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By William R. Patterson

ACCORDING to the phase diagram for the Mn-Ni system,' the high-temperature, fcc y-manganese solid solution is stabilized to below room temperature, in the range approximately 22 to 28 wt pct Ni. However, pearson2 cites evidence in the literature showing that for manganese contents greater than about 75 wt pct the quenched phase in Mn-Ni alloys is fct. This is in keeping with zener's3 suggestion that in manganese-rich alloys the fcc high-temperature phase undergoes a diffusionless or martensitic transformation to a fct structure upon quenching. Work by Basinski and christian4 on manganese-rich compositions in the similar alloy system Mn-Cu established that in alloys of greater than about 82 wt pct Mn the y-manganese phase underwent a fee fct martensitic transformation upon quenching to room temperature. Striking evidence for this martensitic transformation was the highly twinned or banded microstructure, an example of which is shown in Fig. 1. Similar microstructures have also been found in quenched Mn-Cr5 and Mn-Au6 alloys. In the present investigation, we attempted to obtain similar evidence of a fcc — fct martensitic transformation in manganese-rich Mn-Ni alloys. Manganese alloys in the range 10 to 30 wt pct Ni were prepared by arc-melting, under argon, at atmospheric pressure. The alloys all were 50 g in size, and negligible weight loss occurred during melting. The starting materials were electrolytic manganese and nickel, both of 99.9+ pct purity. The alloys were subsequently homogenized 48 hr at 1750°F, hot-rolled 50 pct at 1700°F, annealed 2 hr at 1700°F, and water-quenched to room temperature. All heat treatment was done in purified argon. Both X-ray and metallographic techniques were used to examine the structures of the quenched alloys. X-ray diffractometer studies were conducted on powder specimens obtained from filings rean-nealed 2 hr at 1700°F in argon and water-quenched. Identification of the intensity peaks from the diffractometer counter traces showed that below about 10 to 12 pct Ni the y phase decomposed partially upon quenching to give an a- + ?-manganese structure. In the range approximately 12 to 25 pct Ni, the structure was found to be fct ? manganese with a c/a ratio approaching 1.0 at 25 pct Ni. Beyond approximately 25 pct Ni, the structure remained fcc. These results, including lattice-parameter determinations, are given in Table I. Metallographic examination. was carried out on specimens polished and etched after quenching, and also on polished specimens reannealed and quenched. In the first case, the distinctive twinning or banding so prevalent in Mn-Cu alloys was sought, while in the second, the surface relief effect generally regarded as being truly characteristic of a martensitic transformation was sought. The microstructure of representative alloys in the range 12 to 25 pct Ni is shown in Fig. 2. The structure of the Mn-15 pct Ni

Jan 1, 1965

By R. S. French, W. R. Hibbard

FOR tensile deformation, if the stress value is defined by the ratio of the load to the actual area, and the strain value by the natural logarithm of the ratio of the immediate length to the original gauge length of the sample, the resulting data when plotted with logarithmic coordinates result in a linear relation extending from the initial plastic yielding through the maximum load and in some cases, such as for copper and brass, to fracture'.'. The normal form of the curve, therefore, is a parabola, satisfying the following equation: S = Kem [1] where S and e represent true stress and strain, K is a constant, and m is a coefficient evaluating the slope of the curve and designated therefore as the strain hardening coefficient. Hollomon² has reported that this coefficient is a function of the yield strength as effected by grain size in alpha brass, and the carbon content and heat treatment of steel. In the case of steel, the value of the proportionality constant is a function of the carbon content. It was further shown in that paper2 and also by Low and Prater -hat, if the power relation between stress and strain remains valid, the strain hardening coefficient m, is equal to the strain at the maximum or necking load. Thus, an added significant feature is that this coefficient may serve as an index of the capacity for deformation prior to localized necking and subsequent fracture, e.g. drawability. The constant K may be defined as the strength of the material at unit strain. Together the K constant and the m coefficient describe an alloy's physical properties as far as strength and ductility are concerned for a particular yield strength and, in the case of steel, a particular carbon content. The work of Lacy and Gensamer4 gives data on alloy ferrites from which very close estimates of the strength of ternary and higher iron alloys have been made. It was the purpose of this investigation to develop similar data for commercial copper base alpha solid solution alloys. Preparation of Specimens Commercial binary alloys of copper with aluminum, beryllium, cadmium, nickel, silicon, tin and zinc were investigated. In addition, laboratory castings were made of a 1 pct silicon alloy and a 2 pct aluminum alloy to complete these particular series. Two types of copper were used, oxygen free OFHC and tough pitch FC. The analyses of these alloys are shown in table I. Standard ASTM sheet tensile specimens were used to determine the usual physical properties of each alloy and to obtain stress data at strains from 0.0005 to 0.01. Small (1/4 in. x 3 in. x tk.) samples

