Thermocapillary convection in a target irradiated by an intense charged particle beam

A mathematical model is proposed for the heat-and-mass transfer in a target irradiated by an intense charged particle beam. It includes mechanics of continua equations and a kinetic equation for fast particles that are closed by a wide-range equation of state. A method for solving the model equations, which is based on the division of motion into vortex and potential flows, is proposed, and a numerical experiment is performed. Thermocapillary convection is shown to be the main mechanism of liquid-phase mixing in the target. Convective mixing is found to be effected when the pulse duration is much shorter than the characteristic thermal diffusivity time. Thermocapillary convection is shown to provide mixing on scales of 1–20 μm depending on the irradiation conditions.     

Possibilities for achieving steady-state growth conditions during oriented crystallization of gallium antimonide by the vertical Bridgman method using the “Polizon” setup

The possibility of controlling the heat-and-mass transfer processes to achieve steady-state conditions of gallium antimonide crystallization by the vertical Bridgman method with a upper heat supply was studied using the “Polizon” setup. Steady-state conditions near the crystallization front are achieved due to elimination of the Marangoni convection, growth axis orientation along the gravity vector, minimization and optimization of the radial and axial temperature gradients, respectively, and crystallization during steady motion of the temperature field along a cell with a sample without its mechanical motion with respect to heaters. The experimental results were compared with numerical calculations of the heat-and-mass transfer processes and crystallization parameters, including those for microgravity conditions.     

Coupled phase transitions under periodic perturbation

The influence of periodic perturbation on the system of two nonlinear stochastic equations, which model low-frequency pulsations in crisis and transient modes of heat-and-mass transfer with phase transitions, has been investigated by numerical methods. When studying the influence of the periodic perturbation on the system, a researcher should largely take into account the phase diagram. It is shown that nonequilibrium phase transitions from asymmetric cycles of phase trajectories to centrally symmetric ones occur in the absence of noise. These transitions are accompanied by the stochastic resonance response, which enhances as the frequency of the external periodic force decreases.     

The influence of heat transfer conditions at the hot particle-liquid fuel interface on the ignition characteristics

The problem of ignition in the conditions of nonideal contact between liquid fuel and a single metallic particle heated to high temperatures is numerically solved. A gas-phase ignition model is created with regard to the heat-and-mass transfer processes in the gas region near the ignition source and the layer separating the particle and the fuel. The scale of the impact of the heat source surface roughness upon the ignition characteristics in a hot particle-liquid fuel-oxidant system is determined.     

Modelling of convective processes during the Bridgman growth of poly-silicon

An original 3D model was used to numerically examine convective heat-and-mass transfer processes in the melt during the growth of polycrystalline silicon in vertical Bridgman configuration. The flow in the liquid was modelled using the Navier — Stokes equations in the Boussinesq approximation. The distribution of dissolved impurities was determined by solving the convective diffusion equation. The effects due to non-uniform heating of the lateral wall of the vessel and due to the shape of the crystallization front on the structure of melt flows and on the distribution of dissolved impurities in the liquid are examined.     

Cluster hydrodynamic model of the heat and mass transfer in crystal growth and its significance for space materials science

Two heat-and-mass transfer models are considered as applied to modeling of crystallization from melts in zero gravity, i.e., the cluster hydrodynamic and integral viscosity increase models which take into account the additional melt flow drag force near the phase interface. It was shown that the consideration of this force is required to correctly describe the anomalous impurity distributions in semiconductor single crystals grown under conditions of orbital space flight. The advantages of the first model were indicated. A new efficient method for solving ill-conditioned systems of finite-difference elliptic equations was developed. Calculations of experimental benchmarks with phase transition showed good agreement between calculated and experimental results.     

Intensification of aeration and mass transfer in wastewater treatment by discrete-pulse energy input

The article focuses on the application of thermophysics in environmental protection, namely the wastewater treatment due to mass transfer enhancement and acceleration of the reaction of biological oxidation. Intensification results from the effect of the discrete-pulse energy input (DPEI) method on the treated medium (wastewater). The method is implemented by means of a new heat-and-mass equipment, namely, an aerator-oxidizer of rotor type.     

