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By S. S. Clarke

LATE in 1942, the increasing demand for zinc, coupled with the growing shortage of miners and the knowledge that some abandoned mines would have to be reopened for prospecting and development, led to considerable thought as to the possibilities of further mechanization in order to conserve man power. The ore bodies, locally termed "sheet ground," are an important ore bed in some mines and are in the lower part of Boone formation of the Mississippian Series. Some mines contain interbedded layers of nearly pure galena and sphalerite in horizontal sheets ranging in thickness from a thin seam to several inches and is persistent over large areas. This type of ore body offered the best opportunity for study and experiments. The use of jumbo drill carriers was advanced but some doubt was expressed as to the adaptability of jumbos as then in use to mine headings as compared to post and arm mounting (Fig I). Another consideration was the introduction of truck haulage when several mines were trackless. A drill frame, built to carry 2 4-in. drifters, was mounted on a truck chassis. This design proved a failure as it was not rigid and the resiliency of the tires and springs allowed too much play. Long screw jacks were then used to hold the truck firmly in place, but placing the jacks and securing the truck required more effort and time than setting up post drills, so the truck carrier was abandoned. The use of a bull dozer underground had been under consideration for some time to be used in "brunoing" the broken dirt from behind pillars and other inaccessable places so the slusher drags could load without double dragging the dirt. A dozer with hydraulic blade lift was purchased and R. I. Tuthill, Superintendent of Section 30 Mines, suggested that a long drill arm be substituted for the blade, and the drills mounted on the cross member. The hydraulic lift would permit drilling holes at any required spacing. The "cat" was very mobile and answered the problem of a trackless mine. The initial tests showed that the "cat" would make a good carrier, but the hydraulic controls Were not positive enough to keep the drills in alignment while drilling. The next step was to build a small hoist. This hoist was attached to the power take-off on the "cat" and by means of sheaves and a double line of 3/8-in. hoist cable, a positive control for raising and lowering the boom was obtained. To avoid serious injuries to the drillers should the cable break, a safety chain was fastened to the drill boom and hooked into a slot in the back of the "cat" frame. A different power unit was obtained for the "cat," as a state law prohibited the use of internal combustion engines in mines. A custom machine shop had just placed on the market a small hoist powered by a Model A Ford engine that had been very ingeniously converted to a slide valve engine using compressed air. To use this unit on a "cat," our master mechanic de-