Jan 1, 1951

By Wayne A. Greenwalt

A method that determines venture participation when the decision maker's level of risk aversion varies according to venture profitability and risk investment is presented. The decision maker's fundamental aversion to risk is established by the selection of a desired working interest for a venture that anticipates only a discounted payout.

Jan 1, 1982

PROF RICHARD ÅKERMAN Stockholm, Sweden PROF RICHARD BECK Friberg, Germany ANDREW CARNEGIR New York, N.Y. DR. JAMES DOUGLAS New York, N.Y. PROF HATON DE LA GOUPILLIERE Paris, France SIR ROBERT A. HADFEILD London, England PROF HANS HOFFER Leoben, Austria PROF HENRI LOUIS LE CHATELIER Paris France M FLORIS OSMOND Paris, France ALEXANDRE POURCEL Paris, France DR. ROSSITER W. RAYMOND New York, N.Y. PROF ROBERT W. RICHARDS Boston Mass. DR. ING H. C. EMIL SCHROEDTER Dusseldorf, Germany JOHN E. STEAD Middlesborugh, England JAMES M. SWANK (Associate) Philadelphia, Pa. PROF DIMITRY CONSTANTIN TSCHERNOFF St Petersburg, Russia PROF TSUNASHIRO WADA Tokyo, Japan CHARLES D WALCOT Washingtion D.C.

Jan 1, 1917

By AIME AIME

ON THE occasion of the eightieth birthday of Captain Robert W. Hunt, the Iron and Steel Committee of the Institute, desiring to commemorate the great contributions made to the steel industry by Captain Hunt during his long career, conceived the idea of a Hunt Medal to be awarded annually by the Institute for meritorious contributions to the art of making steel. The project was received enthusiastically by all to whom it was proposed, especially by Captain Hunt's partners and employees who considered it their right, and asked for the privilege of -. - raising the necessary funds within their own circle. This was agreed to, and the Institute has received from them $7500 as an endowment fund to provide an annual award, and $1000 for the expenses of providing of medal.

Jan 1, 1920

By D. W. Brunton

Discussion of the paper of D. W. Brunton, presented at the Spokane meeting, September, 1909, and published in Bulletin No. 33, September, 1909, pp. 837 to 855. WILLIAM' KENT, New York, N. Y.:-The Institute may congratulate itself on the opportunity of reading the splendid address of President Brunton. It is au admirable summary of the progress that has been made in the mining and metallurgical arts in recent years. The paper rightly give's the chief credit for this progress to the aid which has been rendered to these arts by the advances in mechanics, chemistry, and electricity. It is notable that most of the headings in Mr. Brunton's address refer to the work of the mechanical engineer, the electrical engineer, and the chemist, rather than to that of the specialist in mining-operations. It seems that. the most successful mining engineer of the present day is the one who makes the most intelligent application of the inventions and designs of engineers and others who are not directly engaged in mining. A tabulation' of the headings of the address, grouped as below, shows this most clearly. Work of the Mechanical Engineer-Rock-drills, hoisting-machinery, tramming, pumping, ventilation, dredging, sampling, concentration, briquetting, fume-recovery. Work of the Electrical Engineer-Electric machinery for hoisting, pumping, tramming, lighting and signaling, electric . transmission, electric smelting. Work of the Chemist and Metallurgist-Explosives, chlorination, cyanidation, roasting, lead-smelting, and copper-smelting. Work of the Geologist-Economic geology. Work of the Mining Engineer-Mine-mapping, surface-mining, timbering, tunneling; and planning and supervision of the work in general. The mining engineer of the present day, who is in responsible charge of a large plant, finds his chief work not in doing

