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By Olga A. Gomon, Alexey N. Lozhko

The technology of heat treatment for metal frequently includes multiple fast heating and cooling of the products surface. If the product is heavy-weight or long-size, its moving from a zone of cooling to a zone of heating and return require a long time. Other important condition of ensuring qualitative surface at heat treatment is intensification of cooling phase. It is known that turbulization of a flow activates heat exchange and increases efficacy of cooling without increasing volume flow rate of water. Additional difficulty is to ensure the regularity of heating and cooling on length of a product. The technology of cyclic heat treatment of rolling products, at which mobile zone of turbulent heat exchange is formed on the surface of a product, was developed and realized. The submission of water occurs through to face spray systems. Each of the systems has six long-range atomizers, which are located circularly. Two flows of water move towards one another along a surface of a product. When they collide, the right zone of turbulent heat exchange creates heat transfer in this zone of 10-15 time more intensive than on other surface of a product. The effect of moving turbulent zone on length of a product is reached by changing the proportion of volume flow rate of water, which is created by face sprays. The speed of movement for turbulent zone along a surface of a product is chosen so, that the cooling takes place on a small depth only. Then after passing the turbulent zone over a determined site of a surface, its temperature recovers fast owing to hot internal layers. The parameters of process were determined by mathematical simulation of cooling in an installation. The equations for dynamics of movement of collision point of flows, which were received this way, are interesting supplementary products of research. The experiments show that frequency of movement of turbulent zone is an important technological parameter. It defines mechanical properties of a surface and should be chosen depending on a profile of product and metal grade. The results of comparison of mechanical properties of a surface of various rolling products, which were received by developed and conventional technologies, are described in this report. Dependence of regularity of mechanical properties on frequency of movement of turbulent zone is adduced.

Jan 1, 1998

By William J. Mallio

Substantial differences between in situ and conventional technology require that in situ ore grade be established for deposit as distinct from the total contained metal value. Establishing an in situ ore grade involves determining the fraction' of the contained metal that can be leached by the fluid. This depends on the proportion of the ore minerals that occur on fluid flow paths as defined by the permeability distribution. Mechanisms involved in the in situ mining of sulfides are: oxidation of the sulfur, solution of the metals, complexing of the released metals, and a transport to a recovery point. Metal ions may be delayed or lost due to inefficiencies in these pro-cess steps or by reactions of the metal ions in solution with the rock. These reactions can involve precipitation of new phases, exchange of the metals of the interest with Ca or Na in clays or zeolites, retention of metals in oxidized mineral grains, or secondary enrichment of other sulfides along the paths of the solution flow. The efficiency of solution of metals and potential loss or delay mechanisms are controlled by local equilibria (the Eh, pH conditions) present in different parts of the ore zone. Permeability distribution in the rock mass and the coincidence of ore minerais with flow channels must be determined before a deposit can be judged suitable for in situ mining. Laboratory studies indicate that the natural permeability system is dependent on the degree of cementation of veins by late generation hydrothermal activities. The major conclusions of the study are:, 1. Deposit selection is critical; suitable deposit types include deep lying sedimentary deposits, selected zones of porphyry systems and vein controlled hydrothermal deposits; 2. Adequate laboratory and geochemical analyses should be undertaken through quantitative petrographic study and permeability mapping; and 3. Economic incentives for in situ mining must consider limitations of recovery caused by inefficiencies in dissolution and transport associated with particular deposits.

Jan 1, 1981

By Srinath Viswanathan, Zhijing Zhang, Ramana G. Reddy

"The viscosity measurements were carried out on melts of 380 aluminum alloy containing 20 volume % SiC particulates under various shear rates at different temperatures using a Brookfield viscometer. Results showed that viscosities of the melts increased with decreasing temperature and decreased with increasing shear rate. These results were compared with those of 356 alloy and it was found that the temperature had a more significant effect on viscosity of 356 alloy than that of 380 alloy containing SiC particulates. Based on the present experimental data an empirical viscosity model, which considers the effects of both solid fractions in the melt and shear rate, is proposed.IntroductionDiscontinuously reinforced metal matrix composites materials (MMCs) such as aluminum alloy containing SiC particulates have considerable potential for applications in the automotive industry because of their superior stiffness, higher specific mechanical properties, better dimensional stability and strength retention at elevated temperatures when compared to their monolithic counterparts. They have a great advantage in the specificity of their properties, meaning that specific materials can be engineered for specific applications. With such freedom of design, materials engineers have to accumulate a very large database of mechanical properties. Among these properties, the viscosity of alloy slurries is very important for producing, casting and forming process of metal matrix composites materials because viscosity has a decisive influence on fluid flow. The understanding of the rheological behavior of alloy slurries is necessary for these materials to become economic reality. Therefore, a study was carried out to measure the viscosities of 380 aluminum alloy containing 20 volume % SiC particulates under various shear rates and temperatures. In addition, a viscosity model representing the primary features of the alloy slurries was developed."

