Time Temperature Distribution Research Articles

How to Crystallize Glass with a Femtosecond Laser

The crystallization of glass through conventional thermal annealing in a furnace is a well-understood process. However, crystallization by femtosecond (fs) laser brings another dimension to this process. The pulsed nature of the irradiation necessitates a reevaluation of the parameters for optimal crystallization and an understanding of the particularities of using fs laser. This includes adjusting the laser pulse energy, the repetition rate, and the writing speed to either initiate nucleation or achieve substantial crystal growth. Therefore, a key challenge of this work is to establish reliable calculations for understanding the link between the size of the crystallized region and an ongoing transition (e.g., solid-to-solid, liquid-to-solid), while accounting for the aforementioned laser parameters. In this context, and based on previous work, a temperature distribution (in space and time) is simulated to model the thermal treatment at any point in the glass. By setting the condition that the temperatures are between the glass transition and melting temperature, the simulated crystallized region size can be compared with experimental observations. For that purpose, knowledge of the beam width at the focal point and of the absorbed beam energy fraction are critical inputs that were extracted from experiments found in the literature. After that, the management of the crystallization process and the width of the crystallization line can be achieved according to pulse energy, e.g., crystallite size, and also the effect of the scanning speed can be understood. Among the main conclusions to highlight, we disclose the laser conditions that determine the extent of the crystallized area and deduce that it is never of interest to increase the pulse energy too much as opposed to the repetition rate for the uniform crystallized line.

The analysis of the stability of the Cauchy problem in the cylindrical double-layer area

Ceramic protective coats, for instance, on turbine blades, create a double-layer area with various thermophysical properties and they require metal temperature control. In this paper, it is implemented by formulating a Cauchy problem for the equation of thermal conductivity in the metal cylindrical area with a ceramic layer. Due to the ill posed problem, a regularization method was applied consisting in the notation of thermal balance for the ceramic layer. A spectral radius for the equation matrix was taken as the stability measure of the Cauchy problem. Numerical calculations were performed for a varied thickness of the ceramic layer, with consideration of the non-linear thermophysical properties of steel and a ceramic layer (zirconium dioxide). A polynomial was determined which approximates temperature distribution in time for the protective layer. The stability of solutions was compared for undisturbed and disturbed temperature values, and thermophysical parameters with various ceramic layer thickness. The obtained calculation results confirmed the effectiveness of the proposed regularization method in obtaining stable solutions at random data disturbance.

Approximate Solution of Optimal Pulse Control Problem Associated with the Heat Conduction Process

Abstract We consider the approximate solution of the control problem with minimum energy for an object described by the heat equation, with the process described by the linear equation of parabolic type and the system controlled by impulsive external influences. Our optimal control problem deals with finding a control parameter belonging to the class of admissible controls that provides the desired temperature distribution in a finite time with minimal energy consumption (energy consumption is described by the quadratic functional). Previous works dedicated to optimal impulse control problems have mostly used the Pontryagin’s maximum principle. However, from a practical point of view, this approach does not lead to satisfactory results. This is due to the fact that the corresponding boundary value problems in this case have no solution in a traditional class of absolutely continuous trajectories. In this work, we propose a method based on the moment relations. We seek for the approximate solution of the corresponding boundary value problem in the form of finite Fourier sum and state our optimal control problem in a finite-dimensional phase space. As a result, we obtain an optimal impulse control problem in a finite-dimensional function space. Taking into account the given condition for a finite time, we reduce the obtained problem to the L-problem of moments. Thus, the problem of finding a control parameter is reduced to the solution of the system of Fredholm integral equations of the first kind, with the norm of the sought solution not exceeding a given number. By Levi’s theorem, every element of Hilbert space can be represented by the sum of the elements of two orthogonal subspaces. This assertion makes it possible to find control parameters in analytical form. We also establish the convergence of the chosen approximation.

