Time-dependent Temperature Profiles Research Articles

Gyrokinetic flux-driven simulations in mixed TEM/ITG regime using a delta-f PIC scheme with evolving background

In the context of global gyrokinetic simulations of turbulence using a particle-in-cell framework, verifying the delta-f assumption with a fixed background distribution becomes challenging when determining quasi-steady state profiles corresponding to given sources over long time scales, where plasma profiles can evolve significantly. The advantage of low relative sampling noise afforded by the delta-f scheme is shown to be retained by considering the background as a time-evolving Maxwellian with time-dependent density and temperature profiles. Implementation of this adaptive scheme to simulate electrostatic collisionless flux-driven turbulence in tokamak plasmas show small and nonincreasing sampling noise levels, which would otherwise increase indefinitely with a stationary background scheme. The adaptive scheme furthermore allows one to reach numerically converged results of quasi-steady state with much lower marker numbers.

Temperature evolution of laser-ignited micrometric iron particles: A comprehensive experimental data set and numerical assessment of laser heating impact

This study examines the effects of laser heating on the ignition and critical combustion characteristics, such as temperature and burn time, of individual iron particles. It provides time-dependent temperature profiles of laser-ignited particles across a broad spectrum of particle size distributions and oxygen concentrations obtained from experiments, which are a useful database for further development and validation of iron particle combustion models. The herein reported datasets significantly complement those existing in the literature. In the current study, the raw data are thoroughly re-evaluated using refined approaches. For the experimental canonical configuration of single iron particle combustion, an ignition system based on laser heating provides several advantages in overcoming temperature field uncertainties and facilitating controlled environments for optical diagnostics. Despite the inherent uncertainties in laser heating, associated with non-uniform intensity profiles and particle size variations, this study addresses the critical question of how these uncertainties affect in situ measurements of particle temperature and time to reach peak temperature. This study, conducted using a numerical model, reveals a dependence of the particle temperature after laser heating on particle size. However, this dependence does not significantly impact the key parameters of iron-particle combustion, such as the maximum temperature and burn time of the laser-ignited iron particle. The study also presents a comparison between the simulated particle temperature histories and those derived from two-color pyrometry measurements for a wide range of particle size distributions and oxygen concentrations. Notably, by implementing a laser-heating sub-model into an iron particle combustion model, assuming external-diffusion-limited oxidation only up to stoichiometric FeO, the temperature evolution up to the maximum temperature is reasonably captured for a wide range of particle sizes (20–53μm) and oxygen volumetric fractions (14–21vol% O2 mixed with N2). However, with increasing oxygen concentration, the external-diffusion limited model significantly overestimates the heating rate and subsequently the maximum particle temperature.

Functional PCA and deep neural networks-based Bayesian inverse uncertainty quantification with transient experimental data

This work focuses on developing an inverse uncertainty quantification (IUQ) process for time-dependent responses, using dimensionality reduction by functional principal component analysis (PCA) and deep neural network (DNN)-based surrogate models. The demonstration is based on the IUQ of TRACE physical model parameters using the FEBA benchmark transient experimental data on peak cladding temperatures during reflooding. The quantity-of-interest (QoI) is time-dependent peak cladding temperature (PCT) profiles. Conventional PCA can hardly represent the data precisely due to the sudden temperature drop at the time of quenching. As a result, a functional alignment method is used to separate the phase and amplitude information in the PCT profiles before conventional PCA is applied for dimensionality reduction. The resulting PC scores are then used to build DNN-based surrogate models to significantly reduce the computational cost in Markov Chain Monte Carlo sampling, while the code/interpolation uncertainty is accounted for using Bayesian neural networks. We compared four IUQ processes with different dimensionality reduction methods and surrogate models. The proposed approach has demonstrated the best performance in reducing the dimensionality of the transient PCT profiles. This approach also produces the posterior distributions of the physical model parameters with which the model predictions have the best agreement with the experimental data.

Dynamic thermal analysis of pulsed blue diode pumped Ti:Sapphire amplifiers

We simulated the time-dependent temperature profiles inside a blue diode pumped Ti:Sapphire (Ti:Sa) laser amplifier for several different pulsed pump configurations using a discrete element method, including temperature-dependent thermal conductivity and specific heat capacity of Ti:Sa crystals. Furthermore, we calculated the resulting focal length of the thermal lenses using the optical path differences through the crystal.