Jan 1, 1999

By David E. Hardt

"One of the critical variables to be controlled during arc welding is the size or geometry of the weld pool. The measurement of pool geometry has become an increasingly important problem with the advance of welding automation and control, and this paper addresses that problem. The basic concept of pool size estimation via measurement of pool dynamics is presented. The theory underlying this concept is discussed and is followed by a review of the current work in this area. It is concluded that pool dynamics can be characterized by natural frequencies of oscillation, for stationary welds, and that these can be measured by appropriate signal processing performed on the arc voltage. However, it appears that only full penetration welds show a strong correlation between weld size and natural frequency. Also, the extension of these results to the realistic case of moving welds has yet to be considered in detail. Nonetheless, this method of in-process measurement for real-time weld process control is still quite attractive where applicable since it can be accomplished simply by modifying the arc current schedule and by signal processing of the arc voltage.INTRODUCTUIONThe study of welding process control has been dominated by research into methods of in processing sensing of the weld pool geometry. While it has been shown feasible to measure the topside pool geometry using video methods [1,2], the penetration or backside bead width have remained elusive quantities. This is particularly true if a topside sensor location is required.The concept of using weld pool motion as a pool geometry sensing method was proposed by Hardt et al. [3] and later demonstrated by Hardt and Zacksenhouse [5] and Richardson and Renwick [6]. The concept is based on the fluid dynamics of a pool constrained by a solid container and by significant surface tension forces (i.e. a small shallow pool, not a ""pond"" or ""lake""). Such a pool, if subjected to external forces, will exhibit a surface motion is a function of that force, the properties of the fluid, the surface tension, and the shape of the container. Thus, if this motion can be excited and measured, and the relationship to the pool geometry determined, a means of sensing pool shape will exist."

Jan 1, 1986

By Hirofumi Tai, Masafumi Morishita, Toshiya Miyake

"In order to prevent corner cracks on cast steel slab and bloom, solidification delay at the corners should be controlled at the proper level. For this purpose, controlling the heat flux from the molten steel to the solidified shell at corners is essential. In this paper, optimization of the submerged nozzle was studied based on flow and solidification analysis.First, for the slab caster, the submerged nozzle shape was optimized. The improved nozzle was tested in actual casting and completely succeeded in preventing corner cracks. It was clearly demonstrated that the solidification delay and the corner cracks were strongly affected by the spouting stream from the submerged nozzle.For the bloom caster, on the other hand, the setting angle of the nozzle was optimized. Numerical simulations demonstrated that the spouting stream from the nozzle causes solidification delay, impinging at the corners under electromagnetic stirring conditions. Optimization of the setting angle of the nozzle is a possible means to reduce the solidification delay at the corners for the bloom caster.Related to the numerical analysis of flow and solidification, the effect of the critical solid fraction at the tip of the dendrite structure on the solidification under electromagnetic stirring conditions was studied."

