Ind. Eng. Chem. Res. 2004, 43, 4703-4708
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Model Analysis of Thermal Lance Combustion Haorong Wang and Vladimir Hlavacek* Department of Chemical Engineering, SUNY at Buffalo, 303 Furnas Hall, Buffalo, New York 14260
Pavol Pranda Department of Chemical and Biomolecular Engineering, University of Notre Dame, Notre Dame, Indiana 46556
The thermal lance process represents the oldest commercial use of oxygen cutting or piercing of massive objects (metallic materials and concrete). The thermal lance combustion model described in this paper has been developed on the basis of heat and mass transfer associated with iron (s)-oxygen (g) combustion reaction. The model includes metallic tube heat conduction and radiation, heat transfer by free convection to the external environment, and forced convection caused by the flowing gas in the lance body. The gas phase is described by a forced convection term and heat transfer from the metallic tube. The reaction term is included in boundary conditions. Experimental measurements have been carried out on an industrial size unit. A comparison with lance burning experimental data has been performed. The model shows lance temperature drops rapidly along the lance. The lance burning temperature has been predicted by the model, and the reaction kinetics of the iron combustion in oxygen has been discussed. Introduction The invention of the oxygen lance is based on an exothermic reaction occurring between iron, provided by the lance body, and gaseous oxygen supply.1 In this process, a piece of the lance rod (usually made of a low carbon steel tube with a hollow center) reacts with oxygen flowing through the metallic tube. The oxidation reaction generates a large amount of heat that is capable of melting/oxidizing the target. The excess gaseous oxygen blows off the molten target in the form of a slag. The process has always been regarded as a crude method of cutting and severing.2 Fast penetration and cutting of concrete and metal materials has many practical applications. The use of high-energy cutting devices for cutting very hard and reinforced structures spans both military and commercial applications. On the commercial side, a number of industries come into play. Among them are mining, heavy construction, plant maintenance, demolition, utilities, quarries, metal producing and casting, marine operations, metallurgy, and civil engineering. There is also an increasing effort to develop tools for fast release of victims in major disasters (earthquake, railway collisions, highway disasters, etc.). On the military side, there are military tactical cutting operations as well as amphibious special operations and maritime damage control operations. Additional governmental involvement includes police, fire/ rescue, shipboard damage control/rescue, and antiterrorist activity. Past research activity and inventions have been focused on improving the lance performance by optimizing the lance design3-5 or replacing the iron material with other metals such as aluminum or titanium to * To whom correspondence should be addressed. Tel: (716) 645-2911 ×2208. Fax: (716) 645-3822. E-mail: hlavacek@ acsu.buffalo.edu.
increase the lance-burning temperature.6,7 Although the technology has been developed and widely used since World War II, no theoretical studies of the lance-burning mechanism have been carried out. With similar lance design various authors have reported different lance burning tip temperatures, ranging from 20001 to ≈5500 °C8 without showing any experimental evidence. In this paper, on the basis of heat transport and reaction kinetics of the oxidation reaction, a mathematical model has been developed to simulate the process of lance burning. The model, using the Lagrangian coordinates, includes metallic tube heat conduction and radiation, heat transfer by free convection to the external environment, and forced convection caused by flowing gas in the lance body. We assume that the reaction occurs in a thin sheet and therefore the reaction term, along with thermal conduction of metallic and oxide layers, occurs only in the boundary conditions. The gas balance includes only a convection term and heat transfer from the hot lance wall. The kinetics of “ironoxygen” combustion reaction has been discussed by using our experimental data and the research results of Steinberg et al.9,10 The theoretical predictions, despite the model complexity, provide a reasonable agreement with the experimental observations. Experiment Setup and Measurement Procedures A sketch of the commercial thermal lance system is depicted in Figure 1. The principle of the commercial thermal lance cutting system is described as follows: oxygen gas comes from the high-pressure cylinder, flows through the oxygen hose, into the torch handle, and finally reaches the lance rod. The oxygen flow rate is controlled by both the cylinder regulator and the torch trigger. The lance rod is made of a low carbon steel tube with a multiplicity of low carbon steel wires inside. The ignition of the system can be produced electrically by touching the lance tip on the striker plate. The electrical
10.1021/ie030729r CCC: $27.50 © 2004 American Chemical Society Published on Web 04/14/2004
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Figure 3. One-dimensional sketch of thermal lance burning at steady state with constant velocity wFe. Figure 1. Commercial thermal cutting setup.