Jan 1, 1910

PROF RICHARD ÅKERMAN Stockholm, Sweden DR. FRANK DAWSON ADAMS Montreal, Canada PROF RICHARD BECK Friberg, Germany ANDREW CARNEGIR New York, N.Y. DR. JAMES DOUGLAS New York, N.Y. PROF HATON DE LA GOUPILLIERE Paris, France SIR ROBERT A. HADFEILD London, England PROF HANS HOFFER Leoben, Austria PROF HENRI LOUIS LE CHATELIER Paris France EZEQUIEL ORDONEZ Mexico City, Mexico ALEXANDRE POURCEL Paris, France DR. ROSSITTER W. RAYMOND New York, N.Y. DR. ING H. C. EMIL SCHROEDTER Dusseldorf, Germany JOHN E. STEAD Middlesborugh, England JAMES M. SWANK (Associate) Philadelphia, Pa. PROF DIMITRY CONSTANTIN TSCHERNOFF St Petersburg, Russia PROF TSUNASHIRO WADA Tokyo, Japan CHARLES D WALCOT Washingtion D.C.

Jan 1, 1917

By Hiland G. Batcheller

HISTORY shows that the nation which makes the most steel is the most likely to win wars. Today the course of war shows that the nations which get there first with the most steel of the right kind will be the ones to win. Not only the most steel, mind you, but the right kind. Adequate production, which was enough for victory before the days of totally mechanized warfare of 1943, must now be accompanied by still better quality as well as more effective distribution. Further, both production and distribution must be flexible enough to permit rapid shifts from one weapon to another for use in varying elements in varying geographical areas. Thus the problem of making enough steel of the right kind at the right time in the face of changing requirements dictated by experience has been and will remain highly complex. This does riot permit us to ease our restrictions on nonessential use. War is a complex business, like the job of making steel for war. Each time we solve one problem, another pops its head up. Yet we are making some progress.

Jan 1, 1943

By W. B. Plank, A. C. Callen

WAR and normalcy do not walk hand in hand, whether it be in industry, the educational field, or in the daily lives of individuals. Schools and departments offering curricula in mineral engineering have been seriously disrupted, beginning with 1942 and reaching a low during 1944. Selective Service regulations and voluntary enlistments have effectually stopped the flow of college-trained men into the mineral industry, and the flow into the colleges is little more than a dribble. The year just closed has been a most serious one for our institutions. Until March many of our faculties had been kept reasonably intact because of the large training programs of the Army and Navy. Although the number of

Jan 1, 1945

By L. S. Darken

IN the study of reactions occurring in liquid iron, alone or in contact with a liquid oxide or slag phase, it has been found that the experimental data over a limited range of concentration can in some cases be repre-sented satisfactorily by the simple equilibrium expression K - (p1)p1 (p2)p2 . (R1)r1(R2)r2 . where (P) denotes the concentration of a product and (R) the concentra-tion of a reactant in the reaction r1R1 + r2R2 + . . . Some of the reactions for which it holds are listed in Table 1. For others, however, the simple equation apparently does not hold. This has been attributed to an improper method of expressing concentration (for instance, weight per cent instead of mol fraction); or it has been supposed that the solutions are not ideal in the sense that the activity of a com-ponent is not proportional to its true mol fraction, But it may be that the problem has been oversimplified by neglecting some molecular species actually present; that is, by considering only the ostensible simple com-ponents and thus leaving out of account possible compound formation. It is the purpose of the present paper to point out how, in a group of related cases, a reasonable consistent assumption relative to the presence of a compound makes it possible to express the experimental data satis-factorily by the simple equilibrium expression when this compound is taken into account, and to bring into harmony data referring to different reactions in liquid iron. There are several a priori reasons for believing that solutions in liquid iron should not deviate far from ideality, provided that the concentration of solute is not too great and is expressed in proper terms. The factors that commonly lead to nonideality in systems at ordinary temperature as ionization or the occurrence of polar and nonpolar molecules-are presumably less effective in metal and in slag systems at high temperature. Again, the type of equation commonly used to express the value of