Jan 1, 1947

By Thomas L. Garrard, James A. Sprague, Rex B. McLellan, Samuel J. Horowitz

A simple rnodel for interstitial solid solutions has been devised in which each solute atom interacts with the solzlent lattice in such a way as to exclude an integral number of nearest-neighbor sites from being occupied by solute atoms. The vemaining interstitial sites ave not affected. In calculating the entropy of such a solution the increase in the number of interstitial sites available to solute atoms due to the ozlerlap of blocked sites is taken into account. The ther-modynamic functions and the solute activity fov the solution rnodel are calculated. It is shown that considevation of the overlap sues vise to a correction term of the order 8' ( where 0 is the ratio of solute to solvent atoms) in the thevmodynamic functions of the solution and the solute activity. The theo,uetical equation for the solute activity was used to analyze the available data for the activity of carbon in austenite at three different temperatures. The use of a computer enabled many comparisons to be made between the experimental activity data and those predicted by both the complex blocking model and the simple, widely used blocking model in which the ozierlapping of blocked sites is not taken into consideration. Even though at the highest concentvations oj carbon the value of 0 is small it is shown that the best fit to the experimental data is found with the complex blocking model. RECENTLY it has been shown by analysis of gas-solid equilibriums that many interstitial solid solutions can be described by the quasi-regular solution model in which the partial energy of solution E, is independent of composition and, apart from a composition-independent term due to nonconfigurational factors, the partial entropy is that of an ideal solution. Dilute solutions of nitrogen in both bcc and fcc iron,' dilute solutions of oxygen and silver,' carbon in a Fe,' and dilute solutions of carbon in ? Fe2 are all quasi-regular. In addition many hydrogen-metal solutions, both dilute and concentrated (with the notable exceptions of the H-Ni and H-Pd systems), can be described by this model.3 However, it has been shown that, at various temperatures, solutions of carbon in ? Fe begin to depart strongly from quasi-regular behavior at low concentrations. A plot of the activity of carbon in ? Fe relative to pure graphite vs atom fraction of carbon (Cc) calculated from Smith's data4 begins to depart from the (nonlinear) plot for a quasi-regular solution at about Cc = 0.02. Several statistical models have been proposed to account for the thermodynamic behavior of carbon in y Fe. Darken and smith4 set up a model in which a carbon atom in its octahedral site in the fcc lattice has either one or no neighboring carbon atoms in the twelve nearest-neighbor octahedral sites. It is assumed that the number of carbon atoms having more than one nearest neighbor is negligibly small and that a solute atom does not interact with another solute atom located at a greater distance than the first shell of interstitial sites. Thus this model contains two characteristic interaction energies. Darken and Smith showed that this model gives reasonable agreement with the measured variation of carbon activity ac with composition. It is noteworthy that Darken and Smith concluded from their analysis of the activity data using this model that there was a repulsive force between carbon atoms in austenite which reduces the concentration of C-C pairs below that corresponding to random mixing. Recently Aaronson, Domian, and pound5 have considered in detail the statistical model developed by Lachere and by Fowler and Guggenheim7 and have shown that it is compatible with the activity data for carbon in austenite. In Darken's model the energy of solution of carbon in austenite is dependent on temperature and concentration; the departure from Henry's law arises from the concentration dependence of the energy of solution. In Aaronson, Domian, and Pound's discussion of the Lacher, Fowler, Guggenheim model the interaction energy wy between adjacent carbon atoms in austenite is strongly temperature-dependent. Aaronson et al . suggested that this temperature dependence of wy and hence the energy of solution of carbon could be explained either by the formation of clusters of carbon atoms (despite the repulsive nature of wy) or by the dual occupancy of the octahedral and tetrahedral sites by the carbon atoms. However, a temperature-dependent heat of solution

Jan 1, 1968

By Ballard H. Clemmons

THE future of the steelmaking industry of the Birmingham, Ala., district is closely related to and, in a large measure, dependent on the development of workable, economic processes of ore concentration. Operations thus far in the area have been possible only because of the fortuitous occurrence of iron ore, fluxing stone, and coking coal-all the primary iron-making materials- within a 25-mile radius of the blast furnaces. Commercial ore of the district consists mainly of a 10 to 20-ft hematite-calcite-silica bed locally known as the "Big Seam," a component of the Clinton formation of Silurian Age. At present mining rates, this ore will be available for a number of years. It is largely mined under 1000 to 2000 ft of cover and transported on 15 to 20" slopes that, in some instances, are as much as 10,000 ft long. Under these conditions, particularly with increasing distances from face to portal, mining costs are gradually becoming disproportionately high. Although not a major factor thus far, it should also be noted that the average annual ore output of the district is gradually be- coming more siliceous.

Jan 1, 1950

The paper describes a cyclic method for processing manganese ores using sodium sulphate as the basic reagent. Sodium sulphate is electrolyzed in a diaphragm cell to give an anolyte sodium sulphate acid and a catholyte containing caustic soda, a part of which is carbonated in a cyclic manner to Form ash. and reduced ore is leached with the anolyte to dissolve the manganese and the impurities are precipitated by addition of catholyte. Manganese in the pregnant solution is precipitated as synthetic rhodochrosite with a carbonated catholyte, and sodium sulphate is regenerated. Calcining the manganese carbonate site a high-grade product and the carbon dioxide is returned to the carbonation step. the results of laboratory tests using cells equipped with synthetic fiber diaphragms and permselective membranes which permit transfer of using or cations during electrolysis are described. The article from which the above abstract is reprinted appears in Trans. AIME (1955) 203, p. 51; Journal op Metals (January 1955).