Figure 2. Flame produced by the thermal lance.
sparks are generated on the lance tip and an exothermic reaction between the iron material and flowing oxygen is initiated. By adjusting the oxygen flow a selfpropagating regime of the combustion can be achieved. The lance rod is represented by a low carbon steel tube (o.d. ) 0.375 in. (0.952 cm), wall thickness ) 0.028 in. (0.071 cm)) with 7 low carbon steel wires inside (o.d. ) 0.09 in. (0.229 cm)). The hollow area between the external tube and internal wires provides a passage for the oxygen gas to flow through the assembly (see Figure 1, upper right corner). With a proper oxygen flow rate, the temperature of the lance-burning tip may reach ≈1800 °C. We have measured this temperature by using a pyrometer positioned 6 ft. from the burning tip. Typically, the flame at the lance tip exhibits some flickering and therefore the receiver of the pyrometer unit could not be focused exactly on the burning tip. The surface temperature of the flame, owing to the strong radiation, is much lower than the temperature inside the flame. The maximum adiabatic temperature of the iron and oxygen system has been calculated by the Gordon and McBride code11 and is ≈3000 °C. Consequently, the iron-oxygen flame temperature is somewhere between 1800 and 3000 °C. The outlet pressure was set at 50 psi (≈345 kPa), and the oxygen flow rate was 282 L/min. The burning rate was calculated by measuring the burning time and the lance consumption length. Figure 2 shows the flame produced by the lance burning in the oxygen stream. The flame is represented by a burning spray of hightemperature iron and iron oxide particles. Model Assumptions In this section, a lance burning model will be developed. The underlying geometry is shown in Figure 3. The following simplified assumptions will be made. (1) The lance is a cylindrical hollow tube. The flame does not oscillate and we suppose a steady state operation.
The temperature changes only in axial direction; we do not assume any flame symmetry breaking associated with angular gradients. There is no radial temperature variation within the lance body. (2) The lance is burning at a constant speed, wFe. We use the Lagrangian coordinates and thus the flame is always kept at the coordinate x ) 0. In other words, we assume the lance is moving toward the combustion surface at a speed of wFe. (3) The iron-oxygen reaction is controlled by the surface reaction on the iron-iron oxide interface.9,10 The heat release due to the chemical reaction between metal and oxygen is confined to the interface and is transferred to the lance through the interface. (4) The oxide layer is very thin and the oxide leaves the layer at the burning temperature. Therefore, solid or liquid reaction products removed from the surface layer do not affect the burning process. Development of Governing Equations The governing differential energy equations for the one-dimensional steady state heat transfer of moving iron tube at the velocity wFe and oxygen flow inside the tube are given by the following for iron tube:
λFe
d2T dT - S1‚σ‚Fe‚(T4 - T04) - FFe‚CpFe‚wFe 2 dx dx S1‚hA‚(T - T0) - S2‚hO‚(T - T0) ) 0 (1)
The first term of the equation is the axial heat conduction in the tube, the second term represents heat convection caused by lance moving velocity wFe, the third term describes the radiation flux from the outer wall, and finally the fourth term takes care of natural heat convection from the tube toward the stagnant environment. The fifth term is the forced heat convection caused by oxygen flow inside the tube. Here λFe is the iron thermal conductivity, CpFe is the iron heat capacity, FFe is the iron density, Fe is the iron emissivity, and σ is the Stefan-Boltzmann radiation constant. The geometrical factors S1 and S2 are the ratios of effective outer and inner perimeters over the crosssection area, respectively. OD is the outer tube diameter and ID is the inner tube diameter:
S1 )
S2 )
OD OD 2 ID 2 2 2
( ) ( )
ID OD 2 ID 2 2 2
( ) ( )
(2)
(3)
hO is the heat transfer coefficient of forced convection caused by the oxygen flow inside the tube. The numer-
Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004 4705
ical value of this coefficient can be calculated by using the Dittus-Boelter correlation:12
NNu ) 0.0243NRe0.8NPr0.4(µOb/µOw)0.14
(4)
Here the Nusselt, Reynolds, and Prandtl numbers are defined as follows:
hO‚ID λO
(5)
ID‚wO‚FO µO
(6)
NNu ) NRe )
following:
CpO‚µO NPr ) λO
(7)
Here λO, FO, and µO are oxygen thermal conductivity, oxygen density, and oxygen viscosity, respectively; CpO is the oxygen heat capacity; and wO is the sum of the lance velocity and oxygen flow linear velocity. Because the oxygen velocity is much larger than the lance velocity, wO can be approximated as the oxygen velocity. The numerical values were calculated assuming oxygen as the ideal gas. Physical properties for oxygen gas at 3000 °C were extrapolated. The calculated value for hO is
hO ) 691.6 W/(m2 K) at oxygen flow of 282 L/min (8) The heat transfer coefficient of the natural convection for air, hA, was calculated from the Nusselt equation12
(
)
OD3‚FA2‚g‚βA‚∆T CpA‚µA hA‚OD ) a‚ ‚ λA λA µ 2 A
Figure 4. Sketch of the reaction boundary.