Jan 1, 1940

E. E. Russell Tratman, New York City (communication to the Secretary): Mr. Glenn's paper brings up again the question of the part played by coal-dust in colliery-explosions. In the discussion of Sir Frederick Abel's paper on " Accidents in Mines," read before the Institution of Civil Engineers,? much was said about the dangerous properties of coal-dust, and several instances were given of the successful use of a spray of water, water and compressed air, or exhaust-steam from an engine, to keep the mine SUEciently damp to prevent the formation of dust clouds. Methods of preventing shots from blowing out; of using water cartridges to prevent flame ; and of using lime cartridges, wedges and other means of breaking down the coal were also discussed. Mr. Emerson Bainbridge referred to the explosive termed " roburite " (ammonium nitrate and

Jan 1, 1895

By Cyril Wells, Robert F. Mehl

THE practical importance of a knowledge of the rates of diffusion of carbon and of alloying elements in steel has often been pointed out 1,13 This importance ties chiefly, though by no means only, in the study of carburizing and in the study of reactions involved in the eutectoid inversion in steel The present paper is one of a series in which the rates of diffusion of carbon and of alloying elements in y-Fe and their mutual effects are measured with precision The present paper reports the results of meas¬urements of diffusion coefficients D of manganese in -y-Fe over wide ranges of temperature, and concentration, and of the effect of carbon and impurities and of grain size upon these diffusion coefficients [$] Data on the rate of diffusion of manganese in y-Fe have been reported by Fry2 and by Paschke and Hauttmann 3 Claussen4 calculated the diffusion coefficient D from Fry's data as 3 X 10-10 sq cm per sec at 960°, which will be shown to be incorrect by many orders of magnitude Paschke and Hauttmann gave a rough value of 9 6 X 10-8 sq cm per sec at 1400° Neither of these workers considered the variation of D with concentration and with temperature, and neither studied the effect of carbon METHOD AND MATERIALS Method -The method employed is identical with that used earlier 5 Owing to the volatility of manganese and the consequent loss of manganese from the outer surfaces of the welded diffusion bars, these surfaces were discarded The diffusion anneals were performed in argon, except one (test 18) in which hydrogen was employed for purposes noted below The temperatures reported are accurate to about 3° and constant within I°C , the diffusion times are reported to the nearest half hour The specimens were furnace-cooled after the diffusion anneal at about 2° per min Layers, usually 0 004 in thick, parallel to the welded interface, were machined from the specimens after the diffusion anneal and analyzed for manganese to 0 01 per cent Mn, the distances of these layers from the interface was measured to ±0 0002 in The concentration-penetration curves obtained were analyzed by both the Grube and the Matano solutions e The D values calculated by these two methods do not differ appreciably 5 The Grube solution was used except in tests in which the effect of concentration upon D was greater than 50 per cent, in such cases the Matano method, which explicitly provides for the variation of D with concentration,1 is the more reliable In general, the number of layers machined from the zones of variable composition were large enough to permit the use of the average layer composition as that of the center of the layer In 3 of the 30 tests, however, this is not justified, and the D values

Jan 1, 1941

By James E. York

THE honor so fairly earned and so incompletely and tardily paid to Henry Cort, the inventor of the puddling-furnace and the, rolling-mill, has been fully set forth by Mr. Charles H. Morgan,1 and needs no further emphasis here. In view of the importance of the rolling-mill in the treatment of iron and steel, the paucity of information concerning it is surprising. With the exception of a hook, written about 35 years ago, by Peter Bitter von Tunner, an Honorary Member of this Institute, and of desultory articles on simple sections, which have appeared in technical journals, I know of no pub¬lication attempting to treat this subject, although volumes have been written on the scientific theory and technical manipulations involved in other branches of the iron- and steel-industry. This strange anomaly may be due to the fact that roll-turning cannot be called a scientific business. It does not ordinarily come within the range of an educated engineer; yet it cannot be performed by an ordinary mechanic. It demands some of the qualifications of an engineer, in designing, and those of a mechanic, in execution. The men who have followed this trade have controlled the training of their successors. In many cases the technical knowledge required bas been handed down from father to son, and there has been a motive of private interest to prevent its public dissemination. Moreover, the statement of the various principles involved in the process would require, besides manual experience, a degree of scientific knowledge which roll-turners do not usually possess; and, finally, any book on the subject, in order to possess real, practical value, would have to be so fully illustrated as to make it very costly to publish. Regarding my own experience, I may say that I served a six-

