Interval finite difference method for steady-state temperature field prediction with interval parameters

A new numerical technique named interval finite difference method is proposed for the steady-state temperature field prediction with uncertainties in both physical parameters and boundary conditions. Interval variables are used to quantitatively describe the uncertain parameters with limited information. Based on different Taylor and Neumann series, two kinds of parameter perturbation methods are presented to approximately yield the ranges of the uncertain temperature field. By comparing the results with traditional Monte Carlo simulation, a numerical example is given to demonstrate the feasibility and effectiveness of the proposed method for solving steady-state heat conduction problem with uncertain-but-bounded parameters.

Numerical simulation of melt flow and temperature field during DC casting 2024 aluminium alloy under different casting conditions

Casting speed,casting temperature and secondary cooling water flow rate are the main process parameters affecting the DC casting process.These parameters significantly influence the flow and temperature fields during casting,which are crucial for the quality of the ingot and can determine the success or failure of the casting operation.Numerical simulation,with the advantages of low cost,rapid execution,and visualized results,is an important method to study and optimize the DC casting process.In the present work,a simulation model of DC casting 2024 aluminum alloy was established,and the reliability of the model was verified.Then,the influence of casting parameters on flow field and temperature field was studied in detail by numerical simulation method.Results show that with the increase of casting speed,the melt flow becomes faster,the depths of slurry zone and mushy zone increase,and the variation of slurry zone depth is greater than that of mushy zone.With an increase in casting temperature,the melt flow rate increases,the depth of the slurry zone becomes shallower,and the depth of the mushy zone experiences only minor changes.The simulation results further indicate that the increase of the flow rate of the secondary cooling water slightly reduces the depths of both slurry and mushy zone.

Stability analysis of a liquid crystal elastomer self-oscillator under a linear temperature field

Self-oscillating systems abound in the natural world and offer substantial potential for applications in controllers,micro-motors,medical equipments,and so on.Currently,numerical methods have been widely utilized for obtaining the characteristics of self-oscillation including amplitude and frequency.However,numerical methods are burdened by intricate computations and limited precision,hindering comprehensive investigations into self-oscillating systems.In this paper,the stability of a liquid crystal elastomer fiber self-oscillating system under a linear temperature field is studied,and analytical solutions for the amplitude and frequency are determined.Initially,we establish the governing equations of self-oscillation,elucidate two motion regimes,and reveal the underlying mechanism.Subsequently,we conduct a stability analysis and employ a multi-scale method to obtain the analytical solutions for the amplitude and frequency.The results show agreement between the multi-scale and numerical methods.This research contributes to the examination of diverse self-oscillating systems and advances the theoretical analysis of self-oscillating systems rooted in active materials.

Investigation on Temperature Field Calibration and Analysis of Wind Tunnel

For wind tunnels,it is essential to conduct temperature and flow field calibration on their test section,which is an important indicator for evaluating the quality of wind tunnel flow fields.In the paper,a truss composed of temperature sensors was used to calibrate the temperature field of a completed wind tunnel section.By adjusting the distance between the temperature measurement truss and the nozzle,as well as the wind speed,the temperature field distribution data at different positions could be obtained.Analyze these data to identify important factors that affect the distribution of temperature field.Simultaneously,the temperature field of the wind tunnel was simulated accordingly.The purpose is to further analyze the fluid heat transfer between air and wind tunnel walls through numerical simulation.Through the above analysis methods,the quality of the temperature field in the wind tunnel has been further verified,providing reference for future wind tunnel tests of relevant models.

Interfacial built-in electric field and crosslinking pathways enabling WS_(2)/Ti_(3)C_(2)T_(x) heterojunction with robust sodium storage at low temperature