Jan 1, 1956

By Coolbaugh, Franklin

CRUSHING of Climax mine-run ore is carried out in two plants: No. 1 plant (flowsheet in Fig. 1) has a capacity of approximately 5000 tons per day. It is used as a stand-by except when maximum production is required. No. 2 plant (Fig. 2) has a top capacity of approximately 17,000 tons per day. The No. 2 crusher is more efficient to operate on reduced tonnages regardless of the wide variation in peak capacities. The system of crushing is similar in both plants: Mine ore, of a size which can be drawn through 48 by 96-in. slusher openings underground, is dumped into the crusher bins from ten-ton mine cars and fed into 48 by 60-in. Buchanan jaw crushers by means of chutes and Ross chain feeders. The jaw crushers are set to discharge at approximately 9-in. size. Jaw crusher discharge is conveyed to 7-ft. Symons standard cone crushers where it is broken to minus-2-in. size,

Jan 1, 1946

By Frank Corwin

It is the purpose of this article to give a brief account. of the experimental work and to show how the increase in efficiency was brought about. Part of the experimental work described in this paper was carried out by the writers, while in the employ of the Anaconda Copper Mining Co., under the direction of M. W. Krejci, Metallurgist, and Arthur Crowfoot, Chief Sampler. Complete records of all of the MacDougall testing work have been placed at our disposal through the courtesy of A. E. Wheeler, Superintendent. II. BRIEF HISTORY OF PRESENT MACDOUGALL PLANT. The first change from the Brueckner cylinders used for roasting concentrates at Great Falls was the construction of a MacDougall roaster of the Herreshoff type. This furnace was first started on June 15, 1898. It bad eight hearths, was lined with fire brick, and had an air-cooled central shaft, but no provision was made for cooling the rabble arms. It was operated for a while, and accomplished the work of roasting, but ran so hot that the rabble arms became twisted and distorted out of shape. To prevent the furnace from becoming too hot a device was then installed to draw the heated gases away from the hearths. This consisted of a pipe connected to alternate hearths of the MacDougall furnace and also connected to the flue. It was equipped with dampers, 'so that the hot gases could be drawn away from any one of the alternate hearths directly into the flue.

Jan 7, 1913

By B. H. Caudle, M. D. Witte

In predicting the performance of a pattern injection operation, the engineer needs to know both the amount of oil to be recovered and the rate at which the recovcry will take place. This paper- describes fluid flow model studies on the effect of mobility ratio on the rate of oil recovery in a five-spot. The results show the change in fluid conductivity (total flow rate/pressure drop) as the sweep-ont pattern increases for mobility ratios between 0.1 (and 10. There data, when cornbitted with a knowledge of reservoir permeabilities and sweep-orit pattern efficiencies, cata he used to predict the cLrmulntivr oil production as a function of time for homogeneous five-spot injection systems. INTRODUCTION The flow potential in a pattern flood element is a function of the mobility ratio and how far the injected flood front has gone.1,2 For a waterflood project having a mobility ratio of one, the conductance—which is the flow rate per unit pressure drop (q/Ap)—-will remain the same throughout the life of the flood. If the mobility ratio is favorable ( < I), the conductance of the project will drop continuously throughout the operation. If, on the other hand, the mobility ratio is unfavorahlc. the conductance ratio will increase continuously. Therefore, if the reservoir engineer wishes to predict either the rate at a specified pressure or the pressure at some rate for a secondary recovery project, he must know how the conductance will vary during the flood. Other investigators have studied this problem using potentiometric models&apos; or analytical solution&apos;. The