Thermal diffusion of hydrogen in zirconium with allowance for thermal stresses

The thermal diffusion of hydrogen atoms in zirconium is studied with allowance for thermal stresses. As a mathematical model, a steady-state temperature in a hollow cylinder is considered. The logarithmic coordinate dependence of this temperature allows an exact analytical solution to be obtained for a diffusion kinetics problem. The results of a theoretical analysis can serve as a test example for studying mass transfer in systems with a more complex coordinate dependence of temperature.     

Intensification of cooling by a pulsed gas-droplet flow: Equipment,parameters, and results

A bench for studying heat exchange between a pulsed spray and a surface heated to a temperature below the boiling point is designed. A calorimeter to measure the integral heat exchange accurate to 1.5–3.0% and equipment generating the pulse spray are described. The main parameters of the forming gas-drop-let flow (the gas and liquid velocities, the variation of the hydropulse duration and the size of flow-constituting droplets when moving toward a heat exchanger, and the liquid concentration distribution over the cross section and along the flow) and respective measuring techniques are given. It is shown that the duration of a droplet train in the flow influences heat-and-mass transfer.     

结霜等截面环肋传热特性

通过适当假设,推导出了结霜等截面环肋传热的数学模型,然后得到其传热热问题的修正解,同时给出其相应的热流量计算公式。与一般简化的肋传热计算公式相比,该解提高了计算精度,并且表达形式简单,可以很方便的应用于工程实践;对结霜肋片的设计有一定的理论指导作用,并可以推广到其他类似的传热等问题中。     

烟气型吸收式制冷机的变工况特性研究

基于分布式冷热电联产系统变工况运行的实际需要,建立了烟气型双效溴化锂吸收式制冷机的变工况模型。制冷机变工况模拟计算时,保持浓溶液流量及换热系数(高压发生器除外)不变,得到了烟气进口温度、烟气流量及冷却水进口温度变化时的制冷机各重要性能参数曲线,发现当烟气流量低于50%时,COP下降较快,冷却水进口温度降低时有利于制冷机运行,但是要注意防止浓溶液结晶。制冷机额定工况模拟计算时,与已有文献进行对比,验证模型的可靠性。     

Modelling of thermogravitation convection in closed volume with local sources of heat release

A mathematical model is presented for unsteady conjugate convective-conductive heat transfer in a closed volume with local sources of heat release under the conditions of a convective-radiation heat exchange on one of external faces of the solution region. The thermogravitation convection regime was analysed for moderate Grashof numbers. The typical temperature and velocity fields were obtained, and the fields of desired quantities were compared for the planar and three-dimensional models in one of the typical sections of the solution region. The work was supported by the Russian Foundation for Basic Research and Administration of the Tomsk Region (No. 05-02-98006, competition r_ob_a).     

封闭圆内开缝圆自然对流换热的振荡特性

本文通过数值计算探讨了封闭圆内开缝圆自然对流换热的振荡特性。数值计算以整个圆为计算区域,采用了非稳态的数学模型和具有QUICK差分格式的SIMPLE算法。在相同条件下计算结果和实验结果符合很好。数值结果显示, 当几何结构一定时,Rayleigh数Ra小于某个临界值时,流动和换热处于稳态,并且关于垂直中心线对称;Ra大于这个临界值时,流动和换热是振荡的,非对称的。数值实验还表明,流动和换热出现振荡时的临界Rayleigh数Rac与开缝圆的开缝度有关,且流动和换热的振荡会出现对称振荡和非对称振荡两种情形。     

Generalized relativistic Chapman-Enskog solution of the Boltzmann equation

The Chapman-Enskog method of solution of the relativistic Boltzmann equation is generalized in order to admit a time-derivative term associated to a thermodynamic force in its first order solution. Both existence and uniqueness of such a solution are proved based on the standard theory of integral equations. The mathematical implications of the generalization introduced here are thoroughly discussed regarding the nature of heat as chaotic energy transfer in the context of relativity theory.     

Stability analysis of unsteady stagnation-point gyrotactic bioconvection flow and heat transfer towards the moving sheet in a nanofluid

The present work investigated the unsteady stagnation-point flow and heat transfer of a nanofluid containing gyrotactic microorganisms past a permeable moving surface. The similarity transformations produced the mathematical model in the simpler form, which is in the form of ordinary differential equations, and the collocation method solved it numerically. The dual solutions are observable when the governing parameters vary. The decelerating flow and weak effect of suction at the shrinking sheet delays the boundary layer separation. Stability analysis showed that the upper branch solution is a solution with the stabilizing feature while the lower branch solution is an unstable solution which implies the flow with separation. This theoretical study is significantly relevant to microscopic biological propulsion integrated with the nano-based system.     