Developing efficient energy storage for sodium-ion batteries(SIBs)by creating high-performance heterojunctions and understanding their interfacial interaction at the atomic/molecular level holds promise but is also challenging.Besides,sluggish reaction kinetics at low temperatures restrict the operation of SIBs in cold climates.Herein,cross-linking nanoarchitectonics of WS_(2)/Ti_(3)C_(2)T_(x) heterojunction,featuring built-in electric field(BIEF),have been developed,employing as a model to reveal the positive effect of heterojunction design and BIEF for modifying the reaction kinetics and electrochemical activity.Particularly,the theoretical analysis manifests the discrepancy in work functions leads to the electronic flow from the electron-rich Ti_(3)C_(2)T_(x) to layered WS_(2),spontaneously forming the BIEF and“ion reservoir”at the heterogeneous interface.Besides,the generation of cross-linking pathways further promotes the transportation of electrons/ions,which guarantees rapid diffusion kinetics and excellent structure coupling.Consequently,superior sodium storage performance is obtained for the WS_(2)/Ti_(3)C_(2)T_(x) heterojunction,with only 0.2%decay per cycle at 5.0 A g^(-1)(25℃)up to 1000 cycles and a high capacity of 293.5 mA h g^(-1)(0.1A g^(-1)after 100 cycles)even at-20℃.Importantly,the spontaneously formed BIEF,accompanied by“ion reservoir”,in heterojunction provides deep understandings of the correlation between structure fabricated and performance obtained.

Mathematical models of steady-state temperature fields produced by multi-piped freezing

题目：少量管冻结稳态温度场数学模型目的：少量任意布置冻结管冻结的稳态温度场无解析解。建立任意布置少量管冻结稳态温度场模型，获得解析解，解决人工冻结温度场理论问题。创新点：1．基于势函数叠加原理，确立人工地层冻结中少量管冻结稳态温度场的通用求解方法；2．建立任意布置的3根和4根非等温冻结管下冻结稳态温度场数学模型，获得其解析解通解及特解。方法：1．通过理论分析，将冻结管简化为热汇点源，确定人工地层冻结热势的拉普拉斯方程表述；2．应用势函数叠加原理建立少量管冻结稳态温度场的通用求解方法；3．建立少量管冻结稳态温度场的数学模型，通过理论推导获得温度场解析解；4．通过数值模拟，验证所提方法、数学模型和解析解的正确性和准确性。结论：1．将冻结管简化为点源（热汇），其冻结形成的热势场服从拉普拉斯方程，其解即为热势函数；2．多根冻结管冻结时，将单根冻结管的热势函数叠加，由冻结管的位置决定每根冻结管的热流，再根据边界条件定解。这一方法（即势函数叠加法）可以用于任意布置冻结管冻结稳态温度场解析解的求解：3．将冻结管简化为点源导致获得的解析解存在一定的误差，但误差仅发生在冻结管附近极小的范围内，并且误差微小，完全满足工程上的精度要求。

Characteristics of the SOL ion-to-electron temperature ratio on the J-TEXT tokamak with different plasma configurations

Accurate measurement of the average plasma parameters in the edge region,including the temperature and density of electrons and ions,is critical for understanding the characteristics of the scrape-off layer(SOL) and divertor plasma transport in magnetically confined fusion research.On the J-TEXT tokamak,a multi-channel retarding field analyzer(RFA) probe has been developed to study average plasma parameters in the edge region under various poloidal divertor and island divertor configurations.The edge radial profile of the ion-to-electron temperature ratio,τ_(i/e),has been determined,which gradually decreases as the SOL ion self-collisionality,v_(SOL)*,increases.This is broadly consistent with what has been observed previously from various tokamak experiments.However,the comparison of experimental results under different configurations shows that in the poloidal divertor configuration,even under the same v_(SOL)*,τ_(i/e) in the SOL region becomes smaller as the distance from the X-point to the target plate increases.In the island divertor configuration,τ_(i/e) near the O-point is higher than that near the X-point at the same v_(SOL)*,and both are higher than those in the limiter configuration.These results suggest that the magnetic configuration plays a critical role in the energy distributions between electrons and ions at the plasma boundary.

