Search Documents

By H. P. Wang, E. M. Perry

"Analytical solutions for investigating the solidification of casting problems with initial superheat and natural boundary conditions have been derived using an integral method. There are two moving interfaces in the solution field, one for the phase change line and the other for the superheat line. Two coupled nonlinear differential equations, representing two moving layers, were calculated by the Runge-Kutta numerical integration scheme. The solutions are in terms of six dimensionless parameters: phase change number, two Biot numbers for interfaces, diffusivity ratio, and dimensionless superheat temperature and time. Parametric studies on these parameters have been conducted to provide generic information about this phase change problem. This analytical information is extremely useful for validating numerical solutions. A simplified I-D finite element model was constructed for the purpose of comparison. The excellent agreement between the analytical and finite element solutions has proven that they are mutually validated.This validated finite element modeling tool was then used for modeling an investment casting process of a super-alloy with a simple geometry: a two-step plate. The nonlinear latent heat release, a common property of alloy materials, was approximated by several piecewise linear segments. The transient temperature response of this 2-D finite element solution, including a metal/mold gap resistance, shows excellent agreement with experimental data.This fundamental work provides a solid basis for further work on the development of a process modeling tool for the complex investment casting process.IntroductionAt present, the investment casting process is used in a variety of industries. In the aircraft engine industry, in particular, investment casting is used to produce parts ranging from turbine blades to engine frames. Because a large single casting can replace many component parts that require machining, fabrication, and assembly, this one-piece casting approach becomes a very cost-effective manufacturing process.The main constraint in using this process for mass production is the long design-to-production lead time. The standard rigging design is still an art, based on the experience of casting experts, rather than on scientific methods. Many trials are often required before making a sound final casting. In order to .reduce the number of expensive casting trials, the development of computer-aided tooling technology is needed.The fundamental physics describing this manufacturing process can be simply described. They reduce to a solid/liquid phase change problem, with two parts - first, the thermal balance of the initial superheat temperature of the molten metal and the preheat temperature of the ceramic shell through heat conduction, and second, the energy release from the mold surface to the ambient by radiation."

Jan 1, 1986

By S-L. Jämsä-Jounela

Fault diagnosis systems have attracted growing interest in a number of engineering fields. The number of applications has increased and successful results have been widely reported. The fault diagnosis system presented in this paper is integrated, and it monitors the states of the process and performs fault detection and diagnosis on the process equipment. The monitoring of process states is carried out by means of Kohonen Self-Organising Maps that is a powerful tool in visualisation and analysis of high dimensional data in engineering applications. This paper presents the results of SOM analysis carried out on the Outokumpu flash smelting process. The subsystems analyzed in more detail are the condition of the concentrate burner, the condition of the gas line on the basis of the pressure distribution in the process and the cooling water circulation of the waste heat boiler, and the condition of the furnace and furnace equipment on the basis of the temperature distribution in the furnace and gas line. Keywords: Fault diagnosis, Process monitoring, Kohonen Self-Organising Maps, flash smelting

Jan 1, 2001

By Adam C. Powell

A new Cahn-Hilliard phase field model of transport-limited electrochemistry describes phase boundary motion due to oxidation and reduction reactions at metal-electrolyte interfaces. Benchmarks demonstrating the accuracy of the method include open circuit voltage and closed circuit current in metallothermic reduction, and linear stability theory in metal electrolysis, including a new stability criterion for reduction of liquid metal from liquid electrolyte. The model is applied here to understanding cathode interface stability in titanium electrolysis e.g. in the SOM process developed with Uday Pal, and to structure evolution in subhalide reduction of titanium dichloride by magnesium developed by Toru Okabe. Potential for application to new fuel cell and battery systems is also discussed.

