) and the rate of crater lake filling (currently ∼27 kg/s) were well-predicted by the numerical modeling done in late spring 2018, which forecast liquid inflow after 3 to 24 months at rates of 10 to 100 kg/s. A second-generation groundwater model, reflecting the current crater geometry, forecasts lake filling over the next several years. The successful 2018 to present forecasts with both models are based on unadjusted in situ permeability estimates (1 to 6 × 10-14 m2 ) and water-table elevations (600 to 800 m) from a nearby research drillhole and geophysical surveys. Important unknowns that affect the reliability of longer-term forecasts include the equilibrium water-table geometry, the rate of evaporation from the hot and growing crater lake (currently ∼29,000 m2 at 70-80 °C), and heterogenous permeability changes caused by the 2018 collapse.

Analysis of heat conduction in a nanoscale metal oxide semiconductor field effect transistor using lattice Boltzmann method

ABSTRACT Thermal transport in the microelectronic devices has been widely investigated to enhance its reliability. Within this context, Metal Oxide Semiconductor Field Effect Transistor (MOSFET) represents the most used technology for electronic devices manufacturing. Due to its size reduction, the macroscopic model for MOSFET device requests some modifications for capturing thermal behavior within it. Hence, a precise mathematical model for phonon heat transport into transistors has become a key task for nano-electronics technology. The present work aims to investigate the ability of a mesoscale mathematical model for the heat conduction in a MOSFET at a Knudsen number of 10. The reported model was based on D2Q8 lattice Boltzmann model coupled with jump temperature boundary condition. The thermal source was supposed to be uniform along the MOSFET channel region. The temperature jump boundary condition was applied and treated by Lattice Boltzmann Method (LBM) in order to reveal the nature of the phonon-wall collisions lengthwise the channel. We have found that the behavior of the proposed model agrees with experimental results in terms of peak temperature rising. Furthermore, the maximum temperature in the interface (Si-SiO2) is around 333 K. In addition, the results show that 30 ps is enough to reach the steady-state condition. The gained results indicate that the LBM joined with jump temperature condition provides accurate results and it can be employed for analyzing heat transfer phenomenon in microelectronic devices.

Sparse thermal data for cellular automata modeling of grain structure in additive manufacturing

Grain growth in the wake of the melt pool formed during alloy-based additive manufacturing (AM) is complex and multifaceted, depending on parameters governing heat transport, fluid flow, and solidification itself. Cellular automata (CA) models have proven effective in providing computationally efficient and physically sound predictions of grain structure for several AM problems, but their efficiency is tied to the performance of heat transport models. CA models use only a small portion of the problem’s temperature data (near the moving melt pool boundary), and much of the CA calculations do not affect the final result due to re-melting of material. Coupling of and communication between heat transport and solidification models, and eliminating operations irrelevant towards final grain structure prediction, will be necessary for using these methods for efficient simulation of large parts. We introduce a procedure of decoupling the CA from temperature field simulation, using files of relevant temperature data written by the heat transport model. This approach is validated against the standard coupling approach using data obtained through the computational fluid dynamics software OpenFOAM. Negligible differences are seen in grain size, volume, and texture distributions for multilayer simulation of test problems, while the quantity of temperature data for these test problems was reduced by four orders of magnitude (from 100s of GB to 10s of MB) and the code performance sped up by a factor of around 50. Variability in microstructure as a function of cell size, substrate, time step, and nucleation parameters is studied, and it is found that cell sizes less than or equal to 1.67 μm and sufficiently small time steps yield statistically equivalent microstructures. Finally, a potential use case for this CA approach—the layer-wise convergence in grain structure starting from extremes in initial grain size—is examined. This approach’s ability to simulate expected trends in nucleation and epitaxial grain growth for large regions of microstructure, simulated independently of heat transport models themselves, should prove useful for investigation of various microstructure uncertainties and prediction of part-scale experimental results.

Evaluation of Heat Effects on Transdermal Nicotine Delivery In Vitro and In Silico Using Heat-Enhanced Transport Model Analysis.

A combined experimental and computational model approach was developed to assess heat effects on drug delivery from transdermal delivery systems (TDSs) in vitro and nicotine was the model drug. A Franz diffusion cell system was modified to allow close control of skin temperature when heat was applied from an infrared lamp in vitro. The effects of different heat application regimens on nicotine fluxes from two commercial TDSs across human cadaver skin were determined. Results were interpreted in terms of transport parameters estimated using a computational heat and mass transport model. Steady-state skin surface temperature was obtained rapidly after heat application. Increasing skin surface temperature from 32 to 42°C resulted in an approximately 2-fold increase in average nicotine flux for both TDSs, with maximum flux observed during early heat application. ANOVA statistical analyses of the in vitro permeation data identified TDS differences, further evidenced by the need for a two-layer model to describe one of the TDSs. Activation energies associated with these data suggest similar temperature effects on nicotine transport across the skin despite TDS design differences. Model simulations based on data obtained from continuous heat application were able to predict system response to intermittent heat application, as shown by the agreement between the simulation results and experimental data of nicotine fluxes under four different heat application regimens. The combination of in vitro permeation testing and a computational model provided a parameter-based heat and mass transport approach to evaluate heat effects on nicotine TDS delivery.