-λoxide
(9)
(10)
The energy balance for oxygen flow inside the lance body reads as follows:
dT + S2‚hO‚(T - TO) ) 0 -FO‚CpO‚wO dx
Here λoxide and Cpoxide are oxide thermal conductivity and oxide heat capacity, both per kilogram of iron, respectively. The symbol p is the reaction extend ratio because the iron material, detached from the burning tip, may not totally react with oxygen. In our development of governing equations we do not consider the effect of evaporation of iron. In a comprehensive study by Steinberg9 on iron combustion in oxygen atmosphere it is assumed that combustion occurs on the solid phase and that the reaction is of the type “solid-gas”. In his work the mass of initial iron and the iron in the slag balanced well and thus there is no reason to consider an iron evaporation term. At the outer oxide surface (see Figure 4)
m
Here λA is the air thermal conductivity, CpA is the air heat capacity, FA is the air density, µA is the air viscosity, βA is the air volume expansion coefficient (assuming the air is the ideal gas, βA ) 1/T). The wall temperature, T, varies from 300 to 3000 K. We used T ) 3000 K to calculate the heat transfer coefficient at the burning area. The symbol g represents gravity which equals 9.8 m/s2, ∆T is the temperature difference of the bulk and the conducting wall, which is ∼2700 K, and a and m are constants (a ) 1.09 and m )1/5).12 The calculated value of hA is
hA ) 32.45 W/(m2 K)
dT dT - λFe + λoxide + (CpFe - Cpoxide)FFe‚wFe‚T + dx dx ∆H‚wFe‚FFe‚p ) 0 (12)
(11)
Here CpO is the oxygen heat capacity, wO is the sum of the lance and oxygen flow linear velocities, and FO is the oxygen density. Because the oxygen velocity is much larger than the lance velocity, lance velocity is ignored. Heat conduction along the x-direction is ignored because of high oxygen flow rate. The boundary conditions are shown in Figure 4. At the surface of iron oxide (see Figure 4) we can write the
dT ) σ‚oxide(T4 - T04) dx
(13)
Here oxide is the oxide emissivity. Assuming a very thin oxide layer, the temperature difference may be considered constant across the oxide layer. Therefore, eq 13 can be combined with eq 12 to formulate an approximate boundary condition at the metal-oxide reaction surface:
at x ) 0 -λFe
dT - σ‚oxide‚(T4 - T04) + ∆H‚wFe‚FFe‚p + dx (CpFe - Cpoxide)FFe‚wFe‚T ) 0 (14)
Here ∆H is the reaction heat for the iron-oxygen reaction. We considered the reaction of iron combustion to follow
Fe + 1/2O2 ) FeO
(15)
According to the literature data the combustion process of iron is controlled by the reaction occurring on the liquid iron oxide/liquid iron (FeO(l)/Fe(l)) interface.9,10,13 It was also reported in the literature that the formation of FeO is the major reaction that takes place in the iron cutting process.14 The XRD analysis of the quenched burning slag indicates no iron was left in the slag (Figure 5). Therefore, we used p ) 1 (p is the ratio of the reacted iron to the total iron removed from the burning tip). Other iron oxides such as Fe2O3 and Fe3O4 were found
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Figure 5. XRD analysis of the quenched lance slag.