The Effects of Thickness and Location of PCMon the Building’s Passive Temperature-Control–A Numerical Study

Building energy consumption and building carbon emissions both account for more than 20%of their total national values in China.Building employing phase change material(PCM)for passive temperature control shows a promising prospect in meeting the comfort demand and reducing energy consumption simultaneously.However,there is a lack of more detailed research on the interaction between the location and thickness of PCM and indoor natural convection,as well as indoor temperature distribution.In this study,the numerical model of a passive temperature-controlled building integrating the developed PCM module is established with the help of ANSYS.In which,the actual weather condition of Beijing city is set as the boundary conditions and the indoor natural convection is simulated with the consideration of radiation model.The effects of PCM’s thickness and location on the internal temperature field are analyzed and discussed.The results show that the room could maintain within the human comfort temperature range with the longest ratio of 94.10%and the shortest ratio of 51.04%as integrating PCM.In comparison,the value is only 26.70%without PCM.The room’s maximum temperature fluctuation can also be improved;it could be lowered by 64.4%compared to the normal condition.When the quantity of PCM is sufficient,further increasing the PCM amount results in a temperature fluctuation reduction of less than 0.1°C and does not increase the comfort time.Placing PCM on the wall induces an apparent variation in indoor temperature along the vertical direction.Conversely,placing PCM on the roof can lead to a heat transfer rate difference of up to seven times.The optimal placement of PCM depends on the difference between the environmental and phase change temperatures.If the difference is positive,placing PCM on the roof is more effective;conversely,the opposite holds.According to the results over the entire cycle,PCM application on vertical walls yields better performance.The significant difference in natural convection caused by the same thickness of PCM but different application positions,coupled with the influence of air movement on the melting and solidification of PCM,further impacts indoor temperature fluctuations and comfort.This study can provide guidance for the application location and thickness of PCM,especially for scenarios where temperature regulation is required at a specific time.

Temperature field model in surface grinding: a comparative assessment

Grinding is a crucial process in machining workpieces because it plays a vital role in achieving the desired precision and surface quality.However,a significant technical challenge in grinding is the potential increase in temperature due to high specific energy,which can lead to surface thermal damage.Therefore,ensuring control over the surface integrity of workpieces during grinding becomes a critical concern.This necessitates the development of temperature field models that consider various parameters,such as workpiece materials,grinding wheels,grinding parameters,cooling methods,and media,to guide industrial production.This study thoroughly analyzes and summarizes grinding temperature field models.First,the theory of the grinding temperature field is investigated,classifying it into traditional models based on a continuous belt heat source and those based on a discrete heat source,depending on whether the heat source is uniform and continuous.Through this examination,a more accurate grinding temperature model that closely aligns with practical grinding conditions is derived.Subsequently,various grinding thermal models are summarized,including models for the heat source distribution,energy distribution proportional coefficient,and convective heat transfer coefficient.Through comprehensive research,the most widely recognized,utilized,and accurate model for each category is identified.The application of these grinding thermal models is reviewed,shedding light on the governing laws that dictate the influence of the heat source distribution,heat distribution,and convective heat transfer in the grinding arc zone on the grinding temperature field.Finally,considering the current issues in the field of grinding temperature,potential future research directions are proposed.The aim of this study is to provide theoretical guidance and technical support for predicting workpiece temperature and improving surface integrity.

Temperature Field in Laser Line Scanning Thermography: Analytical Calculation and Experiment

The temperature field in laser line scanning thermography is investigated comprehensively in this work,including analytical calculation and experiment.Firstly,the principle of laser line scanning thermography is analyzed.On this basis,a physical laser line scanning model is proposed.Afterwards,based on Fourier transform(FT)and segregation variablemethod(SVM),the heat conduction differential equation in laser line scanning thermography is derived in detail.The temperature field of the composite-based coatings model with defects is simulated numerically.The results show that the laser line scanning thermography can effectively detect the defects in the model.The correctness of the analytical calculation is verified by comparing the surface temperature distribution obtained by analytical calculation and numerical simulation.Additionally,an experiment is carried out and the changeable surface temperature obtained by analytical calculation is compared with the experimental results.It shows that the error of maximum temperature obtained by analytical calculation and by experiment is 8%with high accuracy,which proves the correctness of analytical calculation and enriches the theoretical foundation of laser line scanning thermography.

Thermal Properties Reconstruction and Temperature Fields in Asphalt Pavements: Inverse Problem and Optimisation Algorithms

A two-layer implicit difference scheme is employed in the present study to determine the temperature distribution in an asphalt pavement.The calculation of each layer only needs four iterations to achieve convergence.Furthermore,in order to improve the calculation accuracy a swarm intelligence optimization algorithm is also exploited to inversely analyze the laws by which the thermal physical parameters of the asphalt pavement materials change with temperature.Using the basic cuckoo and the gray wolf algorithms,an adaptive hybrid optimization algorithm is obtained and used to determine the relationship between the thermal diffusivity of two types of asphalt pavement materials and the temperature.As shown by the results,the prediction accuracy achievable with this approach is higher than that of the linear model.