Jan 1, 1999

By P. K. Jimack, C. E. Goodyer, A. M. Mullis, P. C. Bollada

"We review the application of advanced numerical techniques such as adaptive mesh refmement, implicit time-stepping, multigrid solvers and massively parallel implementations as a route to obtaining solutions to the 3-dimensional phase-field problem with a domain size and interface resolution previously possible only in 2-dimensions. Using such techniques it is shown that such models are tractable even as the interface width approaches the solute capillary length.IntroductionMulti-scale modelling impinges upon many areas of science, engineering and technology where the interplay between processes occurring on disparate length and/or timescales can affect the properties of systems in a complex, and sometimes unforeseen, manner. One such is the processing of materials where interactions at the atomic scale, through the nano- and microstructural scale can have a profound affect on the macro-scale response of engineering components. Here we focus on one such problem, the crystallisation of alloy melts, to illustrate how a range of advanced numerical techniques make the modelling of such systems tractable.The modelling of solidification structures, in particular the growth of dendritic crystals, is a subject of intense and enduring interest within the scientific community, both because dendrites are a prime example of spontaneous pattern formation and they have a pervasive influence on the engineering properties of metals. For alloy systems, which form the vast majority of engineering materials, solidification involves the rejection of both solute and latent heat from the growing solid, forming a coupled diffusion problem in which both the chemical and thermal diffusion equations should be solved. The multi-scale nature of this problem arises from the disparity between the thermal and solutal diffusivities for most liquid metals, which are typically 10-5 m2 s-1 and 10-9 m2 s-1 respectively. The ratio of these two, referred to as the Lewis number (Le =Dia), is therefore typically of the order 10,000 and gives a measure of the multi-scale nature of the problem. In fact, in many cases the thermal diffusivity is so much larger than its solutal counterpart that thermal diffusion is considered instantaneous, wherein the system can be approximated as isothermal such that the multi-scale calculation does not need to be performed. This is certainly a reasonable approach in most conventional castings. However, there is a class of solidification problem in which this approach is far from satisfactory, namely Rapid Solidification (RS). The application of isothermal phase-field models in such situations are highly likely to produce spurious results or to fail totally, particularly for temperatures below To (the temperature at which the free energies of the solid and liquid phases are equal at the concentration of the bulk alloy), wherein partitionless solidification may occur."

Jan 1, 2013

By Carlos Maurício. F. Vieira, Lázaro A. Rohen, Sérgio N. Monteiro, Rafael G. de Castro, Gustavo X. Borges, Maycon A. Gomes, Frederico M. Margem, Anna C. C. Neves

Economic and environmental benefits are motivating studies on natural fibers, especially lignocellulosic extracted from plants, have been studied to substitute synthetic fibers, such as glass fiber as reinforcement in polymer matrices. By contrast to synthetic fibers, natural fibers have the disadvantage of being heterogeneous in their dimensions specially the diameter. About the hemp fiber, little is known of their dimensional characteristics. The aim of the present work was to statistically characterize the distribution of the diameter of hemp fibers. Based on this characterization, diameter intervals were set and the dependence of the tensile strength of theses fibers with a corresponding diameter was analyzed by the Weibull method. The diameter was measured with precision using a profile projector. Tensile tests were conducted on each fiber obtain mechanical strength. The results interpreted by Weibull statistical showed a correlation between the resistances of the fiber to its diameter.

Jan 1, 2015

By Ilie Butnariu

Steel manufacture in VOD procedure needs a very attentive correlation and pursuit of the technological stages ,on the background of keeping the influence factors within best performances zones. For a better co-ordination of the main stages specific to this process ,this work presents a detailed study of the optimization possibilities for each stages ,beginning with the furnace charging ,going on with the pre-aftinage and aftinage stages in the electrical furnace and then with the refinement stages in the VOD installation. One has intended the effective emphasis of the main influence factors with global implications on the process and especially on the purity and quality of the stainless steel ,Among the main novelties proposed by this work , we can emphasize the following: - a computer assisted charging method ,with the possibility of using a large scale of wastage, also respecting the density proportions of the components of the charges; - the advanced recuperation of the elements of the charge by reducing the combustion of the valuable elements ; - the optimization of the oxygen blast conditions and of the aftinage stage ,by establishing some calculations concerning critical carbon content , that requires the oxidation to be continued very carefully; - the simulation of the thermic and chemical parameters by modeling the alloying process of the stainless steel in the case of some large amounts of additions.

Jan 1, 1994

By Go-Gi Lee, Jae-Young Jung, Myung-Duk Seo, Hyun-Na Bae, Seon-Hyo Kim

"Bubbles form at the anode during the electrowinning of magnesium and cause hydrodynamic acceleration and electrical field disturbance. A three-dimensional computational model was developed to investigate the effects of the geometry of the electrochemical chamber and the size distribution of bubbles on the fluid flow in the pilot plant. The results are validated by measurements of the surface characteristics of molten salt and the bubbles formed. Fluid flow at the surface was recorded with a high speed camera, and the distribution of bubble size is determined by inspecting the video images frame by frame. The measured size distribution of the bubbles is entered into the computer simulation of a multi-phase flow. A sloped roof is installed above the electrodes, to enhance the flow of the molten salt, thus resulting in higher current efficiency, lower energy consumption, and higher quality of magnesium metal.IntroductionTitanium's excellent properties of low density, high specific strength, high temperature strength, and exceptional resistance to corrosion are highly beneficial to diverse applications including aerospace, automotive, construction, and medical implants. Although the Kroll process[l] and Hunter process have been used for the extraction of titanium in the 20th century, their complicated engineering stages and high production cost, have led to further research into new processes such as FCC Cambridge, Armstrong and TiRO. Despite these intense research efforts, no process has yet been developed that is more economical than the Kroll process, by which most of the global commercial titanium is still being produced."