Jan 1, 2006

By D. Papazoglou

This work was undertaken to investigate the thermodynamic and kinetic feasibility of using hot sulfur dioxide bearing gases from smelting processes to selectively sulfate the nickel in nickel laterite ores for subsequent extraction in water. The environmental benefits ofthis approach, as opposed to releasing the gas to the atmosphere, and the economic benefit of directly utilizing the S02 rather than converting it to sulfuric acid are strong drivers for such a process. A thermodynamic analysis indicated that selective sulfation of the nickel could be feasible under appropriate conditions and these were explored through a series of laboratory scale experiments. Laterite samples were reacted at temperatures between 500 and 800°C with an equilibrated mixture of sulfur dioxide, oxygen and nitrogen in a fixed bed reactor. Tests were conducted on saprolitic ore from Bulong, Western Australia, limonitic ore from New Caledonia and garnieritic ore from Indonesia. Nickel extractions were highest from the limonite and relatively low from the other ores. The maximum selective extraction of nickel from the limonite in a single stage sulfation was 73%. Sulfation of other elements present in the laterites was also examined. A two-stage process was also identified which involved sulfation using a strong sulfation potential followed by weaker sulfation potential to attempt to convert ferric sulfate formed in the first stage to ferric oxide. This increased the extraction for the limonite ore to around 84% Ni, 95% Co and 2% Fe. Direct sulfation of laterite could be feasible in locations where sulfide smelting or roasting operations are relatively close to laterite deposits.

Jan 1, 2003

By Nobuyuki Higashiyama, Ikuo Yonezu

"Hydrogen-absorbing alloys containing rare-earth elements are used in high capacity nickel-metal hydride secondary batteries,' hydrogen storage systems for portable fuel cells, and refrigeration systems. New hydrogen-absorbing alloys containing rare-earth elements have also been developed and introduced into these applications. High performance in nickel-metal hydride secondary batteries is strongly demanded because of the remarkable advancements in portable electric appliances. A large hydrogen absorption capacity, high electrochemical reactivity and superior corrosion resistance in an alkaline solution are required for hydrogen-absorbing alloys used in nickel-metal hydride batteries. The aim of this investigation is to improve the performance of conventional LaNi5 type hydrogen-absorbing alloys. For example, Mm(Ni-Co-Al-Mn)„ type hydrogen-absorbing alloys with various non-stoichiometric compositions were developed. In addition, a new process of rapid quenching process was applied for preparing these hydrogen-absorbing alloys in order to improve their performance.IntroductionRecently, the trend in electronic appliances toward portability has increased the demand for high capacity of secondary batteries as power sources. Since nickel-metal hydride batteries were first commercialized in 1990 in Japan, they have become increasingly popular as power sources for cellular phones, portable computers, electric shavers, and other, products.The performance of a nickel-metal hydride battery, such as its discharge capacity, high rate capability, and charge-discharge cycle life, strongly depends on the characteristics of the hydrogen-absorbing alloy negative electrode. Many types of hydrogen-absorbing alloys have been developed so far. For a hydrogen absorbing alloy to be used as the negative electrode material, (1) it must allow a large amount of hydrogen to be absorbed and desorbed in an alkaline solution, (2) its reaction rate should be high, and. (3) it must have long term durability under repeated charge-discharge cycling. However, LaNi5, a typical rare earth-nickel type alloy, shows significant capacity deterioration during repeated charge-discharge cycling. Therefore the first step in its development was to obtain sufficient corrosion resistance of the LaNi5 alloy for its use as an electrode material. A partial replacement of nickel with cobalt and a substitution of the lanthanum- content with misch metal (Mm), a mixture of rare earth elements such as lanthanum, cerium, praseodymium and neodymium, were very useful in improving the charge-discharge cycle life. However, the discharge capacity of the alloy was still not sufficient for a practical battery. A study of the effect of the partial substitution of aluminum and manganese showed that the best alloy composition was Mm(Ni-Co-Al-Mn)x, as follows.The stoichiometry x of Mm(Ni-Co-Al-Mn)x largely affects the discharge capacity and cycle life. Theose alloys with non-stoichiometric alloys with the compositions of [Mm(Ni-Co-AMn)x: 4.7<x<4.8] have a large capacity and a long cycle life. Nogami' et al. reported that 'a non-stoichiometric alloy with a Mm(Ni-Co-Al-Mn)x (x=4.76) composition showed approximately 10% higher discharge capacity than the stoichiometric alloy (x=5) [1] and greater influence of x on the electrochemical properties of multi-component AB„ type hydrogen-absorbing alloys for batteries."