Estimation of the power of a geothermal energy recovery system that uses a heat exchanger

Access to new sources of renewable energy free of CO2 emissions is one of the priority needs of the global economy. At great depths underground there are geothermal sources with temperatures of up to several hundred degrees. Recovery of energy from such sources may take place using a heat exchanger placed in rocks at great depths. Before starting the exploitation of such resources, it is necessary to estimate the performance and power of the source with the assumed system parameters. In the conducted research, simulations of the energy acquisition system in the Matlab-simulink environment were carried out. The model of heat flows with distributed variables was used for the simulation, describing changes in the temperature distribution in time and space. The steady-state power of the system, which is possible to download over a long period of time, was also estimated. The most important conclusion from the conducted is that after some time, depending on the power consumed, the system may experience a significant decrease in power. The decrease in power is caused by the cooling of the rocks around the heat exchanger and the thermal resistivity of the medium, which are the rocks.

Molecular dynamics simulation of deposition of amorphous carbon films on sapphire surfaces

The growth of amorphous carbon films on a sapphire surface was investigated using classical molecular dynamics simulation. The kinetic energy of carbon particles was set as 10 eV and ReaxFF potential was used to express the interaction between different kinds of particles. The results of the temperature distribution in both deposition time and deposition space are reported. Simulation results reveal that the grown amorphous carbon film consists of four regions, namely interlayer, low density, stable growth, and surface regions. In the interlayer region, the interlayer between substrate and pure carbon film is formed. In the low density region, a pure carbon film is grown while the film density decreases initially and then increases. In the stable growth region, the film density remains almost constant. The film density decreases rapidly in the surface region. The radial distribution function (RDF) analysis suggests that a structure similar to that of diamond exists in the stable growth region of the film. The lower film density in the low density and surface regions was interpreted to indicate the existence of abundant sp1 chain structures, which is supported by the depth profile of the sp fractions. The present results are in good agreement with previous experimental and simulation results and demonstrate the suitability of the ReaxFF potential in the simulation of amorphous carbon growth on sapphire substrate. Our study provides a good starting point for the simulation study of amorphous carbon films on sapphire substrates.

Second cell growth optimized by heating mode during two-step supercritical CO2 foaming polymer process

The batch foaming of supercritical fluids faces numerous challenges, such as poor controllability due to dynamic temperature changes during depressurization foaming, and prolonged saturation time and heterogeneous temperature distribution during temperature rising foaming, which leads to lower productivity and non-uniform cells. To overcome these challenges, a unique two-step foaming method in combination with microwave enhancement was proposed. The two-step foaming method involved depressurization foaming for cell nucleation and initial growth, followed by temperature rising foaming for subsequent cell growth, producing foams with higher expansion ratio. Meanwhile, a conduction-microwave (C-M) heating mechanism which integrates different heating schemes to enhance heating efficiency and uniformity was innovatively proposed. The effect of the microwave radiation time, power, initial environmental temperature, and content of CO2 in polymer on the foaming by C-M heating was studied. Compared to existing methods, the foaming by C-M heating produces polystyrene (PS) foam with lower density and more uniform cells.

Thermal behavior of CMC solutions under simulation of radio frequency pasteurization

Pasteurization and enzyme-inactivation are an economical and convenient way to provide safety and shelf-life stability. However, long heating time and non-uniform temperature distribution are the main issues of traditional thermal processing for enzyme-inactivation. Because of the volumetric heating and high heating rate, radio frequency (RF) treatment is considered as one of the most promising physical enzyme-inactivating methods. A 6 kW, 27.12 MHz RF heating system was applied to explore the effect of cylindrical container dimension and solution concentration on the thermal behavior of high-viscosity liquid food. Carboxymethylcellulose (CMC) solution as a non-Newtonian fluid was selected as a model liquid food in this study. The target temperature for enzyme inactivation was 70 °C. The experimental results showed that the electrode gap, container length, and container diameter affected the heating rate and uniformity of the liquid food. Furthermore, when the concentration of CMC solution increased from 0.5% to 2.0%, the heating rate of the solution firstly increased and then decreased, while the heating uniformity index of the solution increased from 0.008 ± 0.001 to 0.056 ± 0.002. The simulation results showed that the higher electric field strength led to a higher heating rate, temperature, and velocity of natural convection of the solution at the ends of the container. Then, the recirculation zones from the ends to the center of the container were formed, which was diminished with the increasing concentration solution, resulting in the increased maximum temperature difference of solution. The results of this research may provide useful data for subsequent continuous flow studies and information on potential RF enzyme-inactivation in high-viscosity liquid foods.

