Mathematical model of metallurgical thermal processes and application

There are lots of physical changes and chemical reactions in the processes of iron and steel making, these processes are quite complex in the aspect of heat transfer.The processes of iron and steel making can be approximately divided into three kinds.The first kinds are the processes of fusion metallurgy which involve enormous chemical reactions,such as blast furnace,converter,electric furnace and coke oven.The second kinds are the processes of heating and cooling which are mainly the physical changes,such as walking-beam reheating furnace,annular heating furnace and car-type furnace.The third kinds are the processes of heat treatment which mainly adjust metallurgical structure of metal,such as roller hearth heat treatment furnace, strip continuous heat treatment vertical/horizontal furnace and HPH bell-type annealing furnace.Every process can only be finished in particular thermal equipment.And all the physical and chemical processes mentioned above must obey first principles of engineering thermodynamics,heat & mass transfer,hydromechanics, combustion,metallurgy physical chemistry etc,and which can be summarized as principle of heat transfer,mass transfer,momentum transfer and chemistry reaction.In this paper,based on first principle of heat and mass transfer in iron and steel making processes,a series of mathematical models of thermal equipments and processes are presented.Such as the model of hot-blast stoves,coke oven,CDQ-boiler system,sintering, reheating furnace,soaking furnace,annular heating furnace,roller hearth heat treatment furnace,strip continuous heat treatment vertical/horizontal furnace,HPH bell-type annealing furnace,control cooling of medium plate,burner,heat exchanger and regenerative burner etc.The on-line application of the model is based on experimental certification of the mathematical model.And finally the computer optimization system of metallurgical thermal process is obtained.

MATHEMATICAL MODEL OF ~4He QUANTUM INTERFEROMETER GYROSCOPE

The mathematical model of 4He quantum interferometer gyroscope is presented. The model includes the driven equation, the current equation and the position equation. Therefore, it can sufficiently describe the gyro- scope system. The driven equation shows the thermally driven gyroscope can work for a long time but the pres- sure driven one cannot. From the current equation, the superfluid currents passing through the weak link contain the AC currents which show the rotation flux, and other currents caused by drive. As shown in the position equa- tion, the displacement of diaphragm is the only detectable parameter in the gyroscope system. The model is tested by the simulations based on experimental parameters, and can be used to research performance of the gyroscope and analyse the gyroscope error.

Thermal conductivity model of filled polymer composites

Theoretical and empirical models for predicting the thermal conductivity of polymer composites were summarized since the 1920s.The effects of particle shape,filler amount,dispersion state of fillers,and interfacial thermal barrier on the thermal conductivity of filled polymer composites were investigated,and the agreement of experimental data with theoretical models in literatures was discussed.Silica with high thermal conductivity was chosen to mix with polyvinyl-acetate （EVA） copolymer to prepare SiO2/EVA co-films.Experimental data of the co-films＇ thermal conductivity were compared with some classical theoretical and empirical models.The results show that Agari＇s model,the mixed model,and the percolation model can predict well the thermal conductivity of SiO2/EVA co-films.

Empirical correction of kinetic model for polymer thermal reaction process based on first order reaction kinetics

Based on the theory of first-order reaction kinetics,a thermal reaction kinetic model in integral form has been derive.To make the model more applicable,the effects of time and the conversion degree on the reaction rate parameters were considered.Two types of undetermined functions were used to compensate for the intrinsic variation of the reaction rate,and two types of correction methods are provided.The model was explained and verified using published experimental data of different polymer thermal reaction systems,and its effectiveness and wide adaptability were confirmed.For the given kinetic model,only one parameter needs to be determined.The proposed empirical model is expected to be used in the numerical simulation of polymer thermal reaction process.

