Mathematical models of microwave heating of a coal mass with release of absorbed energy by the heat radiation law

Innovation development of coal power engineering, besides qualitative improvement of traditional technologies, should be based also on invoking novel methods and means both in preparation and efficient combustion of coal and for reduction of toxic emissions. The most activating action on coal fuel is provided by microwave radiation. A microwave field intensifies energy-consuming processes such as drying of coal, its dispersion, removal of impurities, qualitative heating, combustion with improved ecological characteristics, etc. Base information for development of microwave technologies in coal power engineering is a temperature field. In this paper we study approximately analytically a mathematical model of flat coal mass heating when the heat release source, due to absorption of microwave energy, obeys the Bouguer law. A specific feature of this model is the presence of nonlinearity caused by dissipation of energy from the mass surface due to heat radiation. The obtained dependences on the temperature field are the base for calculation of ignition and burnout of coal substance, search for the optimal microwave regimes, estimation of thermal destruction parameters, etc. The present paper is a continuation of authors’ publication in this journal [1].     

Specific features of waveguide heating due to transmission of high-power microwave signals

Waveguide heating due to transmission of microwave signals is studied. Mathematical models are developed to evaluate heat liberation, and differential equations of thermal balance are derived with allowance for different working conditions of waveguides. The results prove the necessity of the further study of the effect of heat liberation in waveguides on strength and functional characteristics.     

薄层物料受激光脉冲热作用的数值模拟

有别于传统的将加热光源作为第二类边界条件的传热计算方法,考虑到激光与薄层多孔材料热相互作用,将激光加热处理为在被加热物料内沿光程按指数规律衰减的内加热源.考虑到薄层多孔材料在大功率微秒脉冲激光作用下可能会出现极为明显的非傅立叶效应,采用非傅立叶导热的双曲型模型描述多孔材料内的传热过程,并用有限差分方法对其进行数值求解,重点分析并讨论了薄层多孔材料的非傅立叶导热现象与物料的光学性质之间的相关关系.     

NATURAL CONVECTION IN ROTATING DRUMS WITH INNER SURFACE HEATING

Two flow visualisation techniques, microencapsulated liquid crystal and tracer methods, are employed to observe the thermal and fluid flow fields, respectively, in a liquid that is enclosed in a rotating drum with inner surface heating. The flow patterns and temperature distribution thus obtained are correlated to determine the conditions for formation of thermally stratified layers. A method is developed to construct a three-dimensional structure of a hot plume ascending from the heating surface by synthesizing three flow structures on three mutually perpendicular cross sections (x-y, y-z, and z-x planes) obtained by the flow visualization technique. The method may be extended to obtain the real-time imaging of a three-dimensional hot plume. A combination of the results from the two tests on the heat and fluid flow fields opens a new dimension in the study of natural convection in a rotating system. Additionally, the temperature-time history inside the Eckman boundary layers is monitored to aid in the understanding of transient thermal behavior and rotational effects on the Eckman boundary layers. The conditions for the incipience of thermally stratified layers are disclosed.     

随机相位和随机频率微波加热效应的数值模拟

 利用时域有限差分法（FDTD）并结合蛙跳技术，通过联合求解Maxwell方程组和热传导方程，模拟了水的微波加热过程，计算了烧杯中的水的温度分布；研究了随机相位和随机频率微波功率源合成时水的加热情况，对比了随机相位和随机频率非相干微波功率源与相干微波功率源作用下水的吸热和温升。计算结果表明，随机相位功率源进行合成时，烧杯中的水温分布更均匀，水所吸收的热量也较相干功率源合成加热时有较大增加；而随机频率功率源进行合成时，加热效果没有明显的变化。     