Jan 1, 2011

By Bingliang Gao, Junli Xu, Michal Korenko, Jinzhao Guan, Liangxing Li, Zhongning Shi, Zhaowen Wang, Aimin Liu

Al-Si alloy, a precursor of solar grade silicon, was prepared by direct electrolysis in cryolite molten salt at 950 oC using high purity silica as material, liquid aluminum as the cathode and high purity graphite as the anode. The electrochemical behavior of Si(IV) ion was investigated using cyclic voltammetry method. The electrolysis products were characterized by XRD, SEM/EDS and ICP. The results indicate that the reduction process of Si(IV) on tungsten electrode is a two-step process and there is about 0.6 V gap between the two steps. The contents of boron and phosphorus in the aluminum-silicon alloy are 3 ppmw and 8 ppmw, which will make the directional solidification purification effectively and reduce the cost of preparation solar grade silicon from metallurgical grade silicon.

Jan 1, 2015

By T. Kozuka, K. Sassa, S. Asai

"A new atomization process is developed. The principle of this process is completely different from that of conventional processes. This process uses electromagnetic energy induced by direct electric current and direct magnetic field instead of kinetic energy produced by fluid impingement or disk rotation.Experimental work of this process was carried out using pure tin, and it was found that the crucial factor for a stable operation is the contact state of molten metal with the electrode. In order to control the condition, a delay time controlling unit was developed and combined with this process. It is noticed that this controller works well to produce uniformly sized particles.A linear relation between the impulse and the momentum of atomized particles is found by use of experimental data and is explained by theoretical analysis.IntroductionIn atomization processes prevailing in metal powder technology, kinetic energy is currently employed for atomizing molten metal. That is, molten metal is broken into small particles by other fluid (e.g. water, argon gas, etc) or by impinged upon a rotating solid disk. This splashing process is always accompanied with uncertain factors for shape and size of the particles. The diameter distribution of products, therefore, comparatively spreads over a wide range. From another standpoint, the restriction of atmosphere is inevitable in some of these processes. As a pulverizing technology, the process which can produce uniformly sized particles and permits the choice of atmosphere is strongly desired.On the other hand, a great attention has been paid to the spray casting process as a new near net shape casting. In this process, a small size spraying device is favorable."

Jan 1, 1988

By P. Tapp, T. Evans, N. A. Molloy, J. Lucas

"Consideration of the protoype tuyere geometry for injection of inert gas through the bottom in a basic oxygen steel furnace and a requirement to specify an optimal flow for bottom wear and metal penetration led to experimental investigations[l,2] to apply the results of previous workers to this specific case, Flow velocity profile development within the tuyere was proposed as significant and the experimental scheme was designed to test this. It is proposed that the design criterion for the conditions of optimal flow of the prototype geometry be based on the non-dimensional mass velocity.INTRODUCTIONSharma[3] tested small diameter tuyeres in a laboratory hot model using molten iron to define a flow criterion for prevention of penetration of the bath liquid into the tuyere. Using argon, nitrogen and helium through a range of tuyeres (1 to 3 mm ill ) he proposed the jet Froude number C Fr' ) with the critical value being 2400 - 2500 or higher. Sonic or supersonic velocity was not a sufficient criterion. The tuyere design was a parallel tubular duct of moderate aspect ratio CAR) i.e. the ratio of length to diameter ranging from about 22 to 36 in the experimental furnace.Farmer et al[4] stated their their aim ""to develop a unifying explanation and procedure for the proper design of tuyeres"" but disagreed with Sharma's jet Froude number criterion. Recalculating Sharma's data they proposed instead a fully expanded Mach number of 1.75 with an initial expansion angle of ten degrees as the lower bounds of flow to meet the design requirement. They experimented with tuyeres in a water model using tubular, annular and convergent-divergent nozzles. The aspect ratio of the parallel duct tuyeres was from 533 to 762 using diameters of 1.4, 1.7 and 2.0 mm C the diameters being of tubes to be used full scale). Subsequently these results were applied to a prototype tuyere using a diameter of 1.7 mm with beneficial results in practice. This tuyere had an aspect ratio of 1067."