Physical model of non-adiabatic blowdown of cryo-compressed hydrogen storage tanks

This paper describes a model of hydrogen blowdown dynamics for storage tanks needed for hydrogen safety engineering to accurately represent incident scenarios. Heat transfer through a tank and pipe walls affects the temperature and pressure transients inside the storage vessel and at the nozzle exit, and thus the characteristics of the resulting hydrogen jet in the case of loss of containment. Current non-adiabatic blowdown models are validated against experiments performed with hydrogen storage tanks at only ambient temperature. The effect of heat transfer for cryo-compressed hydrogen is more significant due to a larger difference of temperature between the stored hydrogen and the surrounding atmosphere, especially in case of equipment insulation failure during an incident. Our previous work demonstrated that the heat transfer through a discharge pipe wall can significantly affect the mass flow rate of cryogenic hydrogen releases. Thoroughly validated models of non-adiabatic blowdown dynamics for cryo-compressed hydrogen are missing at the moment. This work develops further the non-adiabatic blowdown model at ambient temperature using the under-expanded jet theory developed at Ulster University, to expand it to cryo-compressed hydrogen storage tanks. The non-ideal behaviour of cryo-compressed hydrogen due to low temperatures is taken into account through the high-accuracy Helmholtz energy formulations. The developed model includes effect of heat transfer at both the tank and the discharge pipe walls. The model is thoroughly validated against sixteen tests on blowdown of hydrogen storage tanks with initial pressure 0.6–20 MPa ab and temperature 80–310 K, through release nozzle of diameter in the range 0.5–4.0 mm, performed within the PRESLHY project. The model well reproduces the experimental pressure and temperature recordings in the storage tank during the entire blowdown duration for the whole set of sixteen tests. In conjunction with the volumetric source model, explained in detail, the physical model allows to perform CFD simulations accurately reproducing the temperature distribution in time and space for the cryogenic hydrogen jet experiment.

Stochastic dynamics of a nonlinear thermal circuit with bistability.

Stochastic dynamics of a nonlinear thermal circuit is studied. Due to the existence of negative differential thermal resistance, there exist two stable steady states that satisfy both the continuity and stability conditions. The dynamics of such a system is governed by a stochastic equationwhich describes originally an overdamped Brownian particle that undergoes a double-well potential. Correspondingly, the finite time temperature distribution takes a double-peak profile and each peak is approximately Gaussian. Owing to the thermal fluctuation, the system is able to jump occasionally from one stable steady state to the other. The probability density distribution of the lifetime τ for each stable steady state follows a power-law decay τ^{-3/2} in the short-τ regime and an exponential decay e^{-τ/τ_{0}} in the long-τ regime. All these observations can be well explained analytically.

Bio-thermal response and thermal damage in biological tissues with non-equilibrium effect and temperature-dependent properties induced by pulse-laser irradiation

Comprehension of thermal behavior underlying the living biological tissues helps successful applications of current heat therapies. The present work is to explore the heat transport properties of irradiated tissue during tis thermal treatment, in which the local thermal non-equilibrium effect as well as temperature-dependent properties arose from complicated anatomical structure, is considered. Based on the generalized dual-phase lag (GDPL) model, a non-linear governing equation of tissue temperature with variable thermal physical properties is proposed. The effective procedure constructed on an explicit finite difference scheme is then developed to predict numerically the thermal response and thermal damage irradiated by a pulse laser as a therapeutic heat source. The parametric study on variable thermal physical parameters including the phase lag times, heat conductivity, specific heat capacity and blood perfusion rate has been performed to evaluate their influence on temperature distribution in time and space. On this basis, the thermal damage with different laser variables such as laser intensity and exposure time are further analyzed.