Flamelet modeling of coal particle ignition

This paper numerically investigates the ignition of a single coal particle during the devolatilization phase in a laminar entrained-flow reactor, for which experimental data are available from Molina and Shaddix [3]. Different numerical approaches are combined to evaluate the non-premixed flamelet approach for coal particle ignition. First, the particle trajectory and the particle heating are simulated with a Lagrangian–Eulerian approach using a detailed pyrolysis model. In a second step, these results are used as transient boundary conditions for a simulation fully resolving the flow, the mixing field and the chemical reactions around the particle. Finally, in combination with the boundary conditions the time-dependent scalar dissipation rate profiles from the resolved particle calculation are used in a flamelet calculation for the particle up- and downstream directions. Very good agreement is obtained in terms of ignition delay as well as temperature and chemical species distributions in the mixture fraction space when the resolved particle calculation and the unsteady flamelet calculation are compared in the downstream direction. Good agreement is obtained when the numerical results for the ignition time and the time-averaged OH distribution are compared with the available experimental data. The results show the capability of the laminar flamelet approach to correctly predict coal particle ignition during devolatilization using accurate scalar dissipation rate profiles.     

Propagation of a normal-superconductor boundary along a high-T c superconducting film heated by microwave radiation

The dynamics of the superconducting-normal (S-N) transition in a thin high-temperature superconducting film heated by microwave radiation is investigated theoretically. The dependence of the rate of propagation of the normal-superconductor (NS) interphase boundary on the intensity of the radiation is obtained by solving the two-dimensional nonstationary heat conduction equation. It is shown that in calculating this dependence it is important to take into account two-dimensional effects connected with nonlinearity of heating over the substrate thickness, the reverse side of which is stabilized with respect to temperature. The results obtained may be important in investigating S-N transitions in superconducting devices used in the microwave range. Zh. Tekh. Fiz. 68, 111–116 (January 1998)     

加热方式对真空冷冻干燥过程的影响

以平板状饱和牛肉为对象，对不同供热方法下冷冻干燥过程的传热传质进行了数值计算与实验研究，分析比较了表面加热与微波加热两种供热方式对冻干过程的影响，为冻干过程中供热方式的选择提供了理论依据及分析方法。     

基于分子运动对流换热和热辐射下煤粉颗粒群粒子的加热分析

本文建立了在烟气对流加热和辐射状态下的煤粉颗粒群加热模型,通过数值模拟,模拟研究了不同锅炉炉膛尺寸下不同煤粉粒子粒径的煤粉群粒子加热时间以及粒子温升的关系,对对流换热和辐射换热在着火热源中所占比重进行了分析,模型很好的模拟了粒子的升温,能够较好的反映出煤粉粒子加热升温机理,为煤粉射流微元加热及着火提供了计算方法。     

Microwave heating of liquid at the forced flow around a flat plate under the conditions of non-stationary radiation-convection heat transfer

A class of nonlinear problems of non-stationary radiation-convective heat transfer under the conditions of microwave action with a small depth of penetration is considered in a forced laminar flow of liquid around a flat plane. The solutions to these problems are obtained using the effective asymptotic procedures at the successive stages of nonstationary and stationary radiation-convective heat transfer on the heat-radiating horizontal plane. The non-stationary and stationary stages of solution are matched using the “longitudinal coordinate-time” characteristic. The solutions constructed on such principles correlate reliably with the exact ones at the limiting values of such parameters as a small and large intensity of external thermal impact, small and large times, etc. The error of solutions does not exceed 1–7 %. As the plate is removed from the leading edge of the plate due to heat radiation, convective heat transfer degenerates from values characteristic of the boundary condition of the second kind to the values characteristic of the boundary condition of the first kind. A strong effect on the nature of variations of the surface temperature and Nusselt number of the complex parameter of microwave and thermal radiation is noted. An important advantage of the developed method for solving this class of external problems is that even before complex calculations it is possible to perform an exhaustive analysis of the fundamental laws of the processes under study. Despite a number of initial simplifications, the latter do not significantly affect the accuracy of results, guaranteeing reliable quantitative information. The developed method can also be extended to the regimes of forced convection with linear dependence of physical properties on temperature using transformation of A.A. Dorodnitsyn. To confirm adequacy of the constructed mathematical model, stationary radiation-convective heat transfer under the forced flow around a flat plate was studied experimentally. The results of comparison of the theoretical and experimental data show that they are in a good agreement. This again confirms the effectiveness of the developed method for constructing theoretical solutions to the nonlinear problems of forced convection using the asymptotic procedures.     

