具有蒸发液滴两相介质近壁流动的数学分析

在双连续介质理论框架下，采用匹配渐进展开方法导出并求解了具有蒸发液滴的汽雾流中层流边界层方程，给出了控制汽雾流的相似判据。对于沿曲面的流动，边界层方程的形式取决于是否存在液滴的惯性沉积。给出了热钝体驻点附近蒸汽－液滴边界层的数值计算结果。它们表明：由于蒸发，在边界层内近壁处形成了一个无液滴区域；在该区上边界处，液滴半径趋于零而液滴数密度急剧增高。液滴蒸发及聚集的联合效应造成了表面热流的显著增加，甚至在自由来流中液滴质量浓度很低时此效应依然存在。     

Heat and mass transfer investigation of rotating hydrocarbons droplet which behaves as a hard sphere

The steady state boundary layer equations around rotating pure hydrocarbon droplet are solved numerically. The droplet is simulated to behave as a hard sphere. The transfer equations are discretized using an implicit finite difference method where Thomas algorithm solves the system of algebraic equations. Moreover, dimensionless parameters of heat and mass transfer phenomena around a rotating hexane droplet concluded. The thickness of the boundary layer is unknown for this model and therefore, it is determined. Further, this work proposes correlations of Nusselt and Sherwood numbers for monocomponent hydrocarbon droplets in evaporation. These correlations consider the rotation phenomena and further, the variation of the thermophysical and transport properties in the vapour phase.     

Heat flux effect on the droplet entrainment and deposition in annular flow dryout

This paper discusses the internal mass transfer process in annular flow dryout. The emphasis is put on the order of magnitude estimation of respective hydrodynamic and thermal mechanisms and the analysis of the heat flux effect on droplet entrainment and deposition. A simple interfacial turbulence model is developed to characterize the turbulence intensity suppression due to interface tension. The heat flux effect on droplet entrainment depends on the competition between the shear force decrease due to vapor effusion and the bubble emission: in low flow condition, the bubble emission outweighs the shear force decrease, thus the net effect is to increase the droplet entrainment; in high flow condition, the situation may reverse. The heat flux impact on droplet deposition is significant only for very fine droplets (less than 1 μm) because of the coupled effect of interface turbulence damping and the radial vapor effusion due to evaporation, but for droplets of medium and large sizes the heat flux effect is negligible. The analysis is then used to develop constitutive equations for droplet entrainment and deposition rates to take into account the interaction between thermal and hydrodynamic mechanisms, which gives improved CHF prediction for limiting quality regime (LQR) CHF experimental data.     

乙醇液滴撞击高温壁面蒸发过程的模拟预测研究北大核心CSCD

采用CLSVOF方法,引入描述壁面润湿特性的动态接触角,建立了乙醇液滴撞击高温壁面的数值模型,对乙醇液滴撞击高温壁面后的沸腾蒸发过程展开了研究,并与实验数据进行了对比验证.研究表明:在相同液滴温度下,壁面温度越高,亲水性越强,乙醇液滴的撞击速度越快,液滴的沸腾时间越早,蒸发完成所用时间也越短.在此研究基础上,基于机器学习算法,建立了液滴蒸发预测模型,对乙醇液滴撞击高温壁面后蒸发剩余量随时间的变化进行了预测研究,并通过将不同机器学习算法的预测结果与模拟结果对比,选出最优预测模型.     

A finite element model based on statistical two-scale analysis for equivalent heat transfer parameters of composite material with random grains

In this paper, a new finite element model based on statistical two-scale analysis for predicting the equivalent heat transfer parameters of the composite material with random grains is presented and its convergence, its error result and the symmetry, positive property of equivalent heat transfer parameters matrix are also proved. Firstly, some definitions of the probability space and the composite material with random grains are described and the STSA formulation predicting the equivalent heat transfer parameters of the composite material are briefly reviewed. Next, a finite element formulation and its corresponding procedure for the composite material with random grains is described. Then, the convergence, the error estimate and the symmetry, positive property of the equivalent heat transfer parameters matrix computed by FE based on STSA are proved. The numerical result shows the validity of the FE model based on STSA and the convergence and the symmetry, positive property of the equivalent heat transfer parameter matrix of the composite material with random grains by the FE model.     

Modeling of aerosol spray characteristics for synthesis of sensor thin film from solution

A model is developed of aerosol spray for synthesis of sensor film from solution. The synthesis technique considered involves atomization of a solution of mixed salts in methanol, spraying of solution droplets, droplet deposition on a heated substrate, evaporation and chemical reaction to produce mixed oxides, and subsequent film growth. The precise control of oxide nanoparticle size distribution and inter-particle spacing in the film is crucial to achieving high sensitivity. These in turn largely depend on the droplet characteristics prior to impingement on the substrate. This paper focuses on the development of a model to describe the atomization and spray processes prior to the film growth. Specifically, a mathematical model is developed utilizing computational fluid dynamics solution of the equations governing the transport of atomized droplets from the nozzle to the substrate in order to predict droplet characteristics in flight. The predictions include spatial distribution of droplet size and concentration, and the effect on these characteristics of swirling inlet flow at the spray nozzle.     