Jan 1, 2000

By B. J. Vorster

AngloGold South Africa region currently consists of 12 Gold Plants. These plants use a combined total of $20 million of cyanide per annum. Of this, the .major portion (60%) is consumed at two Ergo dump retreatment plants. Historically the primary motivation for cyanide control at Ergo has been one of leachlcost optimisation. However, more recently, with the increased public awareness of cyanide in the environment, a secondary but increasingly important motivation for control has been to ensure that only the minimum amount of cyanide is added to the process whilst not compromising leach performance. Following a brief overview of the Ergo process, the methodology in detennining the amount of cyanide to be added is described. The paper then traces the developments in cyanide control from very basic? manual systems to the current automated control system. In line with the increasingly sophisticated control systems, developments also took place in regards to the method of cyanide analysis. The development of these analysers is also discussed. Whilst cyanide is one of the major drivers, if not the major driver of gold dissolution, it cannot be viewed in. isolation particularly with respect to the relationship between cyanide and oxygen as ascertained from the Elsner&apos;s well known equation. Consequently, in order to control cyanide addition, knowledge of the relative cyanide/oxygen profiles is necessary. Various means investigated at Ergo for pulp oxygenation have therefore been included for the sake of completeness. Finally a comparison is made of the control achieved from the current system compared to the? original manual system. The knowledge and experience gained at Ergo is now being used to draw up guidelines for the installation and optimisation work at the other AngloGold plants. The net effect of this will be reduced cyanide consumption for the region, which also, apart from the obvious economic benefit, translates into a reduced environmental; risk.

Jan 1, 1998

By Francis Vanbellen

Umicore Precious Metals Refining operates an integrated precious metals smelting and refining plant in Hoboken, Belgium. Once a smelter and refiner of complex concentrates, the plant today?s feed consists exclusively of industrial and consumer recycled products, making it the world?s largest recycling facility for precious metals. Unlike the fairy tale of the Frog Prince, it took much more than a princess? kiss to successfully realize this makeover. A completely renewed plant has been built over the past decade. The most visible technological innovation was the commissioning of the Pb-Cu smelter. Its flexibility towards very different types of feed makes it perfectly suited as main entry to the Hoboken flow sheet. A new Cu-leaching & electro winning plant and precious metals refinery make up the Precious Metals Operations (PMO) whose targets are fast throughput and maximized yields for gold, silver and the platinum group metals. The Base Metals Operations (BMO), flexibly process the by-products from the PMO, valorizing ?impurities? like indium, tellurium, selenium and others. Off gas and waste water treatments ensure compliance with strict environmental standards. Precious metals recycling is an art that goes beyond mastering a unique flow sheet. Umicore Precious Metals Refining offers a complete recycling service, taking care of sampling and assaying, metals management and logistics. The quality of this integral service is recognized through the attribution of ISO certifications for our operational activities, sampling and the environmental care. And it?s an art that follows Michelangelo?s experience: ?Art is 5% of inspiration and 95% of transpiration.?

Jan 1, 2006

By Yasumasa Hattori

An extensive study including fluid dynamic calculations, cold model tests, pilot plant tests as well as measurements in a commercial flash furnace was carried out in order to develop a new Sumitomo flash smelting concentrate burner. The pressure measurements in the commercial burner indicated that the premixing of the concentrate and reaction air in a burner was insufficient. Pilot plant tests showed that enhancement of the premixing of the concentrate and reaction air is very effective for improving the burner performance. Using the additional pressure drop of the reaction air as an indicator of the premixing, a new type Sumitomo premixed concentrate burner was developed.

Jan 1, 2003

By Kandipati Sreenivasarao

Ion and precipitate flotation involve adding an appropriate collector to aqueous solutions containing metal ions, to form hydrophobic metal-collector complexes or precipitates that can be removed by flotation. With a better fundamental understanding of the effects of physical, engineering and chemical parameters on the performance, ion and precipitate flotation techniques could usefully complement techniques now available for removing metal ions from dilute solutions. The removal of Cu(II), Pb(II), Cd(II), Cr(III) and Cr(V1) has been studied, using different types of collector, according to the nature of the metal-bearing species. The effects of collector/metal ion ratio, and solution and froth height on the flotation kinetics, bubble coverage by the metal-collector complex, recovery of metal and effluent quality are reported. The observed behavior is related to the solubility products of the metal-collector complexes, which were also determined.

Jan 1, 1994

By Reinhard F. Dobner

After a short introduction about the HK&apos;s secondary smelter process and explanations concerning the anodes produced the regulation and buffering of bleed will be described and the principles of technology for processing of bleed will be presented. Modernization aspects, especially installation equipment, and the different types of evaporators used will be described in detail. Besides, experience made with acid-resistant materials - stainless steel, enamel, plastics - will be reported. Environmental aspects such as water and air pollution will be outlined briefly and in conclusion the quality of products obtained as well as quality control will be presented.

