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By Oliver Bowles

The National Granite Commission at its annual meeting in Norfolk, Va., in January, 1930, passed a resolution requesting the Bureau of Mines to conduct an economic study of the granite industry. In compliance with this request a preliminary review has been made of trends, in, the production and uses of block granite. Some unfavorable conditions, were, thus brought to light and certain suggestions regarding a. more orderly and consistent growth in the industry are herein discussed. The results of the study axe, presented in this report for the earnest consideration of the industry and comments are invited, not only on this report but as to future work that might be accomplished by the Bureau of Mines. The authors desire to acknowledge many helpful suggestions and comments from Paul M. Tyler of the Bureau of twines and from Harris F. Sherman, secretary of the National Building Granite Quarries Association. Miss A. T. Coons of the Bureau of Mines rendered valuable, assistance through her wide knowledge of granite statistics.

Jan 1, 1931

By R. E. Murray

"It is a gloomy moment in the history of our country. Not in the lifetime of most men has there been so much grave and deep apprehension; never has the future seemed so incalculable as at this time. The domestic economic situation is in chaos. Our dollar is weak throughout the world. Prices are so high as to be utterly impossible. The political cauldron seethes and bubbles with uncertainty. Russia hangs, as usual, like a cloud, dark and silent, upon the horizon. It is a solemn moment. Of our troubles, no man can see the end." By now you, no doubt, are asking, 'Where did Murray get this bit of philosophy?' Well, I obtained it from an editorial entitled. "The Worst of Times", which was published in the Harper's Magazine in 1847. That's right, 1847! The parallelism between the situation in our country at this time and in 1847 is un- canny. But wait, there is one major exception the size of government. To my knowledge, the citizens of 1847 were not stifled by the extreme governmental excesses that we are experiencing today.

Jan 1, 1980

By Manuel Gomez

Carbon number distributions were obtained for tar acid fractions from five low-temperature tars by low-ionizing voltage mass spectrometry. Quantitative data for phenols representing seven structural compound types were examined by statistical analysis. It was shown that for the phenols discussed, the data could be represented by regression equations expressing phenolic concentration as a function of the reciprocal of the carbon number and the carbon-to-hydrogen ratio of the parent coal. The total concentration of each structural type present was found to depend on the molecular weight and boiling point of the initial member of the group. Carbon distribution data for the tar acid fractions studied support the view that low-temperature tars contain the same chemical compounds but in different proportions.

Jan 1, 1965

By M. R. Hegge

The Jabiluka One and Two uranium deposits occur in Lower Proterozoic metasediments of the Cahill Formation, which is part of the Pine Creek Geosyncline in the East Alligator River area, Nothern Territory. The Jabiluka One deposit coincides with a "window" through unconformably overlying Middle Proterozoic sandstone of the Kombolgie Formation; Jabiluka Two is completely covered by that sandstone. The observed part of the Cahill Formation exhibits four horizons which are favourable hosts for uranium mineralization. These have been folded into an east-southeast-striking, gently plunging, open asymmetric syncline-anticline structure. The host rocks are mainly chlorite and/or graphite schists and their brecciated equivalents which have undergone initial regional prograde metamorphism to the amphibolite facies, then retrograde metamorphism to the greenschist facies. Mineralization consists of pitchblende, mainly filling open spaces and to a lesser extent in disseminated form. Chlorite, pyrite and quartz are commonly associated with the uranium mineralization. A portion of the Jabiluka Two deposit contains economic concentrations of gold. Structural preparation with low-pressure conditions at these sites appears to be the most significant ore control. Genetic hypotheses favour initial deposition in Lower Proterozoic sediments, followed by remobilization during later orogenic events. The deposits bear a marked similarity to some pitchblende deposits in central Canada.