in the slag. Their existence can be explained by further oxidation of FeO with adsorbed oxygen during the afterburning process. At the liquid-solid interface of the iron tube, x ) xm, there is a phase transition effect. The effect changes the temperature gradient on the left side of the interface as follows:
〈 〉
〈 〉
∂T ∂T ) + Hlat‚wFe‚FFe/λFe ∂x right ∂x left T ) Tm at x ) xm (16)
At the other end of the lance (x ) -∞), there is no heat conduction and the temperature equals the surroundings temperature, T0
∂T f 0 T ) T0 ∂x
at x f -∞
(17)
Numeric Integration and Results. The set of governing equations along with the boundary conditions represent a nonlinear boundary value problem for ordinary differential equations. Several numerical methods can be used to solve this problem; we decided to use the shooting algorithm. It is well-known that the shooting algorithm may suffer from strong parametric sensitivity if integrated from the hot to the cold end. Therefore we integrated the problem from x ) -∞ toward x ) 0. Replacing T with y1, dT/dx with y2, and T0 with y3, the governing eqs 1 and 11 may be rewritten as follows:
dy1/dx ) y2
λFe ) λFe(T)
(21)
CpFe ) CpFe(T)
(22)
FFe is constant because it changes little in the temperature range considered. For numerical integration the Runge-Kutta method was used.
At x ) -∞: y1 ) y3 ) 300K (T0) y2 ) 0
(23)
At x ) xm y1 ) 1811K (Tm)
(24)
Here xm is the position of the liquid-solid interface; xm, y2(xm), and y3(xm) can be calculated by integration by using the values given by eqs 21 and 22. Liquid Part of the Iron Tube. Assuming the liquidsolid interface (at xm) has no thickness, and applying the boundary condition (eq 16) at xm
〈y2〉right ) 〈y2〉left + Hlat‚wFe‚FFe/λFe
(25)
Integrating governing eqs 18, 19, and 20 from initial values y1 ) Tm, y2 ) y2right, y3 ) y3left (values from solid part integration) to a point x0, at which y2 equals the dT/dx calculated from boundary condition (eq 14)
(18)
dy2 ) [F‚CpFe‚wFe‚y2 + S1‚σ‚‚(y14 - T04) + dx S1‚hA‚(y1 - T0) + S2‚hO‚(y1 - y3)]/[λ] (19) dy3 S2‚hO‚(y1 - y3) ) dx FO‚CpO‚wO
Solid Part of the Iron Tube. The values of λFe and CpFe, have been considered as unctions of temperature:
(20)
dT ) [-σ‚oxide‚(T4 - T04) + ∆H‚wFe‚FFe‚p + dx (CpFe - Cpoxide)FFe‚wFe‚T]/[λFe] (26) The temperature profile has all properties of the combustion front; a flat portion is followed by an extremely sharp reaction front that is very thin. There-
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fore, the values of λFe and CpFe are considered constant and are estimated at average temperature values in the front. After the integration, we consider x0 as the burning tip, y1(x0) as the burning temperature (Tb) at steady state and y1(x0) as the temperature of the oxygen gas on the tip. The axial temperature profile obtained via numerical simulation is drawn in Figure 6. The figure shows that the temperature drops quickly from quasi-adiabatic value down to almost room temperature at a short distance (∼1 cm). To verify this profile experimentally a thermocouple was placed in the middle part of the lance. Afterward the lance was ignited and the temperature reading did not change once the flame was far from the thermocouple. Once the flame was at x ) 1 cm a discontinuous jump of temperature was recorded. The experiment confirmed the numeric simulation result. This feature enables the possibility to modify the lance by using a nonmelting and nonreacting layer on the lance surface to focus the lance flame. The layer does not detach from the lance during lance burning. The sharp temperature drop near the tip of the burning lance prevents the further destruction of adhesives. A more efficient thermal lance, Sharp-Fire(O), was developed using this idea.15 The numerical integration resulted in the value of lance tip burning temperature Tb, Tb ) 3062 K for p ) 1. This temperature is close to the adiabatic temperature Tad. ) 3325 K. The calculated temperature of oxygen gas at the burning tip is only 307.8 K. Mechanism of Lance Combustion. Substantial work has been published on the kinetics of low-temperature iron oxidation.16,17 In the recent work done by Wilson et al.13 they provided a Langmuir-Hinshelwood-Hougen-Watson reaction model by adapting the phase boundary mechanism of low-temperature oxidation process to describe the burning of iron rods. Considering a Langmuir-Hinshelwood-HougenWatson reaction mechanism, the solid reaction is controlled by two steps: oxygen adsorption on the oxide layer (a) and iron-oxygen reaction in the iron-oxide interface (b). kd
(a) O2 + 2 sites {\ } 2O(chem.ads.) k -d
K)
(27)
kd [O(chem.ads.)]2 ) k-d P ‚(N - [O(chem.ads)])2 O S k
(b) O(chem.ads.) + Fe 98 FeO
(28)
where kd, k-d, and k are the rate constants, K is the equilibrium constant, PO is the oxygen pressure, and NS is the number of sites per unit area. Considering that the rate-controlling step is the reaction of iron with chemisorbed oxygen, the reaction rate equation is given as13
RFe )
kKdP1/2 O 1 + KdP1/2 O
(29)
Here, k is the reaction rate constant usually represented as the Arrhenius function and Kd is the adsorption/ desorption equilibrium constant. Kd ) xK/Ns, and is usually small at high temperature. The numeric expres-
Figure 6. Calculated axial temperature profile.