Mathematical structure of the three-dimensional（3D） Ising model

An overview of the mathematical structure of the three-dimensional(3D) Ising model is given from the points of view of topology,algebra,and geometry.By analyzing the relationships among transfer matrices of the 3D Ising model,Reidemeister moves in the knot theory,Yang-Baxter and tetrahedron equations,the following facts are illustrated for the 3D Ising model.1) The complex quaternion basis constructed for the 3D Ising model naturally represents the rotation in a(3+1)-dimensional space-time as a relativistic quantum statistical mechanics model,which is consistent with the 4-fold integrand of the partition function obtained by taking the time average.2) A unitary transformation with a matrix that is a spin representation in 2 n·l·o-space corresponds to a rotation in 2n·l·o-space,which serves to smooth all the crossings in the transfer matrices and contributes the non-trivial topological part of the partition function of the 3D Ising model.3) A tetrahedron relationship would ensure the commutativity of the transfer matrices and the integrability of the 3D Ising model,and its existence is guaranteed by the Jordan algebra and the Jordan-von Neumann-Wigner procedures.4) The unitary transformation for smoothing the crossings in the transfer matrices changes the wave functions by complex phases φx,φy,and φz.The relationship with quantum field and gauge theories and the physical significance of the weight factors are discussed in detail.The conjectured exact solution is compared with numerical results,and the singularities at/near infinite temperature are inspected.The analyticity in β=1/(kBT) of both the hard-core and the Ising models has been proved only for β0,not for β=0.Thus the high-temperature series cannot serve as a standard for judging a putative exact solution of the 3D Ising model.     

Falkner–Skan Flow with Stream-Wise Pressure Gradient and Transfer of Mass over a Dynamic Wall

In this work, an important model in fluid dynamics is analyzed by a new hybrid neurocomputing algorithm. We have considered the Falkner–Skan (FS) with the stream-wise pressure gradient transfer of mass over a dynamic wall. To analyze the boundary flow of the FS model, we have utilized the global search characteristic of a recently developed heuristic, the Sine Cosine Algorithm (SCA), and the local search characteristic of Sequential Quadratic Programming (SQP). Artificial neural network (ANN) architecture is utilized to construct a series solution of the mathematical model. We have called our technique the ANN-SCA-SQP algorithm. The dynamic of the FS system is observed by varying stream-wise pressure gradient mass transfer and dynamic wall. To validate the effectiveness of ANN-SCA-SQP algorithm, our solutions are compared with state-of-the-art reference solutions. We have repeated a hundred experiments to establish the robustness of our approach. Our experimental outcome validates the superiority of the ANN-SCA-SQP algorithm.     

Using Asymptotic Analysis for Developing a One-Dimensional Substance Transport Model in the Case of Spatial Heterogeneity

We study a solution with an internal transition layer of a one-dimensional boundary value problem for the stationary reaction–advection–diffusion differential equation that arises in mathematical modeling of transport phenomena in the surface layer of the atmosphere in the case of non-uniform vegetation on the assumption of space isotropy along one of the horizontal axes and neutral atmospheric stratification. The parameters of the model at which a boundary value problem has a stable stationary solution with an internal transition layer localized near the boundary between different vegetation types are provided. The existence of such a solution and its local Lyapunov stability and uniqueness are proven. The results can be used for developing multidimensional substance transfer models in the case of a spatial heterogeneity.     

不同运行模式下土壤-空气换热器热性能研究

基于多孔介质传热传质理论,建立了二维非饱和土壤耦合热湿迁移的数学模型。基于有限体积法,利用FORTRAN语言开发了二维椭圆型传热传湿计算程序。利用自编程序对不同运行模式下的土壤-空气换热器系统进行了全面的数值研究。连续模式下系统连续运行24 h;间歇模式1下系统运行60 min,然后停止运行30 min;间歇模式2下系统运行60 min,然后停止运行60 min.结果表明,在连续模式下较高含湿量的土壤比较低含湿量的土壤的系统热性能提升20.13%,含湿量较低的土壤在间歇模式下运行系统热性能较连续模式提升12.7%。