THE metal iron has physical and chemical properties which are somewhat different from those of steels, but a knowledge of the pure metal is a useful starting point in studying the behavior of steels. Solid iron exists in two different crystalline forms, called alpha (a) and gamma (?) iron, the former being the ordinary form at room temperature. When heated above the "A2 point," 1400°F. (760°C.), the metal becomes non-magnetic, and at the "As point," 1670°F. (910°C.), it undergoes a change in crystalline form to become gamma iron. In the range 1400 to 1670°F., it is sometimes called beta (0) iron to distinguish it from the magnetic alpha, but the two are identical in crystal structure. When gamma iron is further heated to 2550°F. (1400°C.), it changes into delta (d) iron, which is identical with beta or non-magnetic alpha iron. Pure iron melts (in a hydrogen atmosphere) at 2795°F. (1535°C.); the melting point is generally lowered by alloys or impurities. PROPERTIES OF IRON AT HIGH TEMPERATURES Many of the properties of iron undergo abrupt changes at the transition temperatures. (1) For example, in heating through the As point a sudden shrinkage in volume occurs. Similarly, melting is attended by sharp physical changes such as an increase in volume. Table 27 contains a summary of the measured physical properties of pure iron at several temperatures. Usually the properties change smoothly within the range of stability of a given form, but this is not always the case. For example, the specific heat reaches a sharp maximum at the A2 point although no transformation occurs. Solvent Powers of Liquid Iron. Liquid iron is capable of dissolving most of the other metals and many nonmetallic elements as well. Of the metals which are liquid at the melting point of iron only lead, silver, and bismuth refuse to dissolve to an appreciable extent. The non-metals presumably dissolve by virtue of the formation of an iron compound; for example, sulphur is thought to dissolve as the compound FeS. However, there is no satisfactory method of proving that this

Jan 1, 1944

By C. Chiou, D. P. Seraphim

The effect of clustering on the superconducting properties of Al-Zn alloys has been studied by the ballistic induction techniques. The superconducting critical temperature, T,, changes when zinc-rich clusters are formed. The change in T, depends on the concentration and may be positive or negative, but always correlates with an effective decrease in the solute concentration of the alloy. Reversion after clustering effectively returns a 5 at. pct Zn alloy to the quenched state. These methods might be use&lly extended to the Al-Mg system, where X-ray data are difficult to obtain. In very dilute Al-Zn alloys, as in other tin,&apos; indium, aluminum,2 or tantalums base solid solutions, there is a decrease in the superconducting critical temperature, Tc, roughly proportional to the temperature independent resistivity, i.e., -0.2°K per pS2cm. With increasing solute concentration, the T, generally reaches a minimum and then increases4 to a value well above that for the pure solvent. The change of T, with solute concentration follows an empirical formulation involving two constants which correlate with the scattering cross section of the impurities. As will be shown below, the Al-Zn alloys more concentrated than 1or2at. pct do not follow the empiricism, probably because they are unstable even when rapidly quenched.5 However, it seems possible to study at least the later stages of solute clustering by precise measurements of the 1&apos;, following various thermal treatments. A few experiments on quenched alloys, aged alloys, and tests on reversion are reported here. The heat treatments selected for obtaining the quenched and aged states were mainly deduced from the work of Dash and Fine.6 For the quenched state, specimens were homogenized at 480°C, quenched to -160°C, and immediately transferred and mounted in liquid nitrogen. Measurements on the superconducting properties and residual resistivities were then made at helium temperatures, after which the specimens were aged at room temperature for 3 to 5 hr, i.e., much longer than the time required for clustering to be essentially completed. The superconducting properties and residual resistivities were once again examined. To reach the reverted state of the A1-5at. pct Zn alloy, the aged specimen was heated for 5 min at 200°C and then tested as above.

Jan 1, 1963

By AIME AIME

PERHAPS the outstanding characteristic of the newly elected President of the Institute is his rare ability to set aside nonessentials, and pick out the few basic elements on which a valid conclusion on any question can be drawn. This holds whether he is appraising a mining enterprise, selecting a man for an important position, deciding whether to buy or sell a bond, or choosing the best method for mining a huge body of ore. For example, he has pointed out that the two primary factors that make for success in a copper-mining venture are a large reserve of reasonably good ore and competent management. Usually the first is not as difficult to gauge accurately as the second. In a big enterprise the quality of the management