变系数瞬态热传导问题边界元格式的特征正交分解降阶方法

提出了一种基于边界元法求解变系数瞬态热传导问题的特征正交分解(POD)降阶方法,重组并推导出变系数瞬态热传导问题适合降阶的边界元离散积分方程,建立了变系数瞬态热传导问题边界元格式的POD降阶模型,并用常数边界条件下建立的瞬态热传导问题的POD降阶模态,对光滑时变边界条件瞬态热传导问题进行降阶分析.首先,对一个变系数瞬态热传导问题,建立其边界域积分方程,并将域积分转换成边界积分;其次,离散并重组积分方程,获得可用于降阶分析的矩阵形式的时间微分方程组;最后,用POD模态矩阵对该时间微分方程组进行降阶处理,建立降阶模型并对其求解.数值算例验证了本文方法的正确性和有效性.研究表明:1)常数边界条件下建立的低阶POD模态矩阵,能够用来准确预测复杂光滑时变边界条件下的温度场结果;2)低阶模型的建立,解决了边界元法中采用时间差分推进技术求解大型时间微分方程组时求解速度慢、算法稳定性差的问题.     

绝对式高能量激光能量计温度特性研究

对绝对式量热法高能量激光能量计吸收腔的内、外壁温度差特性进行了详细的理论研究和实验验证。用第二非齐次边界条件和第二齐次边界条件的热传导方程分别建立了吸收腔在激光加热过程中和激光加热结束后的温度分布，利用模拟实验对激光照射吸收腔的过程进行模拟，得到内、外壁温度差的实验数据。利用数值模拟法，对理论分析结果作数值分析，理论分析结果与实验数据非常接近，从而证明了在激光加热过程中，虽然吸收腔内外壁存在固定的温度差，但当激光结束后，该温度差将迅速减小，吸收腔达到热平衡。     

微波加热技术的应用与研究进展

文章简述了微波加热的发展概况，阐述了微波加热的介电损耗机理和微波加热的特性．从微波加热与解冻、微波干燥、微波改性、微波烧结、微波杀菌等方面，介绍了微波加热技术在国内的研究与应用情况，指出微波加热技术具有广阔的发展前景，今后应重点加强微波与物料问相互作用理论、微波场中物料的传热和传质机制、微波加热工艺与设备、微波加热技术和其他技术的有机结合等方面的研究．     

Heat and mass transfer at gas-phase ignition of grinded coal layer by several metal particles heated to a high temperature

Characteristics of gas-phase ignition of grinded brown coal (brand 2B, Shive-Ovoos deposit in Mongolia) layer by single and several metal particles heated to a high temperature (above 1000 K) have been investigated numerically. The developed mathematical model of the process takes into account the heating and thermal decomposition of coal at the expense of the heat supplied from local heat sources, release of volatiles, formation and heating of gas mixture and its ignition. The conditions of the joint effect of several hot particles on the main characteristic of the process–ignition delay time are determined. The relation of the ignition zone position in the vicinity of local heat sources and the intensity of combustible gas mixture warming has been elucidated. It has been found that when the distance between neighboring particles exceeds 1.5 hot particle size, an analysis of characteristics and regularities of coal ignition by several local heat sources can be carried out within the framework of the model of “single metal particle / grinded coal / air”. Besides, it has been shown with the use of this model that the increase in the hot particle height leads, along with the ignition delay time reduction, to a reduction of the source initial temperatures required for solid fuel ignition. At an imperfect thermal contact at the interface hot particle / grinded coal due to the natural porosity of the solid fuel structure, the intensity of ignition reduces due to a less significant effect of radiation in the area of pores on the heat transfer conditions compared to heat transfer by conduction in the near-surface coal layer without regard to its heterogeneous structure.     