Jan 1, 1997

By Michael Zinigrad

The quality of metallic materials depends on their composition and structure and these are determined by various physico-chemical and technological factors. To effectively prepare materials with required composition, structure and properties it is necessary to carry out a research in two parallel directions: Comprehensive analysis of thennodynamics, kineties and mechanisms of the processes taking place at the solid-liquid-gaseous phase interface during welding processes and development of mathematical models of the specific welding technologies. We have developed unique method of mathematical modeling of phase interaction at high temperatures. This method allows us to build models taking into account the thennodynamic characteristics of the processes, the influence of the initial composition and temperature on the equilibrium state of the reactions, the kinetics of heterogeneous processes, the influence of the temperature, composition, hydrodynamic and thennal factors on the velocity of the chemical and diffusion processes. The model can be implemented in the optimization of various technological processes in welding, surfacing, casting as well as in manufacturing of steels and non-ferrous alloys, materials refining, alloying with special additives, removing of non-metallic inclusions.

Jan 1, 2003

By S. K. Wu, Ray Y. Lin, Sunil Annaji

Infrared joining of TiAI using aluminum foils as the filler material was investigated at temperatures between 1050 °C and 1350 °C in a flowing argon environment for times varying between 15 and 60 seconds. Using aluminum foils, the attempt was to form the Al3Ti phase in the joint as a result of reaction between Al and TiAI at temperatures above the melting point of Al. It has been found based on X-ray diffraction and TEM analysis that, Al3Ti, indeed is the product of infrared joining of TiAI using Al as the joining alloy. Al3 Ti was detected even in the joint processed at 1050 °C for only 15 seconds. Since the aluminum foil used in this study contains 27 at% Si, the t 2 phase in the Ti-Al-Si ternary system is believed to have also formed at the joint/base TiAI interface. Cross sectional studies on the joined specimens have shown different degrees of reaction depending on the temperature and time of joining. Micro hardness evaluations across the joint show that the hardness near the center of the joint is typically smaller than that near the joint edge next to the base material. However, as the joining temperature and time increase, the increment of the hardness at the center of the joint is faster than that around the periphery of the joint.

Jan 1, 1996

By C. Hennesmann, D. Maijer, S. L. Cockcroft, P. Yo

"Die cast aluminum wheels are one of the most difficult automotive castings to produce because of stringent cast surface and internal quality requirements. As part of a collaborative research agreement between researchers at the University of British Columbia and Canadian Auto Parts Toyota Incorporated, work has been underway to predict heat transport and porosity formation in die cast A356 wheels. The basic heat transfer equations have been solved using the commercial finite element package ABAQUS to which specialized routines have been added to predict porosity. Preliminary work on predicting porosity formation focused on using the Niyama parameter as a measure of the probability of porosity. The latest version of the model incorporates a new fundamentally based porosity criterion, which takes into account the effect of hydrogen concentration. The development of this model together with its application to a series of cylindrical test castings as well as a production cast wheel are presented.I. IntroductionDie cast aluminum wheels are one of the most difficult automotive castings to produce because of stringent cast surface and internal quality requirements. Microporosity, in particular, is a common defect that can adversely affect wheel quality. The mechanism of microporosity formation in aluminum alloys is complex owing to its dependence on the interaction of a number of phenomena occurring during solidification including the decrease in hydrogen solubility, the decrease in volume, the development of the solidification structure, and the increase in difficulty in interdendritic feeding [1]. As a result, the amount, size, and distribution of microporosity is affected by a large number of casting parameters including thermal variables, melt composition, grain structure, modification, and inclusion content, making optimization by trial-and-error methodologies difficult.The use of criteria functions, based on thermal conditions during casting, offers a relatively simple approach to predicting microporosity. In practical terms, they are useful because they provide a straightforward method of assessing the impact of varying casting parameters on porosity through various thermal parametersl21 such as thermal gradient, cooling rate, solidification time, and solidus velocity. Drawbacks of criteria functions include insensitivity to varying hydrogen concentration and the limitation to qualitative predictions. Consequently, in aluminum alloys, attempts have been made to develop models incorporating the effects of hydrogen gas and microstructure evolution. However, these types of models represent a significant increase in complexity and sacrifice the simplicity and ease of application of the thermally based criteria functions."