Jan 1, 1977

By M. Vallée

"Geological and technical problems are often considered the most important ones affecting new mining projects. Typical problems and likely causes are reviewed based on current Quality Management and Continuous Improvement (QMCI) perspectives, giving particular attention to the work of W.E. Deming. As the “system approach” is an essential part of these policies, its characteristics are described with particular attention given to cultural- behavioural, organizational and systembased constraints described by J. Gharajedaghi. Given that poor communication and interaction among geologists, mineral processors and mining engineers/operators can seriously affect the adequacy of tests, project planning and execution, and mine profitability, these interrelated processes within the mining systems are analyzed and modelled. The impacts on models and simulations of ignoring typical data, information and knowledge uncertainties are addressed. Adapting W.E. Deming’s Fourteen Points, System of Profound Knowledge and insistence on leadership, and the analysis of mining system constraints, will allow the effective QMCI approach required to reduce geological and technical risks. Whenever we achieve this goal, we will be in a better position to overcome environment-, market-, finance- and community-related problems, achieve higher company and industry profitability as well as more sustained development. RÉSUMÉLes problèmes géologiques et techniques sont souvent considérés les plus importants parmi ceux qui affectent les nouveaux projets miniers. Des problèmes typiques et leur causes sont étudiés dans la perspective de gestion de la qualité et d’amélioration continue (GQAC), en relation avec les travaux de W.E. Deming. Comme l’approche système est au centre de ces méthodes, ses caractéristiques sont décrites en donnant une attention particulière aux contraintes de types culturel-comportemental, organisationnel, et systémique décrites par J. Gharajedaghi. Compte-tenu que les lacunes dans les communications et les interactions entre géologues, minéralurgistes, et ingénieurs/opérateurs miniers peuvent affecter sérieusement la validité des essais, de la planification et de l’exécution des projets ainsi que la rentabilité des exploitations, ces processus connexes font l’objet d’analyse et de modélisation. Les impacts sur les modèles et les simulations de l’incertitude des données, informations et connaissances sont soulignés. En adaptant au système minier les Quatorze Obligations et le Système de connaissance approfondie de W.E. Deming ainsi que l’analyse des trois types de contraintes, nous pourrons développer une approche GQAC permettant de réduire les risques géologiques et techniques des projets miniers et des exploitations. Ceci nous pemettra de mieux faire face aux problèmes reliés à l’environnement, aux marchés, au financement et aux conditions sociales, d’améliorer la rentabilité des exploitations minières et de l’industrie, tout en contribuant de façon accrue au développement durable."

Jan 1, 2003

By C. E. Baltzer

This paper highlights the position of coal supply in regard to the requirements for electric-utility operations. The text and the appended tables outline the trend of thermal power development and fuel use in the electric-utility industry. Mention is made of several argumentative factors influencing the use of coal in relation to competitive oil and gas, and of the importance attached to developing a realistic understanding of the respective problems faced by the supplier and consumer of coal. * * * TREND OF" THERMAL POWER DEVELOPMENT T HE RATE OF ADVANCE in thermal power has been significant during recent years, particularly in the Atlantic Provinces, the Prairie Provinces, Ontario, and British Columbia. While dependence on thermal power in Quebec and the Northern Territories is less than in the remainder of Canada, these regions also eventually will have need for increased amounts of such power.

Jan 1, 1961

By Donald W. Foss

The Shiloh Church deposit is a very significant molybdenum occurrence in an ususual, perhaps unique, geologic environment. Work done to date indicate that several million tons of "ore" may be present, occurring as a matrix in limestone and dolomite breccias. Mineralized rocks cored to date are at or near the surface and the deeper resource potential has not been tested. The prospect is located in Polk County, north- western Georgia (Fig. 1). The "ore zone" was outlined by North American Exploration, Inc. (NAE) using geochemical prospecting techniques. Extensive geological work, including core drilling, has been conducted on the properties, together with geochemical and geophysical surveys. The geology, geochemistry and geophysics of the prospect are discussed. It is hoped that these data can be used to formulate exploration programs in similar terranes located elsewhere in the eastern U.S.A.

Jan 1, 1983

By M Akhtar, E Jak, M Shevchenko

This article presents an overview of the experimental phase equilibria studies of S-containing systems (Ni-Sn-S, Cu-Sb-S, and Cu-Sn-S) and As-containing systems (Fe-Sb-As and Fe-Sn-As). These systems improve the prediction capabilities of FactSage in a 20-component ‘Cu2O’-PbO-ZnOFeO- Fe2O3-CaO-SiO2-S-(Al2O3-MgO-CrO-Cr2O3-Na2O)-(As, Sn, Sb, Bi, Ag, Au, Ni, Co) system for complex pyrometallurgical operations during both refining and recycling. Experiments involved equilibration at predetermined temperatures (300–1200°C) with or without preheating, followed by rapid quenching in a brine. Quenched samples were then directly measured using an electron probe microanalyser. For the Ni-Sn-S system, liquid phases (NiS- and SnS-rich mattes and liquid metal) and solid phases (Ni1+xSn, SnS, Ni3Sn, FCC-Ni, Ni1-xS, NiS2, Ni3Sn4, SnS2, Sn2S3 and β-Ni3S2) were observed. A new Ni3Sn2S2 phase was found to melt incongruently. For the Cu-Sb-S system, liquid metal, matte, FCC-Cu, digenite, Sb, CuSbS2, Cu3SbS3 and Cu3SbS4 phases were observed. For the Cu-Sn-S system, liquid metal, matte, digenite, SnS and Cu3Sn phases were found at liquidus.