A method and a computer program for determining the thermal diffusivity in a solid slab

The authors describe a method for computing the thermal diffusivity of a solid, based on a computer assisted evaluation of the solution of the transient inverse heat conduction problem.The program computes either the unknown diffusivity or simulates the one-dimensional unsteady heat transfer problem. The user may model the boundary conditions by a choice of different functions.The program provides instruction and information at all stages of input and provides tabular output of results. It may be used by anybody wishing to solve or simulate heat transfer processes.     

A model of the electrothermal ribbon printing process

A sequence of mathematical models describing the electrothermal ribbon printing process is developed. The models describe the electrical processes, heat generation and heat transfer within the ribbon and the transfer of ink from the ribbon to paper. Account has been taken of the nonlinear electrical properties of the ribbon. A model of the paper surface has been developed in order to model the transfer of the ink from the ribbon to the paper. The partial differential equations describing the electric field, the heat flow and the stresses in the ink have been solved using standard techniques.     

电渗流中传热传质过程与熵的分析

在壁面存在恒定热通量条件下,分析微通道内电渗流中传热传质过程与熵的生成.建立数值计算模型,分别采用Poisson-Boltzmann方程、Navier-Stokes方程、Nernst-Planck方程和能量方程来描述微通道内双电层电势、流场、离子浓度和温度的分布情况.引入熵产生,进一步研究不同流动参数对流体传热过程的作用,讨论不同流动参数下各热效应的变化规律,并具体分析热效应参数对流体总熵增加及各部分热效应对总熵比重的影响.结果表明,动电参数与Joule(焦耳)热系数的增大会使得传热性能减弱,动电参数对传热性能影响更为明显;流体的总熵为动电参数、传质系数和质量弥散系数的增函数.     

Flow,heat, and species transfer over a stretching plate considering coupled Stefan blowing effects from species transfer

In this paper, we investigate the flow, heat and mass transfer of a viscous fluid flow over a stretching sheet by including the blowing effects of mass transfer under high flux conditions. Mass transfer in this work means species transfer and is different from mass transpiration for permeable walls. The new contribution from this work is, for the first time, to consider the coupled blowing effects from massive species transfer on flow, heat, and species transfer for a stretching plate. Based on the exact solutions of the momentum equations, which are valid for the whole Navier–Stokes equations, the energy and mass transfer equations are solved exactly and the effects of the blowing parameter, the Schmidt number, and the Prandtl number on the flow, heat and mass transfer are presented and discussed. The solution is given in terms of an incomplete Gamma function. It is found the coupled blowing effects due to mass transfer can have significant influences on velocity profiles, drag, heat flux, as well as temperature and concentration profiles. These solutions provide rare results with closed form analytical expressions and can be used as benchmark problem for numerical code validation.     

The heat and moisture transfer balance theory of garment simulation

To establish the human body model to analyze the heat and moisture transfer on body surface, a new explicit definition of rational L-recursion surface is given and the L-recursion surfaces, in Grassmann spaces, are constructed by using blossom method of the homogeneous normal pyramid form. Based on our human body model, the balance theory of garment simulation, the heat and moisture transfer balance equations, called ICAD-balance equations are obtained. The balance theory of garment simulation integrally studies the complex system of human body-fabric-environment. At the same time, the method of obtaining the heat and moisture transfer balance equations is also based on the mass conservation law, the energy conservation law and the Fish law of capillarity. A finite volume method is employed to solve the ICAD-balance equations.     

Identification of nonlinear heat transfer laws from boundary observations

We consider the problem of identifying a nonlinear heat transfer law at the boundary, or of the temperature-dependent heat transfer coefficient in a parabolic equation from boundary observations. As a practical example, this model applies to the heat transfer coefficient that describes the intensity of heat exchange between a hot wire and the cooling water in which it is placed. We reformulate the inverse problem as a variational one which aims to minimize a misfit functional and prove that it has a solution. We provide a gradient formula for the misfit functional and then use some iterative methods for solving the variational problem. Thorough investigations are made with respect to several initial guesses and amounts of noise in the input data. Numerical results show that the methods are robust, stable and accurate.     

Lattice-Boltzmann Models for heat transfer

A multispeed heat transfer lattice Boltzmann model is presented. The model possesses the perfect gas state equation with arbitrary special heat ratio. The macroscopic conservation equations are derived by the Chapman-Enskog method. The one dimensional simulation for the sinusoidal energy distributions are compared with the theoretical results, showing good agreement. The theoretical conductivity in the energy equation is in accordance with the simulations.     