Development of a real-time temperature measurement technique for SiC wafer during ultra-rapid thermal annealing based on optical-interference contactless thermometry (OICT)

A real-time temperature measurement technique with high spatial (≤20 μm) and temporal (≤1 μs) resolutions for SiC wafers during ultra-rapid thermal annealing (URTA) has been developed based on optical-interference contactless thermometry (OICT). This technique consists of hardware (OICT imaging setup) and software (fast temperature extraction program). Under URTA by atmospheric-pressure thermal plasma jet, a clear variation of optical-interference fringes was observed by a high-speed camera and then analyzed by a fast temperature extraction program using image preprocessing and a database. 3.5D (x, y, z and time) temperature distribution in SiC wafer was obtained within 0.43 s.

Control of banana anthracnose by hot water dip: A semi-empirical model coupling heat transfer and Colletotrichum musae inactivation

A semi-empirical model was developed to predict simultaneously time-temperature distribution inside the unripe banana and fungal reduction during the hot water dip, in order to simulate different process conditions for controlling banana anthracnose disease. For this purpose, the kinetic parameters of Colletotrichum musae reduction were estimated based on the thermal death time concept (z = 3.56 °C and D50°C= 1044 s), and evaluated in different simulated media (unripe and fully ripe banana peel agar media). At the same time, a heat transfer model based on the Fourier equation was developed considering two unripe banana domains (peel and pulp). The comparison between the predicted and observed number of C. musae spores after the thermal treatment of unripe banana was satisfactory (coefficient of variation less than 10%), suggesting that the survival ratio is affected by the banana composition. The resulting model can be used to simulate different time-temperature scenarios, and to show how the parameter combinations may affect C. musae reduction in the unripe banana during the hot water dip process.

The Non-Stationary Heat Transport inside a Shafted Screw Conveyor Filled with Homogeneous Biomass Heated Electrically

The non-stationary heat transfer inside a cylindrical channel of a shafted screw conveyor, electrically heated, and filled with a moving biomass was analyzed. The problem of non-stationary heat transport is encountered in the processes of biomass pyrolysis and food products’ sterilization. To solve the heat conduction equation with initial and boundary conditions, the methods of the expansion of the given and unknown functions into a Fourier series in the angular coordinate, and Fourier and Laplace integral transforms in the axial coordinate and time, respectively, were used. As a result of solving this problem, it is shown that the temperature in the reactor consists of two main terms. The first of them is proportional to time, and the second is a superposition of quasi-monochromatic heat pulses decaying with time. Numerical analysis of the temperature distribution in space and time depending on various specific parameters of the system was carried out. The obtained numerical results were compared with those corresponding to the cases of heat sources in the form of a spiral or a shaftless helical screw.

BTE-Barna: An extension of almaBTE for thermal simulation of devices based on 2D materials

We present BTE-Barna (Boltzmann Transport Equation - Beyond the RTA for NAnosystems), a software package that extends the Monte Carlo (MC) module of the almaBTE solver of the Peierls-Boltzmann transport equation for phonons (PBTE) to work with nanosystems based on 2D materials with complex geometries. To properly capture how the phonon occupations evolve in momentum space as a result of scattering, we have supplemented the relaxation-time approximation with an implementation of the propagator for the full linearized version of the PBTE. The code can now find solutions for finite and extended devices under the effect of a thermal gradient, with isothermal reservoirs or with an arbitrary initial temperature distribution in space and time, writing out the temperature and heat flux distributions as well as their spectral decompositions. Besides the full deviational MC solver, a number of useful approximations for highly symmetric devices are also included. Program summaryProgram Title::BTE-BarnaCPC Library link to program files:https://doi.org/10.17632/t58z289tpc.1Developer's repository link:https://github.com/sousaw/BTE-BarnaCode Ocean capsule:https://codeocean.com/capsule/4171806Licensing provisions: Apache-2.0Programming language: C++Nature of problem: Calculation of temperature profiles, thermal flux and/or effective thermal conductivities for nanosystems based on 2D materials.Solution method: For highly symmetric systems confined along some direction(s), the linearized phonon Boltzmann transport equation is solved iteratively by partially suppressing the phonon lifetimes due to boundaries. For more complex geometries, an energy-based deviational Monte Carlo method including off-diagonal terms in the linearized scattering operator arising from the phonon-phonon interaction is used.Additional comments including restrictions and unusual features: Depends on the following external libraries: boost, Eigen, HDF5, MessagePack, MPI, oneTBB, spglib, and almaBTE.

