可变形孔隙介质中热、水耦合力学问题的代数多格子分析方法

研究了孔隙介质中包括热和质量传递的全耦合多相流问题的代数多格子分析方法。数学模型包括质量、线性矩、能量平衡方程和本构方程,以位移、毛细压力、汽压和温度为基本变量,模型中采用了考虑毛细压力关系的修正有效应力概念,并考虑相变、热传导、对流和潜热交换(汽化-冷凝),气相是由易混合的干空气和水蒸气组成,视为理想气体。考题显示出较高的计算效率。     

On the role of radiative heat transfer in air gaps in vertical continuous casting

A recent asymptotic thermomechanical model for the formation and evolution of air gaps in vertical continuous casting in round moulds is used as the basis for understanding the importance of radiative heat transfer between the mould wall and the solidified shell. Asymptotic analysis is used to systematically reduce the model to a moving boundary problem with a boundary condition in integro-differential form. In addition, a dimensionless parameter is found which determines whether radiation is significant or not for prescribed process operating conditions. Sample computations are carried out using parameters relevant to the continuous casting of copper, and the results are used to interpret earlier findings in the literature on the interaction between air-gap width and thermal radiation.     

Stable non-standard implicit finite difference schemes for non-linear heat transfer in a thin finite rod

In this study, first, three non-standard implicit finite difference schemes are proposed for solving the initial-boundary value problem involving a quartic non-linearity that arises in heat transfer involving conduction with thermal radiation. A thin finite rod exposed to radiating heat across its lateral surface into a medium of constant temperature and convection is ignored. Stability and consistency of the third scheme is proved. Numerical results are compared with non-standard explicit finite difference schemes that show fully stability of our third proposed scheme. Then, three non-standard implicit and three non-standard explicit finite difference schemes are proposed for solving the heat transfer problem with additional convection term. It is shown that in the second case when the model involves conduction, radiation and convection terms, the rod reaches steady state sooner. Numerical results for implicit and explicit schemes are compared and the effect of the convection term is discussed.     

基于Monte-Carlo随机有限元方法的随机边界条件下自然对流换热不确定性研究

为分析边界条件不确定性对方腔内自然对流换热的影响,发展了一种求解随机边界条件下自然对流换热不确定性传播的Monte-Carlo随机有限元方法.通过对输入参数场随机边界条件进行Karhunen-Loeve展开及基于Latin(拉丁)抽样法生成边界条件随机样本,数值计算了不同边界条件随机样本下方腔内自然对流换热流场与温度场,并用采样统计方法计算了随机输出场的平均值与标准偏差.根据计算框架编写了求解随机边界条件下方腔内自然对流换热不确定性的MATLAB随机有限元程序,分析了随机边界条件相关长度与方差对自然对流不确定性的影响.结果表明:平均温度场及流场与确定性温度场及流场分布基本相同;随机边界条件下Nu数概率分布基本呈现正态分布,平均Nu数随着相关长度和方差增加而增大;方差对自然对流换热的影响强于相关长度的影响.     

Convective heat and mass transfer in three-dimensional mixed convection flow of viscoelastic fluid in presence of chemical reaction and heat source/sink

Heat and mass transfer effects in the three-dimensional mixed convection flow of a viscoelastic fluid with internal heat source/sink and chemical reaction have been investigated in the present work. The flow generation is because of an exponentially stretching surface. Magnetic field normal to the direction of flow is considered. Convective conditions at the surface are also encountered. Appropriate similarity transformations are utilized to reduce the boundary layer partial differential equations into the ordinary differential equations. The homotopy analysis method is used to develop the solution expressions. Impacts of different controlling parameters such as ratio parameter, Hartman number, internal heat source/sink, chemical reaction, mixed convection, concentration buoyancy parameter and Biot numbers on the velocity, temperature and concentration profiles are analyzed. The local Nusselt and Sherwood numbers are sketched and examined.     

Effects of thermal radiation and space porosity on MHD mixed convection flow in a vertical channel using homotopy analysis method

A study of MHD mixed convection flow through porous space in the presence of a temperature dependent heat source in a vertical channel with radiation has been analyzed. The Rosseland approximation is considered in the modeling of the conduction radiation heat transfer and temperatures of the walls are assumed constants. The governing equations are expressed in non-dimensional form and the series solutions of coupled system of equations are constructed for velocity and temperature using homotopy analysis method (HAM). The effects of various involved parameters on the velocity and temperature field are shown and discussed. The coefficient of skin friction, and the rate of heat transfer coefficient are obtained and illustrated graphically.     