Comparative analysis of time dependent temperature profiles of hydrating mass concretes of different mix ratios

In mass concrete, heat due to cement hydration in most cases is not easily released and is otherwise confined within its core. Consequently, mass concrete may exhibit quite remarkable increase in temperatures internally depending on majorly the vicinity temperature and the proportion of cement in mixture ratio. When the surface tensile stresses resulting from temperature difference between its core and surface exceeds the strength of the concrete, cracks could develop at the surface. Two mass concrete blocks of dimensions 1.10 m × 1.10 m × 1.10 m each and mixes of 1: 2: 4 and 1: 3: 6 with constant water cement ratio (w/c) of 0.60 were used in the study. Type-K thermocouples were used to monitor the temperature variance in mass concretes. BK Precision 710 temperature meter dual input was used to determine the temperature readings at time intervals. Thermometer was used to measure the environment temperatures within the vicinity of the mass concretes. Generally, the trends of the temperature profiles exhibit an initial uniform temperature which rises to peak values at 24 hours of concrete placement and then declined to constant temperature at mostly 120 hours and beyond. The sole source of heat in hydrating concrete is the cement paste, and higher cement content leads to higher quantity of heat release. Therefore, the mass concrete block of mix ratio 1:2:4 exhibited higher quantity of heat release than that of 1:3:6 especially at the core.

Application of finite difference method to 2D heat conduction in young hydrating mass concretes structures.

Finite Difference Method is a numerical approximation scheme usually applied in solving differential equations derived from the knowledge of the behaviour of engineering systems. Due to the unsteady state nature of cement hydration and heat conduction in concretes, Crank Nicholson implicit approach was adopted. Concrete block of size 1.10 m x 1.10 m x 1.10 m, cast with mix ratio 1:3:6, probed thermocouples and digital thermometer were used to verify the numerical computational analysis. The temperature profile depicted a relatively hot core, with peak temperature values occurring at 24 hours of placement. Implicit finite difference method was utilized in determining time dependent temperature profile within mass concretes at early ages. The paper could provide a guide towards proactive decision making in terms of controlling thermal cracks.

Structure-function relationships in the nasal cavity of Arctic and subtropical seals

The heating and moistening of inhaled air, and the cooling and moisture removal from exhaled air, are crucial for the survival of animals under severe environmental conditions. Arctic mammals have evolved specific adaptive mechanisms to retain warmth and water and restrict heat loss during breathing. Here, the role of the porous turbinates of the nasal cavities of Arctic and subtropical seals is studied with this in mind. Mass and energy balance equations are used to compute the time-dependent temperature and water vapor profiles along the nasal passage. A quasi-1D model based on computed tomography images of seal nasal cavities is used in numerical simulations. Measured cross-sectional areas of the air channel and the perimeters of the computed tomography slices along the nasal cavities of the two seal species are used. The model includes coupled heat and vapor transfer at the air-mucus interface and heat transfer at the interfaces between the tissues and blood vessels. The model, which assumes constant blood flow to the nose, can be used to predict the temperature of the exhaled air as a function of ambient temperature. The energy dissipation (entropy production) in the nasal passages was used to measure the relative importance of structural parameters for heat and water recovery. We found that an increase in perimeter led to significant decreases in the total energy dissipation. This is explained by improved conditions for heat and water transfer with a larger complexity of turbinates. Owing to differences in their nasal cavity morphology, the Arctic seal is expected to be advantaged in these respects relative to the subtropical seal.

Analysis of a thick cylindrical FGM pressure vessel with variable parameters using thermoelasticity

Abstract In this study, a closed-form analytical solution is derived to compute the stress formulations for a thick cylindrical pressure vessel made of functionally graded material (FGM) with varying parameters, which are mechanical and thermal boundary conditions. The assumed mechanical boundary condition is the time-dependent pressure acting on the internal surface of the cylinder, while the assumed thermal boundary condition is the transient temperature distribution over the cylinder thickness. The material properties are considered to be graded exponentially in the radial direction, except Poisson’s ratio which is assumed to be constant. The stress and displacement formulations are evaluated using Mathematica software for the uncoupled thermo-mechanical analysis. The results of radial, hoop, and axial stress are plotted at various times for two FGM cylinders, the SS304-Alumina FGM cylinder and the TZM-SIC FGM cylinder, to study the impact of using different materials for the same boundary conditions on the results. The results obtained in this study are beneficial as these contribute to the design and modeling of cylinders that are exposed to time-dependent internal pressure and transient temperature profiles.