A computational framework based on FEA, ML and GA for estimation of welding residual stresses

The present work describes a computational framework based on finite element (FE) analysis and machine learning (ML) and genetic algorithm (GA) to accurately estimate and minimize the residual stresses in welding. The FE analysis comprises of sequentially coupled thermal and mechanical analyses that are nonlinear due to temperature-dependent thermal/mechanical properties. In the FE analysis, the effective stress function (ESF) algorithm is used for accurate computation of the temperature-induced elasto-plastic stress field during welding. The ESF algorithm accounts for the large variation of yield curves due to temperature changes in welding. To improve the accuracy of the thermal and mechanical analyses, an optimization process combining supervised machine learning and binary coded genetic algorithm is utilized. This optimization technique is implemented to derive an accurate phase-change model for the thermal FE analysis of SS304, which is otherwise a burdensome and costly task to obtain from calorimetric experiments. The results obtained through the derived phase-change model are validated through welding time-temperature distribution reported for a welding experiment in literature. The same optimization process is further used to obtain a set of weld operating conditions (such as weld voltage, current, welding speed, and the gap between plates) for SS304 that reduce the tensile residual stresses. It is found that the accurate estimation and reduction of welding residual stresses can be realized by using the present computational framework. • A detailed FE analysis is presented for the estimation of residual stresses in welding. • ESF algorithm implemented in the FE analysis is found very useful. • An optimization methodology is proposed based on machine learning and genetic algorithm. • Proposed optimization scheme is used to estimate the phase-change model and weld parameters. • Accuracy in estimation of welding temperature field is improved and tensile residual stress is minimized to a certain extent.

Machine learning based soft sensor and long-term calibration scheme: A solid oxide fuel cell system case

To quickly and accurately obtain the multi-dimensional state in a sealing reactor is critical for the safety and high performance of industrial system. In this work, a generic machine learning based multi-dimensional soft sensor and a long-term calibration scheme is proposed by using the case of steam reforming solid oxide fuel cell (SR-SOFC) system. Firstly, based on a validated SR-SOFC system model, the temporal-spatial temperature distribution (TSTD) characteristics are analyzed and a TSTD characteristic model is constructed by Multivariable Linear Regression. Then, the central node temperature of the stack is estimated by applying the Least Square Support Vector Machine and the SR-SOFC stack temperature distribution is accurately obtained by explaining the TSTD characteristics model with the central node temperature. In addition, the temperature distribution is calibrated by Stochastic Gradient Descent algorithm to eliminate the estimation error resulting from stack degradation in a long term. The simulation results show that the proposed method can obtain the SR-SOFC stack temperature distribution in time and effectively, the average error is less than 1 K. The proposed estimation strategy can be easily expanded to other scenarios with similar operation conditions.

Monitoring the formation of polyurethane foams with an infrared camera: Classroom activity

Foams prepared with polyurethanes (PU), a polymer with units in the main chain joined by urethane linkages, are commonly used in isolation panels, seals, automative seats, and bedding. The reaction causing the formation of polyurethane foams is a conventional, yet spectacular, way to attract the attention of polymer chemistry students. Infrared cameras are a relatively inexpensive apparatus that allow for semi-quantitatively temperature monitoring at the surface of objects. Because the formation of polyurethane is exothermic, the polymerization reaction and the expansion of the foam can be easily detected by an infrared camera. Information such as volume expansion, maximum temperature, temperature distribution in time and space, and reaction time can be retrieved from short videos. These data can be correlated and discussed in relationship with the reactivity of the components for synthesizing the foam. The primary goal of this activity was to investigate the exothermic reaction of polyurethane foam using an infrared camera which has been successfully used for monitoring the exothermic formation of polyurethane foams. These values can be discussed in term of reactivity of isocyanates (aromatic and aliphatic/cycloaliphatic) for a given formulation of polyols. The highly visual content of such experiments is attractive for children and students. Chemicals for performing the experiments can be donated either individually or as ready sets (“polyols”) from the industry. It is anticipated that the investment required for buying the infrared camera can be redeemed by using it for other types of exo- or endothermic reactions and for teaching heat transfer in physics class.