Jan 1, 1939

THE John Fritz Medal Board of Award, at its regu¬lar annual meeting Oct. 19, awarded its gold medal to Herbert Clark Hoover. Thus ended a process of selection begun a few years ago. The award was tentatively made a year ago by the Board, which is composed of sixteen recent past-presidents of the four national societies of Civil, Mining and Metallurgical, Mechanical, and Electrical Engineers, having together a membership of nearly 60,000. The sixteen members of the Board are: American Society of Civil Engineers : C. E. Grunsky, Robert Ridgway, George S. Davison and John F. Stevens ; American Institute of Mining and Metallurgical Engineers: William Kelly, J. V. W. Reynders, Samuel A. Taylor and E. DeGolyer; American Society of Mechanical Engineers: Fred R. Low, D. S. Jacobus, Dexter S. Kimball and Charles M. Schwab; American Institute of Electrical Engineers: Farley Osgood, M. I. Pupin, C. C. Chesney and Bancroft Gherardi.

Jan 1, 1928

By W. G. Sinclair

The wartime momentum of exploration continued throughout the year 1945 despite the end of hostilities in mid-August. The table below illustrates drilling activity in the various categories: Completed wells. . . . . . . . . . . . . . . . . . . . . . . . 401 Wildcats.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .104 Wildcat discoveries, oil.. . . . . . . . . . . . . . . . . . . 2 Wildcat discoveries, gas-condensate.. . . . . . . 4 Development wells.. . . . . . . . . . . . . . . . . . . . . .297

Jan 1, 1946

By Charles Goodale

THE principles and theory on which the U. S. mining law of 1872 was based are well understood, and have been discussed at great length by many writers. The papers by Dr. R. W. Raymond1 in the Transactions of the American Institute of Mining Engineers have covered the subject very fully, with explanations of practical results in many adjudicated cases. It is believed that the following instance of the application of the law in recent years will have some weight in a discussion of proposed changes in our mining laws. The litigation between the St. Louis Mining & Milling Co., and the Montana Mining Co., Ltd., a British corporation, over portions of the Drumlummon lode covered more than 20 years, and resulted in a judgment for damages in favor of the St. Louis Co. of such an amount that the Montana Co. declined to pay the judgment, and therefore lost the entire property. The Drumlummon lode claim in the Marysville district, Mont., was located in 1876 by Thomas Cruse. When he staked out his claim, he assumed that the discovery on the Drumlummon vein, and another showing of mineral about 200 ft. distant, were on the same vein, and the center line of the claim was given a course of N. 57&apos;2&apos;E. Development of the Drumlummon vein soon showed that its strike was about N. 15 E., and that the other outcrop was on the North Star lode; so it was inevitable that the Drumlummon vein would cross one or both side lines of the location, and the Montana Co. found it advisable to acquire adjoining claims on both sides of the Drumlummon, in order to avoid possible litigation over apex rights. They bought the Marble Heart, but would not purchase the Hopeful (see Figs. 1 and 2), at the terms proposed for the reason that exploration in the Cruse level had shown the vein to be barren in that region. The owners of the Hopeful were sinking an incline from that claim in 1889, and the Montana Co. enjoined them, contending

Jan 5, 1914

By Charles Catlett

(Chattanooga Meeting, October, 1M.) THE terms " developed " and " undeveloped " are necessarily relative and cover a wide range; but the latter is here applied to cases in which the information at hand falls short of a clear demonstration of values, and conclusions must be reached from a study of the geological conditions of the particular deposit, interpreted in the light of similar and closely related deposits. Such an inquiry might be characterized as an effort to reach reliable conclusions from insufficient data. But the engineer engaged in commercial work finds himself often face to face with apparently such problems; and while he may realize with regret that a small amount of intelligent development would add enormously to the value of his conclusions, he is compelled to recognize the demand of a business situation for a prompt decision as the basis of immediate action. In a case within my knowledge, the question involved was the purchase of 50,000 acres of coal-land, and 10 days was the limit within which this question must be decided. Of course, it was impossible to make a satisfactory examination within that time; but the &apos;instructions were "to make the most complete examination and the most positive recommendation possible." Such instructions are often given; for, no matter how much time an investor may have, he is likely to put of his decision until the last moment, and then discover that he needs more light and advice. It does not follow that engineers, after full explanation and mutual understanding of the situation, should decline to undertake examinations thus limited. In the case just mentioned, while only the broadest view was possible, half the time available was sufficient to show that the property was a good purchase. The timber alone was subsequently resold for more than the entire purchase-price of the