Glycated Hemoglobin HbA1c:Permittivity Experimental Applications with Some Mathematical Concepts,Temperature and Frequency Variations

Diabetes disorder turns smoothly to be a global epidemic disorder and the glycated hemoglobin(HbA1c)starts to be an efficient marker of it.The dielectric spectroscopy on different human normal-and diabetic-blood samples is used to characterize and to estimate the HbA1c concentration.“dc-”and ac-measurement of the complex conductivity in the temperature range from 280 K up to 320 K,and in the frequency range from one Hz up to 32 MHz have been performed.The thermal activation energy,ΔEσ,of dc-electric conductivity lies in the range 95 meV<ΔEσ<115 meV;while the thermal activation energy,ΔEτ,of RBCs relaxation time is aboutΔEτ=140 meV.The experimental data have been modeled by a physical-model and good fittings have been found between calculated and experimental values.The effective number of charges,nG,T,is estimated after Cole and Cole curves.One has found that nG,T increases with both temperature,T,and with the glycation rate GG.This increase may shed some light on an effective and possible way to treat(and to detect)diabetes disorders via eliminating the excess electric charges produced by glycation processes.The present work sheds the light on the possible combination of focused ultrasound with magnetic resonance imaging to study the dielectric-thermal variations of glycated-RBCs,which can lead to very precise and non-invasive monitoring of glycation concentration in vivo and in vitro via magnetic resonance-thermometry.

Study on the Model of Thermal Channel Spinning Process for PET Polymer

A mathematical model to describe the TCS process inPET high-speed melt-spinning is established.The de-velopment of crystallinity,molecular orientation andmorphological features of high-speed-spun PET fiberin TCS process is investigated at take-up speeds rangingfrom 3600-4400 m/min and thermal channel tempera-tures ranging from 160-200℃ by simulation.The pro-files of tensile force,running velocity,temperature,bi-refringence,crystallinity and diameter in the TCS spin-line for various process conditions are obtained.Thepredicted results using this model are compared with themeasured crystallinty,diameter and birefringence.Theresults indicate that they are in fairly good agreement.The"necking point"in the TCS spinline can be predictedby this model,and its position changes with the corre-sponding process parameters such as take-up speed andthermal channel temperature.It is found that the neck-ing point moves towards the spinneret when the take-upspeed or the thermal channel temperature increases.

GURTIN-TYPE VARIATIONAL PRINCIPLES FOR DYNAMICS OF A NON-LOCAL THERMAL EQUILIBRIUM SATURATED POROUS MEDIUM

Based on the porous media theory and by taking into account the efects of the pore fuid viscidity, energy exchanges due to the additional thermal conduction and convection between solid and fuid phases, a mathematical model for the dynamic-thermo-hydro-mechanical coupling of a non-local thermal equilibrium fuid-saturated porous medium, in which the two constituents are assumed to be incompressible and immiscible, is established under the assumption of small de- formation of the solid phase, small velocity of the fuid phase and small temperature changes of the two constituents. The mathematical model of a local thermal equilibrium fuid-saturated porous medium can be obtained directly from the above one. Several Gurtin-type variational principles, especially Hu-Washizu type variational principles, for the initial boundary value problems of dy- namic and quasi-static responses are presented. It should be pointed out that these variational principles can be degenerated easily into the case of isothermal incompressible fuid-saturated elastic porous media, which have been discussed previously.

Control of Surface Thermal Scratch of Strip in Tandem Cold Rolling

The thermal scratch seriously affects the surface quality of the cold rolled stainless steel strip. Some researchers have carried out qualitative and theoretical studies in this field. However, there is currently a lack of research on effective forecast and control of thermal scratch defects in practical production, especially in tandem cold rolling. In order to establish precise mathematical model of oil film thickness in deformation zone, the lubrication in cold rolling process of SUS410L stainless steel strip is studied, and major factors affecting oil film thickness are also analyzed. According to the principle of statistics, mathematical model of critical oil film thickness in deformation zone for thermal scratch is built, with fitting and regression analytical method, and then based on temperature comparison method, the criterion for deciding thermal scratch defects is put forward. Storing and calling data through SQL Server 2010, a software on thermal scratch defects control is developed through Microsoft Visual Studio 2008 by MFC technique for stainless steel in tandem cold rolling, and then it is put into practical production. Statistics indicate that the hit rate of thermal scratch is as high as 92.38%, and the occurrence rate of thermal scratch is decreased by 89.13%. Owing to the application of the software, the rolling speed is increased by approximately 9.3%. The software developed provides an effective solution to the problem of thermal scratch defects in tandem cold rolling, and helps to promote products surface quality of stainless steel strips in practical production.