Revisiting “Non-Thermal” Batch Microwave Oven Inactivation of Microorganisms

Over the last few decades there has been active discussion concerning the mechanisms involved in “non-thermal” microwave-assisted inactivation of microorganisms. This work presents a novel non-invasive acoustic measurement of a domestic microwave oven cavity-magnetron operating at fo = 2.45 ± 0.05 GHz (λo ~ 12.2 cm) that is modulated in the time-domain (0 to 2 minutes). The measurements reveal the cavity-magnetron cathode filament cold-start warm-up period and the pulse width modulation periods (time-on time-off and base-time period, where time-on minus base-time = duty cycle). The waveform information is used to reconstruct historical microwave “non-thermal” homogeneous microorganism inactivation experiments: where tap-water is used to mimic the microorganism suspension; and ice, crushed ice, and ice slurry mixture are used as the cooling media. The experiments are described using text, diagrams, and photographs. Four key experimental parameters are indentified that influence the suspension time-dependent temperature profile. First, where the selected process time > the time-base, the cavity-magnetron continuous wave rated power should be used for each second of microwave illumination. Second, external crushed ice and ice slurry baths induce different cooling profiles due to difference in their heat absorption rates. In addition external baths may shield the suspension resulting in a retarding of the time-dependent heating profile. Third, internal cooling systems dictate that the suspension is directly exposed to microwave illumination due to the absence of surrounding ice volume. Fourth, four separated water dummy-loads isolate and control thermal heat transfer (conduction) to and from the suspension, thereby diverting a portion of the microwave power away from the suspension. Energy phase-space projections were used to compare the “non-thermal” energy densities of 0.03 to 0.1 kJ·m-1 at 800 W with reported thermal microwave-assisted microorganism inactivation energy densities of 0.5 to 5 kJ·m-1 at 1050 ± 50 W. Estimations of the “non-thermal” microwave-assisted root mean square of the electric field strength are found to be in the range of 22 to 41.2 V·m-1 for 800 W.

Gyrokinetic simulations of turbulence and zonal flows driven by steep profile gradients using a delta-f approach with an evolving background Maxwellian

Long global gyrokinetic turbulence simulations are particularly challenging in situations where the system deviates strongly from its initial state and when fluctuation levels are high, for example, in strong gradient regions. For particle-in-cell simulations, statistical sampling noise accumulation from large marker weights due to large deviations from the control variate of a delta-f scheme makes such simulations often impractical. An adaptive control variate in the form of a flux-surface-averaged Maxwellian with a time-dependent temperature profile is introduced in an attempt to alleviate the former problem. Under simplified collisionless physics, this adaptive delta-f scheme is shown to reduce noise accumulation in the zonal flows and the simulated heat flux in a quasi-steady turbulent state. The method also avoids the collapse of the signal-to-noise ratio, which occurs in the standard non-adaptive scheme, and, therefore, allows one to reach numerically converged results even with lower marker numbers.

Method to Estimate Thermal Transients in Reactors and Determine Their Parameter Sensitivities without a Forward Simulation

Thermal response time is an important parameter for the control of fast reactors. Modern thermal hydraulic codes allow for the modeling of transient responses and can also be used to understand the dominant factors that affect them. However, simulations can be computationally expensive, particularly for performing parametric analyses of how thermophysical properties affect transient behavior. Here, we present a method for using linear stability analysis to estimate thermal response time and determine the key parameters that affect transient behavior without performing a forward simulation. The approach can also be used to corroborate simulation results and is tested against simulation results produced with a 2D finite difference model. The results show that this approach produces time-dependent temperature profiles that are within 2 × 10−5–0.1% of the numerical results for a single node perturbation. Changes in temperature have the greatest effect on thermal response time, followed by changes to thermal conductivity.