Mar 1, 1909

By H. M. Chance

The iron-ore deposits of the Hartville district are located near the new town of Guernsey, about 100 miles north of Cheyenne. The writer has been familiar with them since 1887, having visited the district several times for different clients— his last examination having been made in November and December, 1897. The deposits extend in a general N.E.-S.W. direction from a point in Section 33, Range 65 W., Township 28 N., on the west side of Whalen cañon, through Sections 4, 5, 6, 7 and 8 of Township 27 N. in the same Range, and over into Sections 1 and 12 of Township 27 N., Range 66 W. General Characteristics. The ore is a remarkably pure red hematite, extremely low in phosphorus, and carrying a small percentage of silica, as shown by analyses given below, and similar in many respects

Jan 1, 1901

By Richard Miller

WORK was undertaken two years ago at the Hammond Laboratory for the purpose of determining the magnitude of the elastic range in single crystals of pure metals by means of creep tests, the assumption being made that if a true elastic range exists, the elastic limit represents the maximum stress for no creep. A sensitive extensometer was constructed, and creep tests were made on zinc single crystals at a variety of loads and temperatures1. It was soon discovered that there is tip measurable elastic limit in ductile zinc single crystals at, or above, room temperature. The inference that pure metallic single crystals may not possess a definite elastic range was not justified, however, since zinc had been tested in creep only above its recrystallization temperature, and several investiga-tors2,3,4 had already shown that above the recrystallization temperature polycrystalline metals will flow under very small stresses, while below that temperature stresses of a much larger magnitude are required. For that reason, it was decided to extend the study of the elastic limit to other metals having a higher recrystallization temperature than zinc. Aluminum and silver were selected, because of the ease of obtaining pure materials and of preparing large single crystals, and because the crystallo-graphic glide system of these metals is well known. Owing to the limited time available, the elastic range was investigated by slow tensile tests rather than by creep tests.

Jan 1, 1937

By J. D. H. Strickland, K. J. Jackson

IN previous papers&apos; &apos; details were given of the constructlon and use of an apparatus to study the rate of chlorine consumption and the rate of sul- fate and sulfur production when dilute aqueous chlorine solutions were allowed to react with pyrite and galena in acid solutions at or near room temperature. The reaction with pyrite was very rapid, and hence entirely transport-controlled in its kinetics, and produced only ferric and sulfate ions. The behavior of galena was much more complex and was studied in some detail. Sulfur monochloride could be detected as a reaction product and both

Jan 1, 1959

By J. A. Woolf, E. S. Leaver

The presence of soluble base metals in precious-metal ores usually precludes cyanidation as the best method of treatment. The laboratory experiments described in this paper show the possibility of cyanidation of gold-silver ores containing less than 0.5 per cent. of cyanide-soluble copper and the effect of zinc in the cyanide solution. Part I.—Copper in Cyanidation The proposed process of cyanidation of precious-metal ores containing copper is based on the regeneration of about 80 per cent. of the cyanide used in the dissolution of the copper. The method of regeneration involves a combination of the sulfide and the acid precipitation of the copper and silver. The resultant solution is made alkaline with lime, and the gold is precipitated with zinc dust. Solubility of Copper Minerals in Cyanide Solution In order to determine the solubility of copper minerals, including metallic copper, under the usual conditions for cyanidation, experiments were conducted with synthetic ores. Each ore sample was prepared by mixing the particular pure copper mineral with barren sea sand. Both the mineral and sand were ground to pass 100 mesh before they were thoroughly mixed. The percentage of copper in each head sample was determined by direct assay, excepting the metallic copper sample, which was computed on weights before mixing. Table 1 gives the results. Azurite, bornite, chalcocite, cuprite, malachite and finely divided metallic copper are readily and completely soluble under the usual conditions for cyanidation. Enargite and tetrahedrite are sufficiently soluble to cause an excessive loss of cyanide, and they also cause fouling of solutions with arsenic and antimony. Precious-metal ores containing small percentages of chalcopyrite or chrysocolla may give satisfactory returns with the usual cyanidation.