Modelling and analysis of thermal networks through subnetworks for multizone passive solar buildings

An efficient method is presented for the computer analysis in the frequency domain of multizone passive solar buildings. This method models heat conduction and convection between rooms, heat flows which are often not accounted for in order to reduce computation time. Heat transfer through a building is modelled by a thermal network. Massive walls are represented as two-port elements, analogous to non-inductive electrical transmission lines. Nodes representing exterior surfaces, whose temperatures do not have to be explicitly determined, are eliminated by the Norton theorem. The resulting simplified, but still complex networks, are split into subnetworks corresponding to rooms by removing a few simple components; the solutions for the subnetworks are found by means of the nodal formulation and are then coupled to give the system solution, without ever having to solve directly the initial complex network. There are no errors introduced by this decomposition process. This significantly simplifies the analysis of the building network and provides physical insight into the modelling and coupling of its subsystems.     

Influence of surface mass transfer on mixed convection flows over non-isothermal horizontal flat plates

Non-similar solution of a steady mixed convection flow over a horizontal flat plate in the presence of surface mass transfer (suction or injection) is obtained when there is power-law variation in surface temperature. The surface temperature is assumed to vary as a power of the axial coordinate measured from the leading edge of the plate. A non-similar mixed convection parameter is considered which covers the whole convection regime, namely from pure free convection to pure forced convection. Numerical results are reported here to account the effects of Prandtl number, surface temperature, surface mass transfer parameter (suction or injection) on velocity and temperature profiles, and skin friction and heat transfer coefficients.     

Transient conduction in a plate with counteracting convection and thermal radiation at the boundaries

During the flash dehydroxylation of powdered kaolinite it is desirable that a rapidly propagating thermal wave penetrates the cold powder particles in a way that raises the particle interior to the reaction temperature of 600°C without the particle exterior being heated beyond 1000°C. In a production unit this is achieved by performing the heat treatment in a device where particles are heated by convection from hot gas and are subject to heat loss by thermal radiation to cool walls. This paper concerns the fundamental heat transfer problem of the process, decoupled from the thermal effects of the dehydroxylation reaction. Using a plate as the approximation for the particle shape a semi-analytical solution for the plate temperature distribution is obtained as a function of the five dimensionless process parameters: Biot number, radiation number, wall/gas and particle/gas temperature ratios and mode of convection. Accuracy is demonstrated by comparison with an existing numerical solution for the limiting case of pure radiative heating of a plate initially at absolute zero.     

Magneto-Compound Reaction of Convective Flow via a Porous Inclined Plate with Heat Energy Absorption

The current study is concerned with the unsteady heat and mass transfer of MHD free convection flow via a porous inclined plate that accelerates exponentially with temperature and concentration. Heat emission, source/sink, radiation absorption, and reaction are taken into account in the energy and species equations. The innovative part of the work is the analysis of the flow phenomenon with a heat source or sink and radiation absorption along the chemical reaction. The governing PDEs are reduced into ODEs via the non-dimensional variables and afterward solved analytically utilizing the perturbation strategy. Graphical representations of liquid temperature, speed, and concentration as well as the Sherwood \& Nusselt quantities and the skin friction factor are displayed in tabular form for different combinations of appropriate stream quantities. The analysis of a resistance quantum grows with the size of the magnetic, whereas the rates of mass and heat transfer decline with increasing radiation, reaction, and Schmidt number. Thermal-velocity and concentration-velocity profiles interact reciprocally with the accelerating radiation, heat source, and compound reaction. The growth of speed and thermal profiles is clearly visible due to the absorption and Prandtl values. The present results are in strongly consistent with the earlier published results. There are numerous applications for this research in many sectors and material processing for understanding drag in seepage flows on heated/cooled and inclined surfaces.     

CFD modelling of the flow and reactions in the Olympic Dam flash furnace smelter reaction shaft

The performance of flash furnace burners can be evaluated quickly and efficiently using CFD modelling. Gas flows are modelled using the conventional Eulerian approach, while Lagrangian particle tracking is used to model the flow of solid feed through the burner and into the reaction shaft. A composite particle model has been developed that considers the solid feed to be made up of single particles containing appropriate quantities of concentrate, flux and dust. Solid fuels (such as coal) can also be included in the composite particle. Reactions between the solids and gas are then modelled using standard heat and mass transfer relationships. Results from the modelling process are shown for BHP-Billiton’s Olympic Dam copper flash smelter with the burner that was used from 1998–2003. Flow patterns, temperature and gas composition distributions, particle dispersion and residence time, and overall extent of sulphur removal are predicted and used to evaluate furnace performance. However, results are sensitive to the assumed size of the composite particles, and plant measurements are required to determine the appropriate composite particle size to predict quantitative data.     