Jan 1, 1996

By Neil Rowlands

Particle liberation studies are commonly used in the determination of the proportion of locked and liberated phases in ground ores at various stages of mineral processing. These studies may range from a qualitative assessment of a polished specimen in an optical microscope to a full quantitative analysis of the liberation characteristics of fine grained complex sulfide ores using scanning electron microscopy and high level image analysis. However, the conversion of quantitative data to meaningful information on a mill operations level is by no means a simple task. This paper reviews the errors inherent in the SEM/Image Analysis technique and looks at the various methods available to minimize errors in data collection.

Jan 1, 1992

By Xiao Long, Ting Wu, Lilong Zhu, Qian Wang, Shengping He

"During the continuous casting of peritectic steel slabs, mould fluxes with high crystallization capacity are usually chosen for improving slab surface quality. However, the lubrication condition of casting shell also could be deteriorated. Since precipitation of crystals within liquid slag film can change the composition and property of liquid slag over solid-liquid slag film interface region, its impacts on continuous casting process also are not clear. In order to clear this phenomenon, an experiment method was put forward, and mould fluxes for peritectic steel slabs continuous casting were selected and examined. The results reveal that after crystals have been separated, the crystallization capacity of leftover liquid slag increased with different levels, which could deteriorate the lubrication condition of casting shell and cause a series of problems. Thereby, mould fluxes with high crystallization capacity at beginning for heat transfer control and then weaker after crystallization should be considered in the future.IntroductionIn the continuous casting of peritectic steel slabs, contradiction between heat transfer control and slab shell lubrication by mould fluxes has been treated as a key problem for maintaining a smooth manufacturing process [ 1]. Strong and uneven horizontal heat flux over the meniscus region will cause uneven solidification of casting shell, especially for peritectic steel slab with enormous volume change caused by phase transition. All of those could cause surface defects like longitudinal crack [2-4]."

Jan 1, 2013

By J. W. Holzenthaler

Teams continue to play a major role at the Phelps Dodge Mining Company El Paso Operations, especially during the present time of low copper prices. The El Paso Operations' teams have taken the initiative during this copper market downturn and have helped reduce operating costs significantly. Because of this, Phelps Dodge El Paso Operations has continued to grow within the team process by creating a total, non- exempt salaried workforce. In the last year alone, the El Paso Operations have implemented three major initiatives to accommodate the team process. The first was the creation of "guiding principles", a policies and procedures handbook. Second was the "zero and beyond" safety initiative. Third was team compensation. In addition, the Copper Products Company has now adopted a work-team environment, following the lead of the refinery.

Jan 1, 1999

By Yuzuru Sato

Viscosity has been measured for various molten binary alloys of nickel with iron, cobalt and chromium in order to clarify the behavior of viscous flow of molten nickel alloys. The entire concentration range for iron and cobalt and 0-67at% of chromium content were studied. The measurement method was an oscillating cup viscometry using an alumina crucible that was precisely machined. The temperature was up to about 1880K for all the measurements. The results represented good Arrhenian relationship although some measurements included overcooled temperatures. The isothermal viscosities increased monotonously with an addition of iron and chromium into nickel. The addition of cobalt increased after stationariness. The isothermal viscosities showed concave curves. Activation energies increased monotonously by adding all the elements into nickel. These phenomena were considered to be related to the thermodynamic properties such as the heat of mixing and the structures of mixture melts.

Jan 1, 2003

By G. Diáz

The PLACID process applied to the recycling of spent lead-acid batteries is being developed by an European Consortium within the Brite-Euram II programme. The status of the project entitled "Lead Recovery from Lead Oxide Secondaries" is described in this paper. The main laboratory and batch experimental results and the preliminary feasibility study are summarised. The description of the demonstration pilot plant and continuous campaigns programme for 1995 are also included. An interesting global approach is proposed, integrating the Placid process in the existing spent battery recycling pyrometallurgical facilities. This yields important improvements in the overall process. Grids would be easily treated by the conventional pyrometallurgical route, obtaining lead alloys,, while battery pastes, slags and fumes would be fed to the Placid process, obtaining pure electrolytic lead (>99.99 %), ideal for battery paste manufacturing. The implementation of the Placid process into the existing battery recycling pyrometallurgical facilities is analyzed from technical, environmental and economical viewpoints. Greater overall lead recovery, lower operating costs, reduced waste production, environmentally safer residues and much better lead product quality are the key advantages. The authors draw the following final conclusion : Integration of the Placid process with conventional pyrometallurgical treatment is a feasible and very attractive alternative route for spent lead-acid battery recycling.