Jun 17, 2024

By David J. Hatem, K. Bhattarai

The increasing popularity of alternative methods in delivery of underground infrastructure projects has given rise to innovative and collaborative contracting strategies to allocate and manage the unique risks associated with the work. This paper presents approaches and recent examples of how risk has been dealt with using various alternative delivery methods, including Progressive Design Build (PDB) and Construction Manager/General Contractor (CM/GC). Based on the experience gained from these examples, recommendations for an innovative and collaborative risk baselining approach using contingency sharing are presented that should advance the overall goals of equitable risk sharing and compensation.

Jun 13, 2023

By S. Cotten

The regulations for current coal mine refuge alternative (RAs) require that there be sufficient life support to sustain survival of the maximum number of RA occupants for a minimum of 96 hours. This minimum duration assumes that rescuers can access the RA through the mine within four (4) days of the onset of the mine emergency. But what if mine rescue teams cannot reach the miners within the RA before the RA air supply is severely limited or exhausted? What could be done to extend the duration of the RA life support capability into the 97th hour and beyond? In addition, what might be done to enable more rapid rescue of the miners if they could not be reached through the mine in a timely manner? This paper describes a systems approach to address the potential need to extend the duration of RA life support beyond current design limits. New capabilities that need to be developed in advance of such a dire need include more reliable emergency communications, highly mobile and efficient drilling rigs, enhanced directional drilling techniques, and a standardized RA external life support interface along with RA internal design modifications to accommodate use of an external supply. The following sections describe the need, intent, and technology gaps associated with each of these capabilities. Government agencies and the mining industry should consider initiation of a program to investigate, design, and develop effective means of extending the current 96-hour time restriction on coal mine refuge alternative life support. The development process should begin with a focused study to refine the overall operational concept, investigate the current state-of-the art of critical technologies, identify specific technology development priorities, and make recommendations for a development program to provide in an organized, efficient, and timely manner a solution for extended refuge alternative life support and occupant rescue.

Jan 1, 2011

By Persifor Frazer

INTRODUCTION For various reasons I have not specified the locality where the research indicated in the following pages was undertaken. It will suffice to say that it was on the grounds of a villa once remote from, but now completely surrounded by, its neighboring city, and in close proximity to an industrial establishment of great extent and importance manufacturing many kinds of steel articles and employing upwards of thirty chimney-stacks for power and process work. The problem was to discover the cause or causes of the mortality to trees and plants on the place, and to trace these causes to their origin. Before undertaking this experimental work, the bibliography accompanying this paper was compiled and studied. It appears from an examination of the careful scientific work performed by the ablest French, German, and English chemists during the last 25 years that they are unanimous in assigning the principal-in fact, the overwhelmingly predominant-cause of the destruction of vegetation to sulphur oxides, resulting either from direct- oxidation of sulphur in oil of vitriol works, etc., or from the oxidation of the sulphur from the minerals associated with commercial coal. Schröder and Schertel showed in 1884 that the sulphates deposited upon the leaves are not injurious to the plants; and Freytag proved that free sulphuric acid could not be found

May 1, 1907

By George Oprea, Tom Troczynski, Joe A. Rigby, Waiman Lo

The refractory lining of the tuyere line in Peirce Smith converters have usually much shorter life in service than the rest of the lining, above or below it. There are already recognized chemical, thermal and mechanical factors which contribute to the wear of the lining. Our study presents the experimental results on microstructural changes occurring on these tuyere line bricks in a nickelcopper converter. The experimental bricks, after use at the tuyere line, were investigated using SEM/EDS and XRD techniques, to identify the mineralogical changes due to interactions with the nickel-copper matte or fayalite type slag at the process temperatures. The microstructural changes were correlated with physical and mechanical properties of the brick before and after use and a wear mechanism was suggested. Although the matte does not theoretically react with the mineralogical components of the brick, a partial oxidation of the Ni-Cu sulphides was identified using a line analysis by SEM/EDS in the densified layer at the hot face, which allows for mineralogical changes at the matte-refractory interfaces, with a high probability of microcrack formation due to the thermal cycling during use. These microcracks were also identified to open through inter-granular fractures parallel to the hot face, which appeared to be the main cause of lost lining during use. The reactions between the fayalite slag and refractory brick could eventually play a role in chemical dissolution of the brick only in the superficial layer at the hot face, as no slag components were identified deep into the brick.