DSMC方法下给定热流边界条件的实施

本文详细讨论了DSMC方法中流体温度、能量及边界热流的统计方法,发展了一种从边界热流求得与壁面碰撞分子反射速度的方法。该方法被称为逆温度抽样算法(ITS,Inverse Temperature Sampling)方法。在此基础上,本文发展了DSMC方法中壁面处给定热流边界条件的实施方法。计算结果表明: ITS方法能准确抽样反射分子的特征温度,进而求得分子反射速度。基于该方法的给定热流边界条件可以准确求得壁面处温度分布,以及流场内的压力、速度。     

Numerical modeling of high-temperature heat and mass transfer at laser nitriding of titanium

Numerical modeling of the processes of heat and mass transfer under the action of laser radiation on a titanium surface in a nitrogen medium has been performed. The problem statement includes a system of two-dimensional nonstationary nonlinear equations of heat conduction and diffusion with the corresponding initial and boundary conditions. The problem was solved taking into account the laser beam motion. The character of the distribution of the alloying elements in the zone of laser heating has been investigated. The results obtained make it possible to conclude that the concentrations of the alloying component are essentially inhomogeneous.     

Susceptor-Assisted Enhanced Microwave Processing of Ceramics - A Review

Susceptor-assisted microwave processing is a rapidly growing technology due to its superiority over the conventional processing. In contrast to the conventional heating from the surface, the microwave heating occurs volumetrically via direct interaction with the material. Correspondingly, the microwave heating rates are in general much faster than the heating rates in the conventional furnaces, where heat has to be transferred from the heat sources to the material via conduction, convection and radiation. The need for the susceptor stems from the fact that the majority of the ceramics are low lossy materials and they cannot couple well with the microwave at room temperatures. The susceptor provides an easy and non-invasive technique to exploit the rapid microwave processing even for the highly microwave transparent ceramics, such as alumina, silicon nitride, quartz, etc. This article critically evaluates the susceptor-assisted microwave sintering and solid state synthesis of ceramics which have been reported over the last two decades. A wide range of ceramics has been considered and each case has been analyzed in terms of the enhancement of the processing rates and product qualities (grain structure, material properties, etc.) compared to the conventional processing. It has been shown that the susceptor-assisted microwave processing can greatly reduce the processing time while providing an easy pathway to achieve the desired product qualities. The use of the appropriate susceptor is the key to achieve the fast, smooth, and reliable microwave processing of ceramics and this article provides the required database for the appropriate design of the susceptor based on the process requirement.     

气动加热下高温陶瓷材料内的瞬态耦合换热

采用控制容积法结合蒙特卡罗法与谱带模型,数值模拟了气动加热下高温陶瓷内的辐射与导热瞬态耦合换热.分析了冷却边界条件、各向同性散射和表面特性对高温陶瓷内瞬态温度分布的影响.结果表明,高温下陶瓷内的辐射换热作用十分明显,陶瓷材料的表面特性对瞬态温度分布影响很大,各向同性散射也有明显影响.     

Modelling transient heat conduction in solids at multiple length and time scales: A coupled non-equilibrium molecular dynamics/continuum approach

A method for controlling the thermal boundary conditions of non-equilibrium molecular dynamics simulations is presented. The method is simple to implement into a conventional molecular dynamics code and independent of the atomistic model employed. It works by regulating the temperature in a thermostatted boundary region by feedback control to achieve the desired temperature at the edge of an inner region where the true atomistic dynamics are retained. This is necessary to avoid intrinsic boundary effects in non-equilibrium molecular dynamics simulations. Three thermostats are investigated: the global deterministic Nosé–Hoover thermostat and two local stochastic thermostats, Langevin and stadium damping. The latter thermostat is introduced to avoid the adverse reflection of phonons that occurs at an abrupt interface. The method is then extended to allow atomistic/continuum models to be thermally coupled concurrently for the analysis of large steady state and transient heat conduction problems. The effectiveness of the algorithm is demonstrated for the example of heat flow down a three-dimensional atomistic rod of uniform cross-section subjected to a variety of boundary conditions.     

Radiative effects on magnetohydrodynamic natural convection flows saturated in porous media

A boundary layer solution is presented to study the effects of joule heating on magnetohydrodynamic natural convection flow. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. Four different cases of flows have been studied namely an isothermal surface, a uniform heat flux surface, a plane plume and flow generated from—a horizontal line energy source a vertical adiabatic surface. Numerical results presented for the perturbation analysis four boundary conditions with various parameters are tabulated.