Jan 1, 2001

By Antti Roine

Sulfidic zinc concentrates are usually roasted in a fluidized bed furnace into sulfur-free oxide form. Metallic zinc is produced from this oxidic calcine using hydrometallurgical leaching, solution purification and electrowinning stages. The roasting step is necessary because zinc oxides are easier to dissolve using traditional leaching methods than zinc sulfides. The Kokkola Zinc smelter uses various types of zinc concentrates and secondary materials as feed mixture. This makes it difficult to find optimum process parameters for the roaster when the composition and particle size distribution of the feed mixture varies even on a daily basis. Certain conditions may even cause difficult accretion problems or increase the amount of calcine in the process off-gas line excessively. A thermochemical heat and material balance model was developed for process advisor, in order to estimate the effects of different process parameters (temperature, process air coefficient, concentrate feed, oxygen enrichment, water feed, etc.) on the heat balance, roasting temperature and calcine composition. This model was constructed using the heat balance module of HSC Chemistry 4.0 software. The prevailing chemical compounds in the concentrate and calcine were verified using mineralogical analyses and equilibrium calculations. The roasting process seems to operate near chemical equilibrium conditions, if the behavior of the main components is considered. This paper describes briefly the basic principles of the calculation model and outlines the results with several diagrams and discussion. The calculated results were in reasonable agreement with the recent process air oxygen enrichment and water feed test campaigns carried out at Kokkola in 1999.

Jan 1, 2000

By Y. Ide, K. Kishitake

It is expected that an Al-Cr-N composite nitride film may have a higher resistance to oxidation at elevated temperatures than the well-known Ti-Al-N films. The formation conditions of Al-Cr-N films by a de reactive sputtering method and their properties were studied in this study. The films characterized with respect to their high temperature properties such as chemical composition, crystal structure, microhardness, wear and· friction. The crystal structure of the Al-Cr-N films changed from hexagonal phase to cubic phase with an increase in Cr content in the films. The resistivity to thermal oxidation of the Al-Cr-N films is superior to that of usual TI-Al-N films. A half of the friction coefficient in the Al-Cr-N film was obtained comparing with that in the ordinary TI-Al-N film at room temperature and the wear rate of Al-Cr-N film was 2 order smaller than that of TI-Al-N film. The Al-Cr-N films show a small friction coefficient at 500°C and then they are recognized to have good tribological characteristics.

Jan 1, 2000

By Kang-In Rhee

A series of processes to recover the gold from electronic scrap which contains initially about 200-600 ppm Au have been developed. First, mechanical beneficiation including shredding, crushing and screening was employed. Results showed that 99 percent of gold component leaves in the fraction of under 1 mm of crushed scrap and its concentration was enriched to about 800 ppm without incineration. The scrap was leached in 50% aqua regia solution and gold was dissolved completely at 60°C within 2 hours. Other valuable metals such as silver, copper, nickel and iron were also dissolved. This resulting solution was boiled to remove nitrous compounds in the leachate. Finally, a newly designed electrolyzer was tested to recover the gold metal. More than 99% of gold and silver were recovered within an hour in electrowinning process.

Jan 1, 1995

This symposium is dedicated to the lifetime achievements of Professor H.Y. Sohn. It covers the scientific fields, processing routes and investigation techniques in which Prof. Sohn has worked during his career and is based in the equally important three topical areas: Principles, Technologies, and Industrial practice. Professor Sohn was General Chair of the very first TMS Fall Extraction and Processing Symposium in 1983 in San Francisco which led to the Annual such symposia as this International symposium. Furthermore, the theme of that symposium was sulfide smelting, which is also included in this symposium. [ ] Professor Sohn was born in a beautiful dynastic capital Kaesung, Korea on August 21, 1941. He received his B.S. degree in 1962 from Seoul National University, M.Sc. in 1966 from the University of New Brunswick, Fredericton, N.B., Canada, and his Ph.D. degree in 1970 from theUniversity of California at Berkeley all in Chemical Engineering. After working as a Research Associate at the State University of New York at Buffalo and as a Research Engineer at Du Pont?s Engineering Technology Laboratory, Dr. Sohn joined the Department of Metallurgical Engineering at the University of Utah in 1974 and currently holds the ranks of Professor of Metallurgical Engineering and Adjunct Professor of Chemical Engineering.