3D finite element analysis of evaporative laser cutting

A three-dimensional computational model of evaporative laser-cutting process has been developed using a finite element method. Steady heat transfer equation is used to model the laser-cutting process with a moving laser. The laser is assumed continuous wave Gaussian beam. The finite element surfaces on evaporation side are nonplanar and approximated by bilinear polynomial surfaces. Semi-infinite elements are introduced to approximate the semi-infinite domain. An iterative scheme is used to handle the geometric nonlinearity due to the unknown groove shape. The convergence studies are performed for various meshes. Numerical results about groove shapes and temperature distributions are presented and also compared with those by semi-analytical methods.     

A Note on the Stefan-Boltzmann Problem for Heat Transfer in a Fin

A fin is traditionally thought of as an extension of a surface to facilitate the transfer of heat away from a larger body to which it is attached. In this paper, the authors study some mathematical properties of a nonlinear heat transfer model for a fin and its relation to an associated linear model. Specifically, they prove that the solution exists and is unique, and they determine bounds for the temperature. Further, they prove the monotonicity of the temperature distribution, and they obtain an estimate for the maximal difference between the temperatures as determined by the nonlinear and linear models.     

Theoretical analysis of an optimal control problem of conductive–convective–radiative heat transfer

The problem of optimal heat removal from a three-dimensional domain is considered. The specific of the study consist in accounting for the radiative heat transfer. The so-called P₁ approximation of the radiative heat transfer equation is used, which reduces the model to a nonlinear elliptic system. A problem of optimal boundary control of this system is considered. The solvability of the control problem is proved, and necessary optimality conditions of first order are derived. Examples of non-singularity of these conditions are given.     

Optimal paths for minimizing entransy dissipation during heat transfer processes with generalized radiative heat transfer law

A common of finite-time heat transfer processes between high- and low-temperature sides with generalized radiative heat transfer law [q ∝ Δ(Tⁿ)] is studied in this paper. In general, the minimization of entropy generation in heat transfer processes is taken as the optimization objective. A new physical quantity, entransy, has been identified as a basis for optimizing heat transfer processes in terms of the analogy between heat and electrical conduction recently. Heat transfer analyses show that the entransy of an object describes its heat transfer ability, as the electrical energy in a capacitor describes its charge transfer ability. Entransy dissipation occurs during heat transfer processes, as a measure of the heat transfer irreversibility with the dissipation related thermal resistance. Under the condition of fixed heat load, the optimal configurations of hot and cold fluid temperatures for minimizing entransy dissipation are derived by using optimal control theory. The condition corresponding to the minimum entransy dissipation strategy with Newtonian heat transfer law (n = 1) is that corresponding to a constant heat flux rate, while the condition corresponding to the minimum entransy dissipation strategy with the linear phenomenological heat transfer law (n = −1) is that corresponding to a constant ratio of hot to cold fluid temperatures. Numerical examples for special cases with Newtonian, linear phenomenological and radiative heat transfer law (n = 4) are provided, and the obtained results are also compared with the conventional strategies of constant heat flux rate and constant hot fluid (reservoir) temperature operations and optimal strategies for minimizing entropy generation. Moreover, the effects of heat load changes on the optimal hot and fluid temperature configurations are also analyzed.     

Convective flow and heat transfer of a viscous heat generating fluid in the presence of a moving,infinite, vertical,porous plate

The analysis of convective flow and heat transfer of a viscous heat generating fluid past a uniformly moving, infinite, vertical, porous plate has been made systematically with a view to throw adequate light on the effects of the plate-motion and the presence of heat generation/absorption on the flow and heat transfer characteristics. The equations of conservation of momentum and energy which govern the flow and heat transfer of the said problem have been solved numerically by the method of Runge-Kutta-Gill. The numerical results thus obtained for the flow and heat transfer characteristics have revealed many an interesting behaviour, of the skin friction and the rate of heat transfer coefficient at the plate.     

A dynamic subgrid-scale model for the large eddy simulation of stratified flow

A new dynamic subgrid-scale (SGS) model, including subgrid turbulent stress and heat flux models for stratified shear flow is proposed by using Yoshizawa’s eddy viscosity model as a base model. Based on our calculated results, the dynamic subgrid-scale model developed here is effective for the large eddy simulation (LES) of stratified turbulent channel flows. The new SGS model is then applied to the large eddy simulation of stratified turbulent channel flow under gravity to investigate the coupled shear and buoyancy effects on the near-wall turbulent statistics and the turbulent heat transfer at different Richardson numbers. The critical Richardson number predicted by the present calculation is in good agreement with the value of theoretical analysis