An advanced dynamic process model for industrial horizontal anode baking furnace

The global aluminum industry is facing new challenges due to new technological developments. Carbon anodes, consisting of mainly petroleum coke and coal tar pitch, are used in the electrolytic production of aluminum. High amperage utilization in the electrolytic cells with the objective of increasing production requires high quality carbon anodes. The anode quality depends both on raw material quality, anode recipe as well as forming and baking conditions of anode manufacturing process. The cost of the baking process constitutes 15 to 25% of the total aluminum production cost [1]. The industrial challenge is to produce better quality anodes consuming less energy, and reducing environmental emissions.A transient two dimensional (2D⁺) process model for horizontal anode baking furnace was developed during this study. The main objective was to develop an efficient furnace model with low computation load and time, using the transient Finite Difference Method and simplified furnace geometry. The model represents several phenomena involved during the anode baking process such as heat transfer (convection, radiation and conduction), fuel combustion, volatile matter (tar, methane and hydrogen) generation and combustion, air infiltration and energy loss to the atmosphere from the walls, the top of the furnace and the foundation. The model was developed using two coupled sub-models; the first one describes the thermal conduction through the solid materials (brick refractory wall, packing coke and anode block) as well as the volatile release, and the second one describes the gas flow, heat and mass transfer as well as the combustion of fuel and volatiles in the flue. Compared to the existing process models (where the gas flow in flue is assumed as unidirectional along the horizontal furnace direction), the present model also considers the gas flow in vertical direction and uses four vertical planes per pit section to predict the temperature of the solids. The model predicts 2D temperature distribution within the flue gas (xy plane) and the pit solid materials (yz plane) allowing then the prediction of the pseudo tridimensional distribution of the solid temperature. This model is a useful tool for the continuous monitoring of anode temperature and studying of the horizontal anode baking furnace behaviour. The effect of any change in operational parameters and the energy consumption on the furnace operation can be predicted.     

Numerical simulation for natural convection of micropolar fluids flow along slender hollow circular cylinder with wall conduction effect

This paper presents a numerical analysis of the flow and heat transfer characteristics of natural convection in a micropolar fluid flowing along a vertical slender hollow circular cylinder with conduction effects. The nonlinear formulation governing equations and their associated boundary conditions are first cast into dimensionless forms by a local non-similar transformation. The resulting equations are then solved using the cubic spline collocation method and the finite difference scheme. This study investigates the effects of the conjugate heat transfer parameter, the micropolar parameter, and the Prandtl number on the flow and the thermal fields. The conjugate heat transfer parameter reduces the solid–liquid interfacial temperature, the skin friction factor and the local heat transfer rate. The effect of wall conduction on the local heat transfer rate, interfacial temperature and skin friction factor is found to be more pronounced in a system with a greater Prandtl number. Moreover, the current results are comparing with Newtonian fluid to obtain the important results of the heat transfer and flow characteristics on micropolar fluids. It shows that an increase in the interfacial temperature, a reduction in the skin friction factor, and a reduction in the local heat transfer rate are identified in the current micropolar fluid case.     

The effect of conjugate heat transfer on MHD mixed convection about a vertical slender hollow cylinder

The problem of steady laminar magnetohydrodynamic (MHD) mixed convection heat transfer about a vertical slender hollow cylinder is studied numerically, under the effect of wall conduction. A uniform magnetic field is applied perpendicular to the cylinder. The non-similar solutions using the Keller box method are obtained. The wall conduction parameter, the magnetic parameter and the Richardson number are the main parameters. For various values of these parameters the local skin friction and local heat transfer parameters are determined. The validity of the methodology is checked by comparing the results with those available in the open literature and a fairly good agreement is observed. Finally, it is determined that the local skin friction and the local heat transfer coefficients increase with an increase the magnetic parameter Mn and buoyancy parameter Ri and decrease with conjugate heat transfer parameter p.     