sion of the equation for small Kd at low oxygen pressure was found as13
RFe ) 7.05 × 103 exp(-2.9684 × -2 -1 -1/2 (30) 104/T)P1/2 O2 ‚gm‚cm ‚s ‚MPa
The reaction rate for a 0.2-cm diameter iron rod was given as13
k′ ) 2.087 gFe‚cm2‚s-1‚MPa-0.5
(31)
Applying eq 31 at 1atm and considering an equivalent hemisphere surface as a reaction surface, the wire burning velocity is given as follows:
w′ ) k′‚
( )
4π‚r2 ‚(0.101 MPa)0.5/(FFe‚π‚r2) ) 2 2k′‚(0.101 MPa)0.5/FFe ) 0.17 cm/s (32)
Here r is the radius of the 0.2-cm diameter rod. The calculated burning speed fairly agrees with the experiment data provided by Kirschfeld,18 w′ ) 0.1641 cm/s. Considering eq 32, the burning speed does not depend on the wire diameter. As shown by Kirschfeld’s work,18 the burning speed decreased with increasing diameter and became constant when the wire diameter increased to about 2 mm. Therefore, w′ may consider this as an asymptotic value for the lance combustion velocity. However, we must recognize the fact that Kirchfeld’s work was performed under a stagnant oxygen flow; the iron lance works at the large oxygen flow. Our experiments revealed that at a flow rate of approximately 40 L/min. the lance extinguished so that a direct comparison at identical conditions is not possible. Our experiment indicates that the lance-burning speed average is 7.65 × 10-3 m‚s-1. The domain of observed speeds is in the region of 7 × 10-3m‚s-1 to 8 × 10-3m‚s-1 and does not depend strongly on the flow rate. Our experimental value of speed of lance combustion is ≈4.5 times larger than the value measured by Kirchfeld for stagnant conditions. This disparity may be explained by the fact that the high oxygen flow substantially decreased the oxide film thickness in the case of lance burning. Conclusions This paper represents a first attempt in the literature to describe in quantitative terms the combustion of
4708 Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004
metallic tubes in oxygen. A mathematical model of thermal lance burning has been developed. We have analyzed the combustion process for the case of iron combustion; combustion of other metals may feature additional characteristics. For example, combustion of aluminum is a highly unstable process and evaporation terms and transient model must be considered. In our experiments with iron combustion we have never observed unstable combustion. The model proposed describes the axial temperature profile of the burning lance. The temperature profile indicates that the lance temperature drops rapidly from the burning tip toward the unreacted part of the lance body. The lance burning temperature calculated by the model is ∼3060 K. The model also predicts ignition-extinction phenomena. The agreement between calculation and experimental values reveals that all major characteristic terms describing the combustion of iron tube in oxygen have been selected properly. The model analysis provides some lance modifications leading to improvements of the cutting process. On the basis of the model the commercial lance was modified and two different versions were developed. The full description of the modified lances has been published elsewhere.15,19 Acknowledgment UB Foundation of SUNY at Buffalo acknowledges the financial support and material assistance from Ceramic and Materials Processing, Inc. Nomenclature A ) Preexponential constant of reaction rate of Fe + O