May 1, 1906

By Jay F. Smith

The Alan Wood BOF Shop consists of two 140 ton furnaces with a rated yearly capacity of 1-1/4 million ingot tons, he hot metal for the BOF Shop is supplied by two 18 foot blast furnaces which produce an average of 2000 tons per day, To achieve the rated ingot ton capacity with this limited supply of hot metal, the preheating of scrap is necessary. This is accomplished in the furnace by using an oxygen-natural gas burner. Piping Arrangement The natural gas and oxygen are piped into the Shop through 8-inch lines to their respective valving stations. As can be seen from Figure 1, the flow of natural gas passes through a flow control valve which is common to both furnaces, after which it divides into two 6-inch lines forming two identical and independent gas control lines, one for each furnace.

Jan 1, 1972

By Gilbert P. Moore

The production of petroleum in Argentina during 1932 was greater than in any preceding year. The total amount produced was 13,012,-756 bbl. This figure represents a decided increase in the production of oil in Argentina and can be attributed largely to the increased activities of the Royal Dutch operations at Kilometer 27 in the Comodoro Rivadavia district and those of the Standard Oil Co. of Argentina in the Salta region. Production from the Royal Dutch wells amounted to considerably more than 10,000 bbl. per day over quite a long period during the year. Of the 13,012,756 bbl. of oil produced during 1932, the Government Agency (Y. P. F.) was responsible for some 5,578,954 bbl., while 7,433,-802 bbl. were produced by private companies. Although in 1930 the Y. P. F. produced about 55 per cent of the total production and in 1930 50 per cent of the total, in 1932 its production had fallen to about 42 1/2 per cent of the total. This decrease in the proportion produced by the Y. P. F. was not due to a decrease in its production but to the decided increase in the production of private companies, particularly those two whose names are given above. One new discovery was recorded during the year. This was a well drilled by the Y. P. F. at Cacheuta in the province of Mendoza which came in pumping 80 bbl. of 15" gravity oil from a depth of 673 meters. This well was completed at approximately the same time that the provincial government of Mendoza granted a concession to the Y. P. F. and declared the whole province as a reserve in which no concessions may be granted for a period of 10 years. Under these conditions, the federally operated Y. P. F. will have no competition in the Cacheuta area from private companies such as they have in the other three fields of the republic. The Y. P. F. wildcat west of Comodoro Rivadavia at Pampa Maria Santissima on the Rio Senguerr was completed as a dry hole during 1932. This we11 was reported as a producer in 1930 by persons returning to this country from Argentina but it appears that they had been misinformed. The site of this test has been abandoned and a new location made north of the Rio Senguerr.

Jan 1, 1933

By Joseph Gurland

EVERAL carbide-cobalt compositions were pre-^-5 pared for the purpose of determining the transverse rupture strength of various carbide-binder systems. The binder content was held at 10 and 37 volume pct Co, so as to be representative of low and high bjnder compositions. The carbides used, WC, Tic, TaC, CbC, VC and ZrC, were selected on the basis of availability, knowledge of their properties, and small solid solubilities in the binder metal at room temperature. The methods of preparation and carbon analysis of the carbides are summarized in Table I. The carbides with cobalt added were ball milled, pressed, and sintered. vacuum sintering was used throughout, except for the WC-Cs alloys, which were sintered in hydrogen. The sintering temperatures ranged from 2500" to 2750°F for the low binder alloys and from 2300" to 2550°F for the high binder alloys. Compositions and properties of the sintered com- pacts are presented in Table 11. For the transverse rupture strength, the average and range of the five best samples of each alloy are listed. Discrepancies between the actual and theoretical densities are attributed to carbon deficiencies in some samples. The theoretical densities were calculated by assuming mixtures of carbides of stoichiometric compositions and cobalt. Representative microstructures are shown in Figs. 1 to 6. The porosity was A-2 or better' in all alloys except those with ZrC. A grain size of about 3 p was