Jan 1, 2006

By Peter K. Liaw, Charlie R. Brooks, David C. Joy, Wei Zhao

In this paper, effects of oxidation, porosity and fiber-fabric stacking sequence on flexural strength of a continuous silicon carbide fiber (SiCr) fabric-reinforced SiC ceramic-matrix composite (CFCC) were studied. The failure mechanisms were correlated with flexural strengths of CFCC samples, both before and after oxidation. Microstructures and fractography were investigated using scanning electron microscopy (SEM). The chemical change after oxidation, such as Si, C, and 0, and their distributions, were detected by the SEM energy-dispersive X-ray spectroscopy (EDXS) line-scan chemical analysis technique. These effects on the strength of the CFCC can be attributed to following reasons: (i) The decrease in the flexural strength after oxidation is mainly due to degradation of the strength of Nicalon fibers and the damage of fiber/matrix interface both caused by high-temperature chemical reactions, (ii) Porosity is not too important in affecting the strength of the CFCC, when the bonding of the forced flow chemical vapor infiltration (FCVI)-SiC matrix is stronger than that of the fiber/matrix interface. However, a higher porosity content will be harmful, because higher porosity will both decrease the effective elastic modulus of the FCVI-SiC and make pore-linkage easier to occur, which is more likely to cause premature failure, (iii) The variation in the lamina stacking sequence of the CFCC changes the elastic stress distributions along the thickness direction of specimens, the magnitude of ceramic matrix-cracking stress, the effective elastic moduli of the laminate, and different crack initiation sites as well as different failure modes, and thus, leading to the scatter in the flexural strength of the CFCC.

Jan 1, 1998

By Maija-Leena Metsärinta

The behaviour of copper and lead in zinc roasting has been studied in laboratory scale roasting experiments as well as in large scale trials in an industrial fluidized bed, with the background of Outokumpu Kokkola Zinc smelter. Commercial zinc concentrates with a low and high ( up to 3 wt % ) copper content and with a low and high (up to 3.5 wt % ) lead content were oxidized to various desulphurisation degrees in the fluidized bed to establish the reaction mechanisms and the paths for copper and lead oxidation in the roasting. Influences of the agglomerate size on the roasting kinetics and micro-scale phenomena were also determined. Optical microscopy was used on the calcine and the findings are presented as numerous photographs of the polished cross sections. SEMIEDS techniques were used for analyzing chemically the phases and particle morphologies present in the samples. Computational thermodynamics was applied to the complex phase equilibria occurring during roasting in the agglomerating calcine. A complete oxidation of zinc concentrate with a high copper and lead content requires a careful control of oxygen coefficient in the roasting in order to maintain a stable operation of the fluidized bed. Oxygen coefficient thus seems to have a significant impact on the hydrodynamic stability of the fluidized bed with fine raw materials.

Jan 1, 2003

By Douglas J. Harvey, Chi-Mou Ni

"This paper presents an analysis technique for the solidification of metal castings. This method, based on a modified finite difference scheme with an irregular mesh, is capable of dealing with the complex geometries of castings. The nonlinearities in material properties of specific heat and thermal conductivity, arising from the phase change during solidification, are accounted for in the step-by-step calculations. Two solidification problems are solved with this analysis technique and the calculated results compare satisfactorily with experimental data. IntroductionCasting process design engineers are often faced with the difficult problem of designing castings to be produced porosity-free. Since the solidification of metal is affected by many interacting variables such as the thermal conductivity, density, and specific heat of both the molten metal and the mold, it is easily seen why this is a difficult task.Typically, casting tooling design is an intuitive process which builds on past successful methods. After processing equipment is constructed, trial castings are made and examined for dimensions and integrity. Changes in the tooling are generally required to improve casting soundness or to reduce cycle time. In the permanent mold process, tooling is complex and difficult to alter after initial construction. The water-cooled steel molds are part of the complete automated system. Associated holding furnaces, pouring ladles, casting conveyers, and utility connections all make other than minor adjustments a costly and time consuming task. An analytical method for using the principles of heat transfer for predicting solidification patterns would be of great value in the permanent mold process by minimizing costly changes."

Jan 1, 1986