Jan 1, 1995

By Matti Leiponen

During the last few years Outokumpu Oy has put forth efforts to develop the material handling in the Pori tankhouse. The final objective is full automation including cell loading. The fully automated material handling provides high quality anodes and cathodes as well as equipment and handling systems capable of very accurate cell loading. The new machines and equipment for accurate cell loading and the methods to produce high quality anodes and starting sheets are described in this paper.

Jan 1, 1987

By A. M. Blount

In 1983, a final ruling of the U.S. Occupational Health and Safety Administration (OSHA) specified that chemicals containing >0.1 % of a carcinogenic substance or > 1 % of a substance hazardous to health must be labelled. Amphiboles of the fibrous or asbestos-type must be quantified at levels of 0. I % whereas the status of non-fibrous types is not finally determined at this time. Tremolite and actinolite can possibly be measured to 0.1 % by XRD, but anthophyllite cannot be so measured. Recently the International Agency for Cancer Research (IARC) has designated quartz as a suspected carcinogen, and its quantity must be measured to the 0.1 % level. Thus, it has become Increasingly important to be able to detect and quantify minerals in bulk samples down to low or "trace" levels. It has been found that minerals needing to be quantified can often be concentrated by microcentrifuge and counted by means of polarized-light microscopy. For example, amphiboles in talc samples can be separated by using a heavy liquid (thallium formate-malonate) of density 2.810. Talc floats, and amphiboles sink. After centrifuging, the denser particles are removed from the bottom with a Pasteur pipette and placed in a clean centrifuge tube. Distilled water is added to the tube containing the denser minerals and the tube centrifuged again. After several washings with distilled water, the sample is removed along with a drop of water to a clean glass slide. A drop of 1 .584 refractive index liquid and a cover glass are placed over the dried sample. The slide is scanned for particles greater than 5 um in length and having an aspect ratio greater than 1:3. These are checked for refractive index, sign of elongation and extinction angle to differentiate them from talc particles on edge and other minerals. Amphiboles have all indices greater than 1.584, and talc has all indices equal to or lower than this value. Alternately the heavies at the bottom of the centrifuge tube can be filtered through a nucleopore filter. After the filter has been washed with distilled water and dried, a 1.584 refractive index liquid renders the filter transparent in two of the four extinction positions so that a count of amphibole particles can be made directly on the filter. The refractive index-density method which is so useful for talc powders should be equally useful for other nonsoluble industrial minerals.

Jan 1, 1989

By B. Q. Li, S. P. Song

"This paper describes an on-going research on developing coupled boundary element and finite element algorithms for the solution of thermal and electrodynamic problems relating to materials processing. The coupled methods are uniquely suitable for field problems involving composite regions, in which detailed information on field distributions within one particular region is of more interest and yet the solution can be obtained only if the effects of other regions are all considered. Problems of this type include heat transfer in multiple regions and also magnetic induction involving an infinite boundary. The hybrid boundary and finite element formulation, algorithm development and the applications are discussed. Two examples are given to demonstrate the capability and accuracy of the coupled algorithm for heat transfer problems. Various treatments of corner discontinuity are discussed. It is found that the double flux treatment is an ideal choice amongst those tested as it is easy to implement and also gives the most accurate solution. 1. INTRODUCTIONElectrodynamic and transport problems occur frequently in materials processing systems. Accurate solution of these problems is of great importance not only for our fundamental understanding of physical principles governing these phenomena in the processing systems but also for optimization of the existing processes as well as development of new processes. For this purpose, many numerical algorithms have been developed. These computational schemes in general can be classified into three categories, that is, the finite element and finite difference schemes and the boundary element scheme. The former two are domain based numerical algorithms while the latter the boundary-based algorithm.The finite element method, which is based on the variational calculus, is a very useful and yet popular engineering numerical method for boundary value problems defined over irregular boundaries. The use of the method requires the discretization of the entire domain. It can be applied to solve both linear and nonlinear problems, but is particularly powerful for nonlinear problems that involve the field variables defined within the computational domain. On the other hand, the boundary element method, with its root in the Green's function method, is very efficient for linear boundary value problems or nonlinear problems that involve field variables only along the boundaries. The primary advantage of the boundary element method lies in the fact that only the boundaries of the computational domain need to be discretized, and hence the dimension of the problem is reduced by one, compared with the finite element method."

Jan 1, 1994