Jan 1, 1930

By Eugene A. Mizikar

A mathetnatical model of heal transfer in continuously cast steel slabs is described. The model, consisting of a unidimensional transient conduction equation and boundary condition equations, has been pvogrammed for computer solution. Temperatuve and solidification profiles calculated for a 6-in. slab, being cast under several conditions of secondary cooling, are presented and compared. Calculated solidification profiles are in agreement with reported expevinle~ztal values. For the mold zone, the predicted slab shell thickness can be described by: Resuilts of the study indicate that multibank spray cooling followed by radiant cooling should be employed when solidifying thick slabs with minimum surface temperature of 1600°F. Under these conditions, a 6-in. slab can be expected to solidify in about 8.3 min. Computer results also indicate that radiant cooling can replace spray cooling during solidification of the final 30 pct of slab with little increase in overall solidification time. CONTINUOUS casting has come to the forefront of the steel industry in recent years because of economic advantages resulting from increased yields and elimination of several processing steps. Considerable work, however, remains to be done regarding modifications to the process and operating procedures. Both a lack of operating plants in this country and the experimental difficulties associated with direct measurements on moving castings have made determination of solidification rates and temperature distributions difficult. An alternate approach is to mathematically simulate heat transfer in a continuously cast section, and then calculate the temperature distributions as a function of the controllable variables of the process. Simulation of heat transfer during solidification requires that a nonlinear mathematical problem be solved. As pointed out by Ruddle,&apos; there are two mathematical approaches to the problem- the analytical approach and the numerical approach. While the analytical approach is certainly the more elegant of the two, it does require a number of inexact assumptions because of the complexity of the problem. For example, noteworthy analytical treatments of heat transfer in continuous casting have been developed by Savage Hills,3 and pehlke4 only by making one or more simplifying assumptions such as invariant thermophysical properties, constant heat-transfer coefficients in the mold, and linear temperature profiles in the shell. Simplifying assumptions such as these can introduce considerable uncertainty in the validity of results calculated with analytical solutions. Numerical solutions, which are considerably more versatile, appear to be better suited for solving solidification problems. Complex variations in the boundary conditions and variable thermophysical properties can be handled readily with this technique. Whereas numerical computations can be long and tedious when done by hand, results can now be obtained quite rapidly with the use of either the digital or analog computer. Several numerical models of heat transfer in continuous casting have been published. In 1963, Adenis, Coats, and Ragones published a numerical model used to calculate temperature distributions in direct-chill-cast magnesium billets. More recently, Donaldson and Hess 6 presented results obtained with a numerical computer model of heat transfer in continuously cast steel billets. In the present study, a model of unidimensional heat transfer in continuously cast slabs is presented. The method of solution on a digital computer is also included. Calculated temperature distributions and solidification profiles for various schemes of secondary cooling along with attempts to verify the model are also discussed. MATHEMATICAL MODEL The schematic representation of the slab continuous casting process in Fig. 1 illustrates that the slab passes through three distinct zones of cooling. Accordingly, the mathematical model consists of three parts: 1) solidification in the mold; 2) solidification in the spray cooling zone ; 3) solidification in the radiant cooling zone. Heat-Transfer Equations. The model was developed bymaking a heat balance on a horizontal slice of slab over the time period required for the slice to proceed from the liquid metal meniscus in the mold to the cutoff station. As shown in Fig. 2, the imaginary slice extends from the center line to the surface of the slab. As the slice moves downward, heat is conducted from the center line to the surface of the slab at a rate governed by the surface boundary condition and thermophysical properties of the metal in the slice. The following partial differential equation describes the conduction of heat in a medium moving at velocity U in direction Z:

Jan 1, 1968

By George Krauss, M. Cohen

The reverse martensitic transfomzation (i.e., the conversion of martensite to austenite on heating) was investigated in Fe-Ni alloys containing 30.5 to 33.5 wt pct Ni. The reversed austenite was found to be sufficiently distorted to exhibit marked differences in mechanical properties and to undergo recovery and re crystallization on further heating. In particular, the yield strength of the reversed austenite was as much as 2.5 times higher than that of the virgin austenite: with five cycles of the direct and reverse martensitic transformation, the yield strength was 2.6 times higher. There was an accompanying decrease in strain-hardening capacity and in stable ductility or uniform elongation. The recrystallization was observed to follow sigmoidal kinetics, but was characterized by an abnormal1y large temperature dependence which was evidently due to carbon segregation at the migrating grain boundaries. Upon recrystallization, the strength Properties reverted to those of the virgin austenite, but the ductility did not fully recover until the annealing temperature was further raised to dissipate the carbon segregation at the grain boundaries. The transformation of reversed austenite to produce second-generation martensite resulted in an unusually imperfect structure, thereby leaditg to additional strengthening. Horlleuer, the martensitic phase was much less responsive in this respect than was the austenite. MOST martensitic transformations are capable of undergoing a reverse transformation back to the austenitic phase on heating.&apos; This reaction, like the direct transformation to martensite on cooling, is usually athermal. In analogy with the Ms andMf temperatures for the martensitic transformation (where M, > Mf), the reverse transformation is characterized by the As andAf temperatures (where As<Af). It is well-known that the finish (Af) of the martensite-to-austenite reaction on heating may occur at a temperature where austenite is not stable relative to other phases in the equilibrium diagram.&apos; Reverse martensitic transformations have been found to influence the properties of the parent austenitic phase in a number of ferrous alloys. The austenite thus produced after one or more reversals is significantly altered in strength, microstruc-ture, diffusivity, and annealing characteristics compared to well-annealed, virgin austenite. The first detailed observations of such phenomena were made by Wasserman3 on an Fe-30 wt pct alloy. He found that the reversed austenite (i.e., austenite formed by the reverse martensitic transformation) was much stronger than the original austenite, and the second-generation martensite (i.e., martensite produced from the reversed austenite) was somewhat stronger than the first-generation martensite. On heating the reversed austenite, recrystallization occurred in a manner similar to that of a cold-worked metal; the Laue spots sharpened and the strength decreased.4 In recent years, Russian workers have shown considerable interest in these reverse martensitic transformations. Most of such investigations5-10 have been concerned with the stabilization of reversed austenite relative to subsequent martensitic transformation, and because of its unusual nature, this phenomenon will be discussed in detail elsewhere." On the other hand, the annealing behavior of reversed austenite and the attendant variation in properties have received little attention beyond the experiments of Wasserman.3,4 Gridnev eta1.,8 in one of the few such studies. followed the hardness change of reversed austenite as a function of time at three annealing temperatures. The marked strengthening of austenite achieved by the reverse martensitic transformation has been referred to as "transformation strengthening" by Wasserman3,4 and as "phase hardening" by Malyshev et a1.7,9,10 to differentiate it from hardening produced by cold working. Both groups of investigators noted that further strengthening of the austenite could be attained by repeated or cyclic transformations, but the first cycle resulted in the most pronounced effect. Evidence of the altered microstructure of reversed austenite has been reported by Maximova and Nikonorova6 and by Edmonson and KO.12 The former found that reversed austenite was much more sensitive to etching than the original austenite, and the latter authors observed a (&apos;ghost" structure resembling martensite in certain areas of the reversed austenite. Enhancement of the self-diffusion rate in reversed

Jan 1, 1962