Jan 1, 1958

By Kent R. Van Horn, W. P. Sykes

Since Honda and Murakamil in 1918 proposed their constitutional diagram of the carbon-free iron-tungsten system, considerable effort has been expended by several investigators in attempts to define more positively the structural features of the alloys. The existence of an intermediate phase corresponding to the formula Fe3W2 (68.7 per cent W) was proposed from evidence of a purely metallographic nature by one of the present authors2 in 1926. Since that time the identity of this phase has been confirmed by Arnfelt3 and by Takeda,4 both of whom employed X-ray methods as well as the microscope and the chemical analysis of isolated microconstituents. According to Arnfelt, Fe3W2, as crystallized from the iron-rich melts at a temperature above 1450° C., contains by analysis 68.7 per cent W. The lattice of this phase is characterized by trigonal symmetry. Arnfelt, moreover, proposed a second intermediate phase formed at some temperature between 1450" and 1000" C. by a peritectoid reaction involving Fe3W2 and the iron-rich solid solution. A melt containing 25 per cent W was cooled to 1000" C. and heated for 100 hr. The precipitated tungsten-rich constituent was separated and found by analysis to contain 62.6 per cent W. This composition agrees closely with that represented by the formula Fe2W (62.2 per cent W). Diffraction patterns from the concentrated precipitate showed a hexagonal unit cell. Takeda confirmed the data of Arnfelt regarding Fe3W2 but was unable to detect Arnfelt's second intermediate phase. While Takeda failed to describe in detail the treatments employed, he stated that in alloys containing 40 per cent W which were quenched after heating at various temperatures between 1200" and 1450" C. no evidence of the second phase (Fe2W) was observed 'either in the microstructure or in the diffraction patterns of isolated residues. He therefore considered the existence of this low-temperature hexagonal compound as disproved.

Jan 1, 1933

By T. H. Aldrich

THE Aldrich Mining Co. holds under lease from the Illinois Central R. R. Co. about 14,000 acres, in the East half of Township 12, Range 12 `V., in Marion county, Alabama, and owns other lands, of which about 1,000 acres adjoin this leased tract, making a total area of about 15,000 acres, all of which is underlain by the coal-seam upon which the company is operating. This seam is nearly horizontal ; and a ravine, diagonally crossing the tract, exposes the outcrop on either side for about 2 miles. The territory has been so divided that nearly the whole of it can be worked out by two collieries. The mines at Brilliant were opened in the Fall of 1898, and shipments began in the following spring. The original plan was to furnish steam-coal for locomotives to the Illinois Central R. R. Co.; and upon this expectation the investment of capital was made. The field was entirely new; and the softness of the coal at the outcrop induced the belief that it could be very cheaply mined. A contract for the delivery of a large quantity of coal to the railroad was accordingly executed. But with the advance of the entries to increasing distances from the outcrop, the coal proved so hard that it could no longer be drilled with a breast-auger; and the expense of mining became so great that the contract for cheap steam-coal had to be cancelled. It became evident that the work must be done with machinery and explosives, if it could be profitably done at all. On the other hand, the excellent quality of this coal opened, at the same time, a possible market not specially contemplated at the outset-namely, that of a first-rate coal for domestic and general uses. Since no other deposit of such coal was known to exist on the line of the Illinois Central, or any other railroad

Jul 1, 1906

Discussion of the paper of EDGAR L. NEWHOUSE, presented at the Salt Lake meeting, August, 1914, and printed in Bulletin: No. 92, August, 1914, pp. 1801 to. 1806. G. C. RIDDELL, East Helena, Mont.-As nearly as I can recall at the present moment, there are only four or five large plants on the continent where the lead on charge is carried in the neighborhood of 40 per cent. These are at Herculaneum, Collinsville, and Federal, Ill.; Trail, B.. C.; and East Helena, Mont. Our object at the latter point is to smelt a maximum amount of Coeur d'Alêne lead sulphides in as compact and self-fluxing a charge as possible, and to this end we are now smelting a mixture that at times carries up to 42 per cent. lead. The monotony of producing the 7,000 tons of bullion shipped each month to. the Omaha and Chicago refineries is relieved somewhat by the fact that the 15,000 tons monthly of Coeur d'Alêne ores that are com-ing to us carry enough zinc to provide the one-half slag used with from 6.5 to 7.5 per cent. zinc clay after day. During the month of March, 1914, three lead furnaces in continous operation, each 136 in. long, averaged 249 tons per furnace clay, exclusive of coke and slag shells, which is smelting at the rate of 5.5 tons per square foot of tuyère area. The