Quantification of thermal dose in moderate clinical hyperthermia with radiotherapy: a relook using temperature–time area under the curve (AUC)

Background Thermal dose in clinical hyperthermia reported as cumulative equivalent minutes (CEM) at 43 °C (CEM43) and its variants are based on direct thermal cytotoxicity assuming Arrhenius ‘break’ at 43 °C. An alternative method centered on the actual time–temperature plot during each hyperthermia session and its prognostic feasibility is explored. Methods and materials Patients with bladder cancer treated with weekly deep hyperthermia followed by radiotherapy were evaluated. From intravesical temperature (T) recordings obtained every 10 secs, the area under the curve (AUC) was computed for each session for T > 37 °C (AUC > 37 °C) and T ≥ 39 °C (AUC ≥ 39 °C). These along with CEM43, CEM43(>37 °C), CEM43(≥39 °C), T mean, T min and T max were evaluated for bladder tumor control. Results Seventy-four hyperthermia sessions were delivered in 18 patients (median: 4 sessions/patient). Two patients failed in the bladder. For both individual and summated hyperthermia sessions, the T mean, CEM43, CEM43(>37 °C), CEM43(≥39 °C), AUC > 37 °C and AUC ≥ 39 °C were significantly lower in patients who had a local relapse. Individual AUC ≥ 39 °C for patients with/without local bladder failure were 105.9 ± 58.3 °C-min and 177.9 ± 58.0 °C-min, respectively (p = 0.01). Corresponding summated AUC ≥ 39 °C were 423.7 ± 27.8 °C-min vs. 734.1 ± 194.6 °C-min (p < 0.001), respectively. The median AUC ≥ 39 °C for each hyperthermia session in patients with bladder tumor control was 190 °C-min. Conclusion AUC ≥ 39 °C for each hyperthermia session represents the cumulative time–temperature distribution at clinically defined moderate hyperthermia in the range of 39 °C to 45 °C. It is a simple, mathematically computable parameter without any prior assumptions and appears to predict treatment outcome as evident from this study. However, its predictive ability as a thermal dose parameter merits further evaluation in a larger patient cohort.

A Positioning Method of Temperature Sensors for Monitoring Dam Global Thermal Field

During the concrete pouring process of a dam construction, timely and accurate temperature monitoring is of great significance to reveal the thermal distribution characteristics and evolution process, and control concrete cracking. In this study, a positioning method of temperature sensors (PMTS) in a concrete dam is developed to determine the arrangement of temperature sensors quantitatively. The proposed positioning method is related to the restructured thermal field based on the natural neighbor interpolation algorithm, and the cross-validation. Based on the method, thermometers, distributed optical fibers and infrared thermal imagers are optimally installed in a super-high arch dam for real-time measurement of concrete temperature. The results show that the PMTS is reasonable and reliable for obtaining the dam global thermal field. The on-site temperature monitoring data indicate that the time and space temperature distribution law of the restructured thermal field is consistent with the actual situation of the super-high arch dam. In addition, the cons and pros, and improvement of the PMTS are further discussed. The proposed PMTS is a valuable method to monitor the global thermal field of concrete dams.

Effects of porosity and area density on upward flame spread characteristics over thin flax fabric

Few investigations have systematically addressed the porosity effects of upward flame spread over fabric fuels, although the porosity is a special property for fabric fuels. The present paper studies the porosity and area density effects on upward flame spreading using 160.0 cm tall and 8.0 cm wide flax fabric samples with various porosities and area densities. The flame shape, flame length, flame spread rate, ignition time, standoff distance and surface temperature distribution are obtained and analyzed. The major findings are summarized as follows: as the porosity increases and corresponding area density declines, the flame spread rate and flame length increase, whereas the ignition time decreases, which is because the oxygen can reach the fuel surface in the pyrolysis region more easily and, subsequently, the heat flux received by the virgin fuels increases. The two parameters of flame standoff distance and surface temperature in the preheating region can be applied to characterize the heat flux received by the virgin fuels. Generally, when the porosity increases and the corresponding area density decreases, the flame standoff distance and the surface temperature at the same distance from pyrolysis front increase, which reveals that the heat flux received by the virgin surface increases.