Electron temperature gradient driven transport model for tokamak plasmas

A new model for electron temperature gradient (ETG) modes is developed as a component of the multi-mode anomalous transport module [Rafiq et al., Phys Plasmas 20, 032506 (2013)] to predict a time-dependent electron temperature profile in conventional and low aspect ratio tokamaks. This model is based on two-fluid equations that govern the dynamics of low-frequency short- and long-wavelength electromagnetic toroidal ETG driven drift modes. A low collisionality NSTX discharge is used to scan the plasma parameter dependence on the ETG real frequency, growth rate, and electron thermal diffusivity. Electron thermal transport is discovered in the deep core region where modes are more electromagnetic in nature. Several previously reported gyrokinetic trends are reproduced, including the dependencies of density gradients, magnetic shear, β and gradient of β (β′), collisionality, safety factor, and toroidicity, where β is the ratio of the plasma pressure to the magnetic pressure. The electron heat diffusivity associated with the ETG mode is discovered to be on a scale consistent with the experimental diffusivity determined by power balance analysis.

Multitemperature Modeling of Thermal Transport across a Au–GaN Interface from Ab Initio Calculations

With device dimensions shrinking toward nanoscale sizes, an accurate understanding and modeling of the thermal energy transfer mechanisms at metal–nonmetal interfaces becomes highly desirable. To model the thermal transport across the Au–GaN interface, we developed a general multitemperature model (MTM) that accounts for both electron and phonon transport and allows for a nonequilibrium phonon population described as a sum of thermal distributions of the phonon branches. The model is populated with material parameters computed from ab initio calculations and used to describe the temperature profile across a Au–GaN junction 400 nm in length subjected to constant temperature differential, continuous-wave laser heating of Au, and constant heat flux on GaN. The calculated steady-state and time-dependent temperature profiles reveal strongly nonequilibrium electron–phonon and phonon–phonon interfacial regions created through energy carrier coupling. Our results indicate that a multitemperature-based model is required for the accurate resolving of the thermal energy flow across metal–nonmetal interfaces. Our MTM will advance the theoretical tool to investigate nonequilibrium thermal transport across metal–nonmetal interfaces.

A multilayered approach to scale-up forced convection-based freezing of human induced pluripotent stem cells

This work presents a multilayered model-based approach to scale-up slow and forced convection-based freezing of human induced pluripotent stem cells. The approach combines a hybrid single-cell freezing model (covering the cell and cryovial layers) with a computational fluid dynamics model (covering the freezer layer). The proposed approach can calculate the cell survival rate considering spatial and time-dependent temperature profiles within a freezer unit. The approach was first demonstrated on a single cryovial problem where it was found that the inlet coolant velocity affected the cell survival rate when fast cooling rates were applied. The freezing of 235 cryovials was then studied, where 18 operation conditions consisting of six cooling rates (three constant and non-constant cooling rates, respectively) and three inlet coolant velocities were investigated. The multilayered approach captured the spatial heterogeneity in the cell survival rates for a given inlet coolant velocity and temperature profile.

Biot’s Variational Method to determine the thermal strain in layered glazings

A critical issue in the structural design of glazed surfaces is the evaluation of the strain consequent to temperature variations due to environmental actions such as solar radiation, which represents one of the main causes of breakage. In the practice, approximate solutions are used, where the temperature profile across the glass thickness is constant or linear, but the consequent thermal stress cannot be adequately estimated from these. On the other hand, sophisticated thermal software is available only for important tasks.Here, we propose a semi-analytical approach, easily implementable in a simple FEM code, to evaluate the time-dependent temperature profile through the thickness of layered glazing, which is based on the variational method proposed by Biot in the Fifties. A prompt evaluation not only of the temperature field, but also of the heat flux, can be obtained. Compared to other numerical approaches, this method rigorously accounts for energy conservation and, since it does not involve temperature gradients in the formulation, it is particularly efficient for problems with steep temperature variations. Temperature profiles that are not necessarily linear can be approximated by Hermite–splines, for a precise evaluation of the thermally-induced stress. Comparisons with a direct numerical solution of the heat-conduction differential equations confirm the accuracy and the effectiveness of the proposed approach.

Simulation of Heat Transfer in Laser Transmission Welding

Abstract A numerical simulation of the heat transfer during laser transmission welding is presented. A finite difference approach was used to solve the one-dimensional unsteady-state heat conduction problem and to investigate the effect of welding conditions on the time-dependent temperature profiles for PA 6. For the needs of the simulation, the process was divided into heating and heat redistribution periods. The absorption coefficient of the laser-transparent part was measured experimentally and that of the laser-absorbing part was fitted using experimental data. The predicted temperature profiles were combined with experimental meltdown data to estimate the heat-affected zone thickness in the welded specimens. Good agreement was found between the estimated and measured heat-affected zone thickness values.