Jan 11, 1914

By C. Chu

An investigation has been made of the radial heat-wave process using a mathematical model in two-dimensional cylindrical coordinates. This model considers combustion, convection and conduction inside the reservoir, but only conduction in the bounding formations. From a study of the general features of the process, an important phenomenon has been revealed, namely, the feedback of heat into the reservoir on the trailing edge of the heat wave. The effects of various process variables on the performance characteristics of the process have also been investigated. It was found that up to the time when the combustion front reaches a given point, the per cent heat loss, provided it is not higher than 40 per cent, is approximately directly proportional to the square root of thermal conductivity arid fuel content, but inversely proportional to the square root of gas-injection rate and oxygen concentration. The effecr of reservoir thickness is more pronounced, since halving the thickness doubles the per cent heat loss. The most decisive factor in determining the center-plane peak temperature is the fuel content of the reservoir. Within the temperature range investigated, doubling the fuel content doubles the peak temperature in the early stage, but the rate of decline of the peak temperature is high. Reservoir thickness is also a very influential factor. The peak temperature is lowered when the thickness is reduced; however, the effect of thickness becomes less pronounced when the thickness is high. Reduction of oxygen concentration increases the peak temperature in the early stage but lowers it afterwards because of the higher rate of decline of the peak temperature. Increase in gas injection rate or decredse in thermal conductivity geives a higher peak temperature which stays high for a longer period. The propagation range of the heat wave is chiefly governed by the fuel content of the reservoir. An increase of 0.2 1b/cu ft in the fuel content increases the propagation range by 100 per cent. The propagation range is more than doubled by doubling the gas injection rate, or reservoir thickness, or by reducing the thermal conductivity by 50 per cent. Comparatively, oxygen concentration has less effect on the propagation range. INTRODUCTION Several investigators have conducted theoretical studies of a radial heat wave. Vogel and Krueger1 studied a system with a moving cylindrical heat source of constant temper- ature, considering conduction in the radial direction only. Ramey2 included conduction in the vertical direction in his studies. Bailey and Larkin2 attacked a more general problem where initial well heating, vertical heat losses and arbitrary frontal velocities were included. In all these studies, however, conduction was considered to be the only means of heat transfer. Bailey and Larkin in a later paper included the effects of convection in a study involving both linear and radial geometries. Vertical heat losses were neglected in the radial case. Katz5 studied a similar problem in a one-dimensional radial model, using a heat-loss coefficient to account for vertical heat losses. Selig and Couch6 mployed a cylindrical model and investigated two limiting cases. In one case they considered no heat loss from the reservoir whereas in the other they assumed a constant temperature at the interface between the reservoir and its bounding formations. Thomas' studied a more general case but assumed a permeable bounding formation so that the convection effect is not confined to the reservoir. In the present work a more realistic and more generalized model is used. It involves a two-dimensional cylindrical system with combustion, convection and conduction inside the reservoir, but only conduction in the bounding formations. The purpose is to establish the temperature distribution both inside and outside the reservoir, to study the general features of the radial heat wave process, and to investigate the effects of various process variables on the performance characteristics of the process. THEORY We fist consider a circular porous reservoir of thickness H extending vertically from y = — H/2 to y = + H/2. The reservoir extends from a well bore radius r, to an external radius re. A stream of oxygen-containing gas is introduced into the reservoir through the wellbore. The oxygen-containing gas reacts with the fuel contained in the reservoir and forms a combustion front wherever the prevailing temperature can support the combustion. It is here assumed that this combustion front constitutes a cylindrical surface source of heat having an infinitesimal thickness in the radial direction and extending vertically throughout the whole thickness H. This is designated as Region I. We next consider a Region II corresponding to the upper and lower formations bounding the reservoir, extending from y = — - to y = — H/2 and from y = + H/2 to y = + m. Since r, is very small, we may assume that the two bounding formations have the same dimensions, symmetric with respect to the center plane of the reservoir. In this way, we may take the upper half of the system alone into consideration. In contrast with