Jan 1, 2009

This report describes the redesign, development and field demonstration of a remote shotcrete lining system, capable of operating in shafts and mines from 8 to 16 feet in diameter at depths up to 1000 feet. The original contractural scope of work outlining problems and remedial measures associated with a previous unit proved inadequate. Significant additional effort was necessary in order to fulfill the project objectives of producing a functionally reliable remote shotcrete lining system. Included with the engineering and technical description of the system, is a comprehensive technology package. Included with this material is ancillary equipment, materials selection procedures, mix-design data, quality control and assurance program, selection and training of personnel and the organizational aspects required to operate the entire system. The report concludes with details of a successfully completed borehole lining operation at the Nevada Test Site. An irregular 104 inch diameter borehole was lined at a rate of 4.8 feet per hour and 20 feet per hour respectively for 8-9 inch and a 2 to 3 inch shotcrete thickness.

Jan 1, 1983

By W. E. Anable

The Bureau of Mines researched methods for recovering copper from cyclone and electrostatic-precipitator dusts of primary copper smelters as part of its program to maximize minerals and metals recovery from primary and secondary domestic resources. Small-scale studies showed that use of 110 pct stoichiometric sulfur and 123 pct stoichiometric carbon, based on producing a 40-pct copper-iron matte, resulted in the recovery of 95 pct of the copper contained in the dust. Typical mattes contained less than 10 pct of the arsenic, 30 pct of the bismuth, and 45 pct of the antimony and tin contained in the dust. Matte was converted to blister copper by injecting up to 200 pct of the stoichiometric oxygen requirement over a period of 2 to 3 hours. Up to 76 pct of the copper contained in the dust was recovered as a crude blister copper containing about 2 pct arsenic, 0.5 pct antimony, and less than 0.1 pet bismuth and tin. A matte-white metal product resulted from carbothermically reducing dust with coal, lime, and silica. Up to 95 pct of the copper was recovered in the combined product.

Jan 1, 1981

By U. F. Kocks

SINGLE slip and a single parallel array of edge dislocations have been obtained in silicon single crystals by homogeneously bending them in a four-point dead-loading device at 1000°C around the [211] axis with [253.] as the tensile axis which encloses an angle of 40° with the glide plane. Other orientations or lower temperatures proved unsuitable. The homogeneity of the bending was checked by the method shown in Fig. 1. The chemically polished specimen was exposed to parallel light from a microscope-stage lamp. The sharpness of the focus of the reflected light is an approximate measure of the circularity of the sample. This method permitted the determination of the actual radius of bent specimens within 10 pct accuracy. The etching solution developed to show up dislocations consisted of the following volume parts: 2 HF, 1 HNO,, 2 CH,COOH, 1 a solution of 5 wt pct of CuNO, in water (Rosi'). The acetic-acid content was adjusted to produce fine well-defined etch-pits in about 2 min at room temperature. The effectiveness of the etch did not depend on the crystal-lographic orientation of the face etched. The number of etch pits produced after a given deformation was checked in the usual way against the Cahn formula' and showed good agreement. As it is to be expected from the orientation of the primary system there are slip steps on the top and bottom faces but not on the side faces (perpendicular to the bending axis), whereas etch pits appear on the side faces but not on the top and bottom faces. This is different only for occasional dislocations of a secondary glide system. All the micrographs included have been taken in places where the most of secondary glide could be seen. From this it is evident that in the homegeneously deformed region the number of secondary dislocations was less than 1 in 1000 of the primary type. Dislocation Distribution—A series of tests with varying amounts of deformation is shown in Figs. 2(a-c). An observation that can readily be made from these pictures is that the linear density of dislocations within slip lines is relatively constant and independent of the amount of deformation. "Slip line" in this context is understood to mean a line that is a straight connection of individual etch pits. The heavily pitted bands which can be seen in each of these three pictures may be resolved fairly definitely, at higher magnifications, into many "slip lines" the distance between them being of the order of 0.5p The distance between dislocations in slip lines is of the order of 2p and it is also fairly constant in going from the neutral zone outward. The higher over-all dislocation density in the outer regions of any sample and the higher total number in a more heavily deformed sample, are effected by a larger number of "slip lines." The relative constancy of the dislocation distance within an individual slip line is surprising. The absence of pile-ups" may imply, if there is no rear- rangement on unloading," that there are no substantial obstacles to slip in this case. It seems that the equilibrium distribution of the dislocations in each active slip plane under the higher external stress on