Mathematical Model and Its Application of Radial Effective Thermal Conductivity for Coil Heat Transfer in HPH Furnace

Temperature uniformity of steel coils in High Performance Hydrogen bell-type annealing furnace has a significant effect on their quality and production. The hot rolled coil can be considered as a periodically laminated material composed of steel layers and interface layers in radial direction. A new formula for the radial effective thermal conductivity has been proposed, which is based on surface characteristic, strip thickness and compressive stress of the rolled coil. Furthermore, it has been used to develop a heat transfer mathematical model for steel coils in the HPH furnace. The calculated annealing curves using this mathematical model are in good agreement with the experimental data.

Effects of calculation approaches for thermal conductivity on the simulation accuracy of billet continuous casting

An unsteady, two-dimensional, explicitly solved fmite difference heat transfer model of a billet caster was presented to clarify the influence of the thermal conductivity of steel on model accuracy. Different approaches were utilized for calculating the thermal conductivity of solid, mushy and liquid steels. Model results predicted by these approaches were compared, and the advantages of advocated approaches were discussed. It is found that the approach for calculating the thermal conductivity of solid steel notably influences model predictions. Convection effects of liquid steel should be considered properly while calculating the thermal conductivity of mushy steel. Different values of the effective thermal conductivity of liquid steel adopted could partly be explained by the fact that different models adopted dissimilar ap- proaches for calculating the thermal conductivity of solid and mushy steels.

ANALYSIS OF THERMAL POST-BUCKLING OF HEATED ELASTIC RODS

Based on the nonlinear geometric theory of extensible rods, an exact mathematical model of thermal post_buckling behavior of uniformly heated elastic rods with axially immovable ends is developed, in which the arc length s(x) of axial line and the longitudinal displacement u(x) are taken as the basic unknown functions. This is a two point boundary value problem of first order ordinary differential equations with strong non_linearity. By using shooting method and analytical continuation, the nonlinear boundary value problems are numerically solved. The thermal post_buckled states of the rods with transversely simply supported and clamped ends are obtained respectively and the corresponding numerical data tables and characteristic curves are also given.

THERMAL-BUCKLING OF THIN ANNULAR PLATES UNDER MULTIPLE LOADS

On the basis of Von Karman equations, the thermal-buckling of thin annular plates subjected to a field of non-uniform axisymmetric temperature and a variety of boundary conditions is discussed. The linearized problem is analyzed and stability boundaries which characterize instability of a plate are obtained by means of numerical and analysis methods.

NONLINEAR VIBRATION AND THERMAL-BUCKLING OF A HEATED ANNULAR PLATE WITH A RIGID MASS

On the basis of Hamilton's principle and dynamic version of von Karman's equations, the nonlinear vibration and thermal-buckling of a uniformly heated isotropic annular plate with a completely clamped outer edge and a fixed rigid mass along the inner edge are studied. By parametric perturbation and numerical differentiation, the nonlinear response of the plate-mass system and the critical temperature in the mid-plane at which the plate is in buckled state are obtained. Some meaningful characteristic curves and data tables are given.

Numerical simulation and experimental verification of solar seasonal soil thermal storage

To analyze the characteristics of solar seasonal soil thermal storage in a solar-ground coupled heat pump system (SGCHPS) in severe cold area,the software FLUENT was used to establish the three-dimensional unsteady state fluid-solid coupling mathematical model of multi-well ground heat exchanger (MWGHE).The User-Defined Functions (UDF) of solar collector and plate heat exchanger were written and dynamically loaded into the model of MWGHE as the boundary conditions.In this way,the dynamic simulation of solar seasonal soil thermal storage was realized.The comparison of simulative and experimental results showed that the overall variation trend of simulative and experimental values achieves a good agreement with time;the relative errors of simulated parameters are all in the allowable range.Therefore,it can be obtained that the models established can be applied in the investigation of performance of solar seasonal soil thermal storage.At the same time,it provides a theoretical basis for the study of heating in SGCHPS and soil heat balance analysis after long-time thermal storage and extraction.