Hyperbolic thermal-plasma wave propagation in semiconductor of organic material

Although the thermo-viscoelastic properties of solids have been reported in many articles, no effort has been made to investigate the coupled thermo-viscoelastic and plasma wave behavior of semiconductors based on the photothermal theory. In this work, a new mathematical model of heat and plasma transport has been constructed for semiconductor of viscoelastic material. Some fundamental theorems on the linear coupled and generalized theories can be easily obtained as special cases. A two-dimensional problem is viewed for a half-space of an organic semiconductor plate whose surface is traction free and subjected to an arbitrary time-dependent heat flux. Laplace and Fourier integral transforms are utilized. The carrier density, temperature, thermal stress, and displacement distributions have been obtained through the use of the theoretical model together with plasma and thermo-viscoelastic effects. The inversion technique for Fourier and Laplace transforms is carried out using a numerical technique based on Fourier series expansions. Comparisons are made with the results anticipated through the coupled idea and generalized theory. The influence of the some parameters on all the regarded fields is examined for different theories.

A dynamic Spatially Averaged Two-Fluid Model for heat transport in moderately dense gas–particle flows

In this study, we derive a spatially averaged two-fluid model for heat transport in moderately dense gas–particle flows. In the context of multiphase turbulence modeling, closure models for the unresolved terms in the filtered transport equations in the presence of mesoscale heterogeneous particle clusters are postulated. In analogy to the drift velocity correction for the resolved gas–particle drag force, we propose to approximate the filtered interphase heat transfer by the resolved heat transfer corrected by a drift temperature. This drift temperature represents the gas-phase temperature fluctuations seen by the particles and can be expressed as a correlation between the solid volume fraction variations and the gas-phase temperature fluctuations, i.e., the turbulent internal energy. Therefore, transport equations for the turbulent internal energies of the phases are derived, where a cluster-induced turbulence production term arises in the gas-phase. Except for the interphase exchange terms, we find that closure models based on single phase turbulence modeling can be applied to the unresolved terms in the transport equations for both the filtered and turbulent internal energies. The interphase exchange terms can be expressed by the variances of the temperatures scaled by correlation coefficients. A dynamic adjustment of the correlation coefficients by using test-filters in coarse-grid simulations is proposed. In an a priori study, the developed closure models show good agreement with the predictions obtained by filtering fine-grid, two-fluid model simulation data of Geldart type A and B particles in three-dimensional wall-bounded fluidized beds.

Nonlocal electron heat transport under the non-Maxwellian distribution function

In laser plasmas, the electron distribution function is not Maxwellian but super-Gaussian due to the inverse bremsstrahlung heating, and the electron heat transport is generally nonlocal because of the large Knudsen number. Starting from the Fokker–Planck equation, we develop a nonlocal electron heat transport model based on the non-Maxwellian distribution function. In our study, we follow the method in Schurtz et al. [Phys. Plasmas 7, 4238 (2000)] and derive a differential equation for calculating the nonlocal electron heat flux based on the non-Maxwellian distribution function. The numerical results show that the non-Maxwellian distribution function would reduce the nonlocal heat flux in the laser heated region. The preheat effect due to nonlocal electron heat transport in the conduction region is also reduced by the non-Maxwellian distribution function. This nonlocal electron heat transport model can be easily implemented in two-dimensional and three-dimensional hydrodynamics codes.

Experimental Validation of Heat Transport Modelling in Large Solar Thermal Plants

Solar thermal plants are often considered as a convenient and environmentally friendly way to supply heat to buildings or low temperature industrial processes. Some modelling techniques are required to assess the dynamic behaviour of solar thermal plants in order to control them correctly. This aspect is reinforced while large plants are considered. Indeed, some atmospheric conditions, such as local clouds, could have significant influence on the outlet temperature of the solar field. A common modelling approach to assess the heat transport in pipes is the one-dimensional finite volume method. However, previous work shows limitations in the assessment of the temperatures and in the computational time required for simulating large pipe networks. In this contribution, a previous alternative method developed and validated in a district heating network is used and extended to a solar thermal plant considering the thermal solar gain and the inertia of the pipes. The present contribution intends to experimentally validate this model on an existing solar plant facility available at the Plataforma Solar de Almeria in Spain.

Numerical Modeling of Heat and Mass Transport with Inner Heat Exchange in Unsaturated Porous Media

We are focused to the numerical modelling of heat, contaminant and water transport in unsaturated porous media in 3D. The heat exchange between water and porous media matrix is taken into the account. The determination of heat energy transmission coefficient and matrix heat conductivity is solved by means of inverse problem methods. The mathematical model represents the conservation of heat, contaminant and water mass balance. It is expressed by coupled non-linear system of parabolic-elliptic equations. Mathematical model for water transport in unsaturated porous media is represented by Richard's type equation. Heat transport by water includes water flux, molecular diffusion and dispersion. A successful experiment scenario is suggested to determine the required parameters including heat transmission and matrix heat conductivity coefficients. Additionally we investigate contaminant transport with heat transmission and contaminant adsorption. The obtained experiments support our method suitable for solution of direct and inverse problems. This problem we have discussed previously in 1D model, but preferential streamlines in 1D thin tubes shadow accurate results in determination of required parameters. In our presented setting we consider a cylindrical sample which is suitable in laboratory experiments for inverse problems.