Jan 1, 1959

By Pertti Paavola, Hikki Rasanen

This paper describes a very exacting tunneling project. Planning and technical realization of this service and transportation tunnel was especially difficult as a matter of vibration control, because the tunnel is situated only a few meters under Maria Hospital, which is one of the most busiest hospitals in Helsinki. In this hospital there are many departments for bedpatients, research and treatment with high-tech equipment, operational surgery and a big laboratory. Besides access tunnels are situated near several apartment buildings. The functionality of the tunnel required the placement of the access tunnels to be straight towards these apartment buildings for which special care for blast induced air pressure had to be taken.

Jan 1, 1997

By Hossein Ghaedi, Hadi Fattahi

Despite the significant role of coal in the economic progress of nations, the occupational and health risks associated with its mining pose a major concern for industry stakeholders. The occurrence of roof collapses in coal mines remains a critical factor leading to substantial loss of life and financial damages for miners. Therefore, accurately predicting the roof fall rate (RFR) holds paramount importance. However, the uncertainty surrounding rock parameters in mines hinders the application of conventional methods to assess roof collapse rates in coal mines. To tackle the challenges associated with predicting roof fall rates in underground coal mines, this study proposes a novel solution by leveraging the Rock Engineering System (RES) method. The investigation is grounded in a dataset comprising 109 data points, encompassing crucial input parameters like depth of cover (DOF), primary roof support (PRSUP), intersection diagonal span (IS), mining height (MH), and coal mine roof rating (CMRR). In the model construction phase, 80% of the data (87 points) were utilized to build the RES model. A critical aspect of this study involves the evaluation of the RES model’s performance against alternative regression techniques, namely linear, power, exponential, polynomial, and logarithmic regression. This comparison was executed using the remaining 24 data points (20% of the dataset) for rigorous evaluation. Employing key statistical metrics such as mean square error (MSE), root mean square error (RMSE), and squared correlation coefficient (R2), the study systematically demonstrated the superior accuracy of the RES-based method compared to other approaches. In conclusion, the outcomes strongly support the efficacy of the RES method in predicting roof fall rates, not only in the specific case studied but also indicating promise for its application in other underground coal projects. This underscores the potential of the RES method as a reliable and versatile tool for forecasting roof fall rates in the complex and critical context of underground coal mining.

Mar 19, 2024

By Imre Gombköto, Barnabás Csoke

"Raw material management means not only mining and processing of primary raw materials like ores, but means also collecting and processing secondary sources of raw materials. Recycling is one of the most developing field of raw material management in Europe, and its solutions are derived from mineral processing roots and principals. Complexity and challenges of the field of recycling results innovative solutions of material processing- Since European Union identified 20 raw materials as critical (CRM) due to lack of primary sources within the border of the EU, recycling become more recognised as source of different raw materials. WEEE is the waste streams contains many of the critical elements and along them at least 15 different species of plastics of which recycling is delayed by a lack of effective separation technique. Most paper deals with separation methods based on different specific gravity, triboelectric charge or surface properties of plastic species. Plastics however have differences of thermal properties and thermoplastics, duroplasts and elastomers can be recognised. The experiments described in the paper aimed to determine thermo adhesive behaviour of plastic species often identified in WEEE streams for separation purposes. According to the results, some plastic types as PS, PP. PC or PVC and PET pairs are possible to easily separate from each other, however different additives are changing thermo adhesive properties of most of the plastics that makes industrial process difficult to develop. Along thermo adhesive behaviour, combination of physical interaction can be used to enhance separation selectivity.INTRODUCTIONPlastics has a relatively long term of history as a light, multi-functional material in construction, packaging, automotive industry and electric and electronic products. There are a numerous types of plastic species can be used for various applications therefore they amount are growing from year to year. This quantity however become part of the waste stream and while metal recycling has been done for decades due to its economic value - cheap plastic parts are less desirable as secondary products. In 2013 an annual 5% of plastic production growth has been estimated with a base data of 265 million tonnes at 2010 (Guiqing & Zhenming, 2013). Since landfill requirements are increasing while—especially in Europe where actual regulations are trying to deflect waste from landfills - landfill capacities are decreasing, costs are become more and more expensive, Applications like energy production based on plastics as a fuel or recycling are some of the options can be applied. Direct incineration of plastics are applied at many plants - in most cases where waste consist of dangerous substances are incinerated because plastics high calorific value helps correct average mixture composition enable operators reaching high enough temperature for combined power and heat generation while most of substances—like PAH, PCB or dioxins—are destroyed. Another path is using low temperature reductive cracking due to pyrolysis process, however the chance having higher concentrate of carcinogen substances in the products are higher since it applies around 400°C during the process."