Modeling Thermal Regulation in Thin Vascular Systems:A Mathematical Analysis

Mimicking vascular systems in living beings,designers have realized microvascular composites to achieve thermal regulation and other functionalities,such as electromagnetic modulation,sensing,and healing.Such material systems avail circulating fluids through embedded vasculatures to accomplish the mentioned functionalities that benefit various aerospace,military,and civilian applications.Although heat transfer is a mature field,control of thermal characteristics in synthetic microvascular systems via circulating fluids is new,and a theoretical underpinning is lacking.What will benefit designers are predictive mathematical models and an in-depth qualitative understanding of vascular-based active cooling/heating.So,the central focus of this paper is to address the remarked knowledge gap.First,we present a reduced-order model with broad applicability,allowing the inlet temperature to differ from the ambient temperature.Second,we apply mathematical analysis tools to this reduced-order model and reveal many heat transfer properties of fluid-sequestered vascular systems.We derive point-wise properties(minimum,maximum,and comparison principles)and global properties(e.g.,bounds on performance metrics such as the mean surface temperature and thermal efficiency).These newfound results deepen our understanding of active cooling/heating and propel the perfecting of thermal regulation systems.

A Thermal-Hydraulic Coolant Channel Module (CCM) for Single- and Two-Phase Flow

A theoretical “drift-flux based thermal-hydraulic mixture-fluid coolant channel model” is presented. It is the basis to a corresponding digital “Coolant Channel Module (CCM)”. This purpose derived “Separate-Region Mixture Fluid Approach” should yield an alternative platform to the currently dominant “Separate-Phase Models” where each phase is treated separately. Contrary to it, a direct procedure could be established with the objective to simulate in an as general as possible way the steady state and transient behaviour of characteristic parameters of single- and/or (now non-separated) two-phase fluids flowing within any type of heated or non-heated coolant channels. Their validity could be confirmed by a wide range of verification and validation runs, showing very satisfactory results. The resulting universally applicable code package CCM should provide a fundamental element for the simulation of thermal-hydraulic situations over a wide range of complex systems (such as different types of heat exchangers and steam generators as being applied in both conventional but also nuclear power stations, 1D and 3D nuclear reactor cores etc). Thereby the derived set of equations for different coolant channels (distinguished by their key numbers) as appearing in these systems can be combined with other ODE-s and non-linear algebraic relations from additional parts of such an overall model. And these can then to be solved by applying an appropriate integration routine. Within the solution procedure, however, mathematical discontinuities can arise. This due to the fact that along such a coolant channel transitions from single- to two-phase flow regimes and vice versa could take place. To circumvent these difficulties it will in the presented approach be proposed that the basic coolant channel (BC) is subdivided into a number of sub-channels (SC-s), each of them being occupied exclusively by only a single or a two-phase flow regime. After an appropriate nodalization of the BC (and thus its SC-s) and after applying a “modified finite volume method” together with other special activities the fundamental set of non-linear thermal-hydraulic partial differential equations together with corresponding constitutive relations can be solved for each SC separately. As a result of such a spatial discretization for each SC type (and thus the entire BC) the wanted set of non-linear ordinary differential equations of 1st order could be established. Obviously, special attention had to be given to the varying SC entrance or outlet positions, describing the movement of boiling boundaries or mixture levels along the channel. Including even the possibility of SC-s to disappear or be created anew during a transient.