Numerical analysis for permafrost temperature field in the short term of permafrost subgrade filling

Purpose-It is of great significance to study the influence of subgrade filling on permafrost temperature field in permafrost area for the smooth construction and safe operation of railway.Design/methodology/approach-The paper builds up the model for the hydrothermal coupling calculation of permafrost using finite element software COMSOL to study how permafrost temperature field changes in the short term after subgrade filling,on which basis it proposes the method of calculation for the concave distortion of freezing front in the subgrade-covered area.Findings-The results show that the freezing front below the subgrade center sinks due to the thermal effect of subgrade filling,which will trigger hydrothermal erosion in case of sufficient moisture inflows,leading to the thawing settlement or the cracking of the subgrade,etc.The heat output of soil will be hindered the most in case of July filling,in which case the sinking and the distortion of the freezing front is found to be the most severe,which the recovery of the permafrost temperature field,the slowest,constituting the most unfavorable working condition.The concave distortion of the freezing front in the subgrade area increases with the increase in temperature difference between the filler and ground surface,the subgrade height,the subgrade width and the volumetric thermal capacity of filler,while decreases with the increase of the thermal conductivity of filler.Therefore,the filler chose for engineering project shall be of small volumetric thermal capacity,low initial temperature and high thermal conductivity whenever possible.Originality/value-The concave distortion of the freezing front under different working conditions at different times after filling can be calculated using the method proposed.

Investigation of the Behavior of a Photovoltaic Cell under Concentration as a Function of the Temperature of the Base and a Variable External Magnetic Field in 3D Approximation

The photovoltaic (PV) cell performances are connected to the base photogenerated carriers charge. Some studies showed that the quantity of the photogenerated carriers charge increases with the increase of the solar illumination. This situation explains the choice of concentration PV cell (C = 50 suns) in this study. However, the strong photogeneration of the carriers charge causes a high heat production by thermalization, collision and carriers charge braking due to the electric field induced by concentration gradient. This heat brings the heating of the PV cell base. That imposes the taking into account of the temperature influence in the concentrator PV cell operation. Moreover, with the proliferation of the magnetic field sources in the life space, it is important to consider its effect on the PV cell performances. Thus, when magnetic field and base temperature increase simultaneously, we observe a deterioration of the photovoltage, the electric power, the space charge region capacity, the fill factor and the conversion efficiency. However the photocurrent increases when the base temperature increases and the magnetic field strength decreases. It appears an inversion phenomenon in the evolution of the electrical parameters as a function of magnetic field for the values of magnetic field B> 4×10-4 T.

THE ANALYSIS OF TEMPERATURE FIELD OFARMORED VEHICLE

论述了负重轮轮胎温度场有限元分析方法；给出了生热率数学模型；建立了具有三重非线性的负重轮力学有限元分析模型和热学分析模型，利用有限元分析软件进行了温度场的计算分析；研究了负重轮轮胎温度场，分析了温升过程，为负重轮寿命分析提供了理论和数据。

Transient multi-physics behavior of an insert high temperature superconducting no-insulation coil in hybrid superconducting magnets with inductive coupling

A transient multi-physics model incorporated with an electromagneto-thermomechanical coupling is developed to capture the multi-field behavior of a single-pancake(SP)insert no-insulation(NI)coil in a hybrid magnet during the charging and discharging processes.The coupled problem is resolved by means of the finite element method(FEM)for the magneto-thermo-elastic behaviors and the Runge-Kutta method for the transient responses of the electrical circuits of the hybrid superconducting magnet system.The results reveal that the transient multi-physics responses of the insert NI coil primarily depend on the charging/discharging procedure of the hybrid magnet.Moreover,a reverse azimuthal current and a compressive hoop stress are induced in the insert NI coil during the charging process,while a forward azimuthal current and a tensile hoop stress are observed during the discharging process.The induced voltages in the insert NI coil can drive the currents flowing across the radial turns where the contact resistance exists.Therefore,it brings forth significant Joule heat,causing a temperature rise and a uniform distribution of this heat in the coil turns.Accordingly,a thermally/mechanically unstable or quenching event may be encountered when a high operating current is flowing in the insert NI coil.It is numerically predicted that a quick charging will induce a compressive hoop stress which may bring a risk of buckling instability in the coil,while a discharging will not.The simulations provide an insight of hybrid superconducting magnets under transient start-up or shutdown phases which are inevitably encountered in practical applications.