Jan 1, 2016

By J. Asfahani

"The inverse slope method (ISM) was applied to reinterpret vertical electrical soundings (VES) data from pits at the Al-Sharquieh phosphate mine, in order to demonstrate applicability and suitability of the ISM for interpreting VES data from sedimentary phosphatic environments. The ISM overcomes limitations of the curve matching method and the complexity of lithological sections. The ISM geo-electrical interpretation results correlated well with lithologies of the pits. This method characterized resistivity and thickness of the phosphatic layer, and identified favourable phosphate-prospecting areas using the newly developed thickness/depth parameter. The ISM is recommended for interpreting VES measurements in similar sedimentary phosphatic regions.RÉSUMÉ La méthode d’inversion de la pente (ISM) a été utilisée pour réinterpréter les données de sondages électriques verticaux (VES) effectués dans des puits de la mine de phosphate Al-Sharquieh, afin de démontrer l’applicabilité et la pertinence de cette méthode pour interpréter les données VES dans des environnements de sédimentation de phosphates. Cette méthode (ISM) surmonte les limitations de la méthode de comparaison de courbes et la complexité des sections lithologiques. Les résultats de l’interprétation géoélectrique ISM correspondaient bien aux lithologies des puits. Elle a permis de caractériser la résistivité et l’épaisseur de la couche phosphatique et d’identifier les secteurs favorables à la prospection pour le phosphate en utilisant le paramètre nouvellement développé épaisseur/profondeur. ISM est recommandée pour l’interprétation des mesures VES dans des régions semblables où se trouve du phosphate sédimentaire."

Jan 1, 2016

By V. Koump, R. H. Tien, W. J. Kim

This paper presents an approximate solution of the problem of freezing of a binary alloy. he alloy is in the form of a one-dimensional slab of finite thickness. The surface temperature of the slab is assumed to be constant and lower than the solidus (or eutectic) temperature. The densities of the liquid and the solid are assumed to be equal. For a given binary alloy system, initial concentration of solute and surface temperature, the solution yields a) the temperature distribution in the solid skin, b) the temperature, concentration, and solid fraction distribution within the solid-liquid region, and c) the positions of the liquidus and the solidus (or eutectic) fronts as a function of time. The results of calculation for Fe-C and Fe-P systems are presented. In this investigation we are considering the problem of solidification of a binary alloy. The alloy is in the form of a one-dimensional slab of finite thickness. The molten alloy is initially at liquidus temperature. At time zero the surface of the slab is reduced to a temperature T, < Te,, where Te, is the solidus (or eutectic) temperature and T, is a constant. The densities of solid and liquid alloys are assumed to be equal and independent of temperature and composition. A qualitative picture of solidification of an alloy, under these conditions, is illustrated in Fig. 1. During the initial stage of solidification, before liquidus front reaches the center of the slab, freezing proceeds by propagation of two isothermal fronts, the liquidus front and the solidus (or eutectic) front. The fraction of solid at the liquidus front is zero; the fraction of solid at the solidus front is unity, The solid fraction and the temperature distribution between the two fronts and the width of the solid-liquid region change with time. During the later stage of freezing, after the liquidus front reaches the center of the slab, the liquidus front disappears. The solid fraction and the temperature at the center of the slab, as well as throughout the solid-liquid region, are now changing with time. The solidification is completed when the fraction of solid at the center of the slab reaches unity. In solution of this problem we seek to determine a) the temperature distribution in the solid, b) temperature, concentration,

Jan 1, 1968