Modelling dynamic 3D heat transfer in laser material processing based on physics informed neural networks

Machine learning algorithms make predictions by fitting highly parameterized nonlinear functions to massive amounts of data. Yet those models are not necessarily consistent with physical laws and offer limited interpretability. Extending machine learning models by introducing scientific knowledge in the optimization problem is known as physics-based and data-driven modelling. A promising development are physics informed neural networks (PINN) which ensure consistency to both physical laws and measured data. The aim of this research is to model the time-dependent temperature profile in bulk materials following the passage of a moving laser focus by a PINN. The results from the PINN agree essentially with finite element simulations, proving the suitability of the approach. New perspectives for applications in laser material processing arise when PINNs are integrated in monitoring systems or used for model predictive control.

Heat Transfer-Based Non-isothermal Healing Model for the Interfacial Bonding Strength of Fused Filament Fabricated Polyetheretherketone.

Fused Filament Fabrication (FFF) as an Additive Manufacturing (AM) method for Polyetheretherketone (PEEK) has established a promising future for medical applications so far, however interlayer delamination as a failure mechanism for FFF implants has raised critical concerns. A one-dimensional (1D) heat transfer model (HTM) was developed to compute the layer and interlayer temperatures by considering the nature of 3D printing for FFF PEEK builds. The HTM was then coupled with a non-isothermal healing model to predict the interlayer strength through thickness of a FFF PEEK part. We then conducted a parametric study of the primary temperature effects of the FFF system, including the print bed, nozzle, and chamber temperatures, on layer healing. The heat transfer component of the model for the FFF PEEK layer healing assessment was validated separately. An idealized PEEK cube design (10x10x10 mm3) was used for model development and 3D printed in commercially available industrial and medical FFF machines. During the printing and cooling processes of FFF, thermal videos were recorded in both printers using a calibrated infrared camera. Thermal images were then processed to obtain time-dependent layer temperature profiles of FFF PEEK prints. Both the theoretical model and experiments confirmed that the upper layers in reference to the print bed exhibited higher temperatures, thus higher healing degrees than the lower layers. Increasing the print bed temperature increased the healing of the layers allowing more layers to heal 100%. The nozzle temperature showed the most significant effect on the layer healing, and under certain nozzle temperature, none of the layers healed adequately. Although environment temperature had less impact on the lower layers closer to the print bed, 100% healed layer number increased when the chamber temperature increased. The model predictions were in good agreement with the experimental data, particularly for the mid-part of FFF PEEK cubes printed in both FFF machines.

Investigation on Suitability of Argillaceous Rocks of Vindhyan Super Group as Host Rock for Deep Geological Repository using Thermal Analysis

Argillaceous rocks are being considered as a potential host rock for deep geological repository (DGR) for hosting vitrified high level radioactive waste canisters by many countries worldwide. Numerical simulation of thermal evolution in the repository environment is an important study for the long term safety performance assessment of a DGR. In this study, thermal dissipation in the near field area of a conceptual repository in Ganurgarh shales from Bhander Group of Vindhyan Super Group, which is the thickest sedimentary succession of India, has been simulated using commercial software FLAC3D, which solves the governing heat diffusion equation using explicit and implicit finite difference methods. Model parameters like thermal conductivity, specific heat, density of the shales are generated in the laboratory. From the analysis of time dependent temperature profile it is observed that maximum temperature of 70.5oC is attained at canister surface after 22 years of heating for a heat loadings of 500 W/overpack. Since the maximum temperature is well below the permissible limit of temperature (100oC), the heat load of the source is increased to 700 W/overpack and in this case the simulated value of maximum temperature is 93­oC. Maximum temperatures at other locations within the near field region are also within the permissible limit.

Transient free convection of variable viscosity liquid in an inclined cube affected by the temperature modulation on a vertical wall

Convective energy transport can be found in various engineering and nature systems. From practical point of view this transport phenomenon within engineering cabinets can be progressed in the presence of temperature modulation. In this research, the transient natural convective heat transference of a temperature-dependent viscosity liquid inside an inclined cube in the presence of time-dependent temperature profile at one vertical bounded surface is investigated. The opposite vertical border is kept at permanent low temperature, whilst other surfaces are thermally insulated. Partial differential equations formulated using dimensionless non-primitive characteristics with appropriate restrictions are worked out by the finite difference technique. Impacts of the domain tilted angle, and wall temperature oscillation frequency on energy transport and flow structures are scrutinized.