Buoyancy and chemical reaction effects on MHD mixed convection heat and mass transfer in a porous medium with thermal radiation and Ohmic heating

The combined effect of mixed convection with thermal radiation and chemical reaction on MHD flow of viscous and electrically conducting fluid past a vertical permeable surface embedded in a porous medium is analyzed. The heat equation includes the terms involving the radiative heat flux, Ohmic dissipation, viscous dissipation and the internal absorption whereas the mass transfer equation includes the effects of chemically reactive species of first-order. The non-linear coupled differential equations are solved analytically by perturbation technique. The results obtained show that the velocity, temperature and concentration fields are appreciably influenced by the presence of chemical reaction, thermal stratification and magnetic field. It is observed that the effect of thermal radiation and magnetic field is to decrease the velocity, temperature and concentration profiles in the boundary layer. There is also considerable effect of magnetic field and chemical reaction on skin-friction coefficient and Nusselt number.     

Analytic solutions for a rotating radial fin of rectangular and various convex parabolic profiles

The homotopy analysis method (HAM) is used to develop an analytical solution for the thermal performance of a radial fin of rectangular and various convex parabolic profiles mounted on a rotating shaft and losing heat by convection to its surroundings. The convection heat transfer coefficient is assumed to be a function of both the radial coordinate and the angular speed of the shaft. Results are presented for the temperature distribution, heat transfer rate, and the fin efficiency illustrating the effect of thickness profile, the ratio of outer to inner radius, and the angular speed of the shaft. Comparison of HAM results with the direct numerical solutions shows that the analytic results produced by HAM are highly accurate over a wide range of parameters that are likely to be encountered in practice.     

An air sparging CFD model for heap bioleaching of chalcocite

A computational fluid dynamics (CFD) solver CFX4.4 is used to implement a steady state model of heap bioleaching of chalcocite, which includes air sparging (forced aeration) based on a previous model entirely under natural convection. The model assumes the oxygen supply limits the reaction rate. A parameter analysis is performed which shows that the factors important to copper leaching are liquid and air flow rates, permeability and fraction of pyrite to chalcocite leached (FPY). The ability to control which parts of the bed received the highest extraction as a function of the liquid and air flow rates was established. Sparging is found to increase the oxygen concentration throughout the heap compared to the circumstance with no sparging (natural convection), and consequently improves the copper extraction significantly. The results show that sparging does not provide any better copper extraction for very high heap permeabilities. The arrangement and spacing of air sparging inlets is analysed in regard to the existence of oxygen starved regions between the inlets.     

Linear and nonlinear electroconvection under AC electric field

Linear and non-linear stability analyses of electroconvection under an AC electric field are investigated using the normal mode method and truncated representation of Fourier series respectively. The principle of exchange of stabilities is shown to be valid and subcritical instability is ruled out. Several qualitative results on stability are discussed on the governing linear autonomous system, and also by using the concept of a self-adjoint operator. Spectral analysis of electroconvection is also made to provide information on the relative dominance of various modes on convection. The quantification of heat transfer is done on the Nusselt number-Rayleigh number plane for steady finite amplitude convection and through time series plots of the Nusselt number for unsteady finite amplitude convection. The effect of the electric number on stream line pattern and Nusselt number is delineated. Time series plots of the amplitudes of thermal conduction and convection are also presented. It is found that the effect of increasing the electric number is to enhance the amplitudes and thereby the heat transport. The sensitive dependence of the solution of the Lorenz system of electroconvection to the choice of initial conditions points to the possibility of chaos.     

Influence of eddies on heat transfer in Couette flow over undulated substrates

In Couette flows over undulated substrates eddies can be generated under creeping flow conditions. In contrast to free surface flows on undulated substrates even smooth bottom undulations allow for eddy generation due to the kinematical constraints. The subject of our paper is how these flow patterns interact with the temperature field in non–isothermal flows. Our analysis of the thermo–mechanical coupling is focused on the two dominant effects, namely convection and thermoviscosity, whereas dissipation heat, buoyancy and temperature–dependence of the remaining material parameters are neglected. We solve the problem in two steps: First, the influence of the eddies on the convective heat transfer is considered by solving the heat conduction equation with convection. For the velocity field we take the solution resulting analytically from Reynolds' lubrication approximation for the isothermal flow. The thermoviscous feedback of the resulting temperature field to the flow is considered in forthcoming papers. For the construction of the solution an analytical approach based on a nonorthogonal series representation of the fundamental fields and a variational formulation of the field equations is used. The results are visualised and the physical effects they reveal are discussed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)