寒冷地区装配式日光温室保温性能仿真

日光温室的保温性能直接影响农作物产量,为了使其提高产量,需要对保温性能进行分析。但由于需要考虑诸多因素,导致分析过程繁复。因此,提出寒冷地区装配式日光温室保温性能仿真研究,利用数学模型化繁为简。计算温室前段与后段曲率,并构建温度场数学模型,使用二次曲线逼近的方式解析该模型;建立有限元分析模型,根据有限元求解思路计算热传递问题,分别确立稳态和瞬态下的热传递微分方程,设置边界条件;结合热传递情况,使用流体动力学算法,计算流体质量、动量和能量守恒公式,进而获得温室不同节点温度。实验结果表明,目标温室的保温性能良好,模拟出的温度与实际温度相符,能够为温室参数改进提供参考依据。

热振子式Z轴MEMS角速度陀螺敏感机理的研究

揭示了一种热振子式Z轴MEMS角速度陀螺的敏感机理。在给出工作原理、热振子的振动模态和陀螺效应的基础上,对敏感结构内的温度场进行了计算。结果表明:(1)开机1.8 s后在敏感结构内形成一个稳定的温度场。(2)热振子在Y方向建立驱动模态,当沿着Z轴输入角速度时,在哥氏力的作用下热振子沿着X方向移动,造成温度场偏移,X方向上对称平行设置的两热线温差ΔT_(X)随着输入加速度az的加大呈现线性增长,温度灵敏度为125 mK/(°/s)。(3)根据输入-输出ω_(z)-V_(Xout)特性曲线,得到数学模型,揭示了该陀螺的敏感机理,陀螺灵敏度为0.095 mV/(°/s),非线性度为2.97%。本研究为优化结构奠定了实用理论基础。

基于热阻调控方法的低温光学系统二级温区传热特性分析

为了实现低温光学系统二级温区的精准控温,同时不引入额外的热负载,提出了一种热阻调控方法,建立了应用于该方法的一维数学模型,运用该数学模型研究了不同真空腔温度条件下不同热阻参数(不同材料参数和几何参数)对二级温区达到热平衡后温度水平和漏热量的影响,同时将该方法和传统的电加热调控方法进行了比较。研究结果表明:当真空腔温度为定值时,随着热阻的增大,二级温区温度升高,漏热量减小;当热阻为定值时,随着真空腔温度的升高,二级温区温度升高,漏热量增大。在文中的研究工况下,当真空腔温度为253.15 K时,二级温区温度水平调节范围为111.1~185.2 K,相应的漏热量从1.75 W减小至1.10 W;当真空腔温度为293.15 K时,温度水平调节范围为120.9~219.4 K,相应的漏热量从2.58 W减小至1.57 W。电加热调控方法使二级温区热负载达到了16.8 W,是热阻调控方法的11倍左右(真空腔温度为293.15 K,二级温区目标温度为220 K左右),随着二级温区温度的升高,电加热调控方法使得系统热负载增大,热阻调控方法与之相反。热阻调控方法使低温光学系统热负载一直处于较低的水平,同时可减少系统对电功率和散热资源的需求。研究结果可为空间应用中的类似低温光学设计提供参考。

日光温室主动蓄放热系统热过程模拟与参数优化研究

为进一步提高日光温室太阳能利用效率,降低加温成本,在当前日光温室主动式水循环蓄放热系统的基础上,构建了系统运行数学模型,利用该模型对系统参数(循环水流量与蓄热水箱体积)进行优化设计。研究结果表明:在兰州地区冬季日光温室生产条件下,当系统循环水流量为0.23 m^(3)·h^(-1),蓄热水箱体积为0.13 m^(3)时,系统性能最优,集、放热效率达到70.62%与98.38%,集/放热单元夜间平均热流密度达到237.84 W·m^(-2)。利用优化后参数,为兰州地区EPS装配式日光温室设计了一套太阳能主动蓄放热加温方案:集放/热单元(高2.05 m,宽1.105 m,厚3 cm)为50个,循环水泵流量为11.5 m^(3)·h^(-1),蓄热水箱体积为6.5 m^(3)。该方案可满足日光温室越冬生产,较优化前节约2个集/放热单元,8.5 m^(3)蓄水池体积,降低了加温成本。