STUDY ON TEMPERATURE FIELD INDUCED IN HIGH FREQUENCY INDUCTION HEATING

A mathematical model was established for the temperature field developed during high frequency induction heating （HFIH） by Maxwell＇s equations. It required solving the coupled equations of the electromagnetic and temperature fields. The numerical simudation was performed using FEMLAB. The comparison of the calculations using the proposed model with experimental results showed a very good correlation. The effects of the heating parameters in high frequency induction such as the distance between the plate and the coil, the applied current, the frequency, and the turns of the coil on the temperature profiles developed in the plate were also discussed using the established model.

Numerical Simulation of Multi-track and Multi-layer Temperature Field on Laser Direct Metal Shaping

To improve the mechanical properties of the parts fabricated by Laser Direct Metal Shaping(LDMS),it is of great significance to understand the distribution regularities of transient temperature field during LDMS process.Based on the“el- ement birth and death”technique of finite element method,a three-dimensional multi-track and multi-layer model for the transient temperature field analysis of LDMS is developed by ANSYS Parametric Design Language(APDL)for the first time.In the fab- ricated modal,X-direction parallel reciprocating scanning paths is introduced.Using the same process parameters,the simulation results show good agreement with the microstructure features of samples which fabricated by LDMS.

Numerical Simulation of Temperature Field and Thermal Stress Field of Work Roll During Hot Strip Rolling

Based on the thermal conduction equations, the three-dimensional （3D） temperature field of a work roll was investigated using finite element method （FEM）. The variations in the surface temperature of the work roll during hot strip rolling were described, and the thermal stress field of the work roll was also analyzed. The results showed that the highest roll surface temperature is 593 ℃, and the difference between the minimum and maximum values of thermal stress of the work roll surface is 145.7 MPa. Furthermore, the results of this analysis indicate that temperature and thermal stress are useful parameters for the investigation of roll thermal fatigue and also for improving the quality of strip during rolling.

COUPLED NUMERICAL SIMULATION ON COLD ROLLER'S TEMPERATURE FIFLD-PHASE TRANSFORMATION - STRESS FIELD DURING ITS QUENCHING PSOCESS

Complicated changns occur inside the steel parts during quenching process. The abruptly changed boundary conditions make the temperature field,micro - structure and stress field change dramatically in very short time, and these variables take a contact interactions in the whole process. In this paper, a three dimensional non - linear mathematical model for queeching process has been founded and the numerical simulation on temperature field,microstructre and stress field has been realized.In the FEM analysis, the incremental iteration method is used to deal with such complicated nonlinear as boundary nonlinear, physical property nonlinear,transformation nonlinear etc.The effect of stress on transformation kinetics has been considered in the calculation of microstructure. In the stress field anal- ysis,a thermo- elasto - plastic model has been founded, which considers such factors as transforma- tion strain,transformation plastic strain, themal strain and the effect of temperature and transforma- tion on mechanical propertier etc. The transient temperature field, microstructure distribution and stress field of the roller on any time can be displayed vividly,and the cooling curve and the changes of stress on any position can also be given.

Numerical simulation of the temperature fields of stainless steel with different roller parameters during twin-roll strip casting

The temperature field of stainless steel during twin-roll strip casting was simulated by experiment and a finite element （FE） model. By comparing the measured result with the simulated values, it is found that they fit close to each other, which indicates this FE model is effective. Based on this model, the effects of roll gap （t） and roll radius （R） on solidification were simulated. The simulated results give the relationship between t or R and the position of the freezing point. The larger the t is and the smaller the R is, the closer the position of the freezing point is to the exit.