reaction CpO ) Specific heat at constant pressure for oxygen CpA ) Specific heat at constant pressure for air CpFe ) Specific heat of iron [J/(kg‚K)] Cpoxide ) Specific heat of oxide [J/(kg‚K)] D ) Diameter [m] (i.d. is inner diameter, o.d. is outer diameter) g ) Gravitational constant [m/s2] Hlat ) Latent heat of iron melting [kJ/kg] ∆H ) Reaction heat of combustion of Fe to FeO [kJ/kg] hA ) Heat transfer coefficient for natural convection [J/(m2‚ s‚K)] hO ) Heat transfer coefficient for forced convection [J/(m2‚ s‚K)] k ) Reaction rate constant K, Kd ) Equilibrium constants PO ) Oxygen pressure [MPa] p ) Reaction conversion ratio, dimensionless RFe ) Reaction rate of iron combustion [kg/(s m2)] S1,S2 ) Ratios of effective perimeter over cross section area [m-1] T ) Temperature [K] T0 ) environment temperature [K] Tm ) melting point of iron [K] Tb ) lance burning temperature [K] TO ) oxygen flow temperature [K] w ) Velocity [m/s] wFe ) Lance burning velocity [m/s] wO ) Oxygen moving velocity [m/s] w′ ) Burning rate [m/s] x ) Cartesian coordinate xm ) Solid-liquid interface position [m] βA ) Volume expansion coefficient of air [K-1]
) Emissivity, dimensionless Fe ) Emissivity for iron, dimensionless oxide ) Emissivity for iron oxide, dimensionless λ ) Thermal conductivity [W/m/s] λFe ) Thermal conductivity for iron [W/m/s] λoxide ) Thermal conductivity for oxide [W/m/s] λO ) Thermal conductivity for oxygen [W/m/s] λA ) Thermal conductivity for air [W/m/s] µ ) Viscosity [Pa‚s] µO ) Viscosity for oxygen [Pa‚s] µA ) Viscosity for air [Pa‚s] F ) Density [kg/m3] FFe ) Density of iron [kg/m3] FO ) Density of oxygen [kg/m3] FA ) Density of air [kg/m3] σ ) Stefan-Boltzmann radiation constant [kg‚s-3‚K-4]
Literature Cited (1) Brandenburger, E. New Oxygen Wire Core Lances. Met. Constr. 1975, 617. (2) Slottman, G. V.; Roper, E. H. Oxygen Cutting; McGrawHill: New York, 1951 (3) Paaso, C.; Cariello, B.; Palumbo, A. Cutting Electrode for Underwater and Land Use. U.S. Patent 5,043,552, 1991. (4) Moor, P. E. Exothermic Cutting Electrode. U.S. Patent 4,391,209, 1983. (5) Henderson, H. R.; Mosinski, D. Exothermic Cutting Electrode. U.S. Patent 4,697,791, 1987. (6) Brower, J. S. Underwater Cutting Rod. U.S. Patent 4,069,407, 1978. (7) Brower, J. S. Underwater Cutting Rod. U.S. Patent 4,182,947, 1980. (8) BROCO Inc. “Prime Cut”; http://www.brocoinc.com/primecut/ index.html. Accessed April 21, 2003. (9) Steinberg, T. A.; Mulholland, G. P.; Wilson, D. B. The Combustion of Iron in High-pressure Oxygen. Combust. Flame 1992, 89, 221-228. (10) Steinberg, T. A.; Kurtz, J.; Wilson, D. B. The Solubility of Oxygen in Liquid Iron Oxide During the Combustion of Iron Rods in High-pressure Oxygen. Combust. Flame 1998, 113, 27-37. (11) Gordon, S.; McBride, B. J. Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications. NASA Reference Publication 1311; National Technical Information Service: Springfield, VA, 1996. (12) Knudsen, J. G.; et al. Heat and Mass Transfer. In Perry’s Chemical Engineer’s Handbook on CD-ROM; Perry, R. H., Green, D. W., Eds; McGraw-Hill: New York, 1999. (13) Wilson, D. B.; Steinberg, T. A.; Stoltzfus, J. M. Thermodynamics and Kinetics of Burning Iron. In Flammability and Sensitivity of Materials in Oxygen-Enriched Atmospheres; Royals, W. T., Chou, T. C., Steinberg, T. A., Eds; American Society for Testing and Materials: West Conshohocken, PA, 1997. (14) Hsu, M. J.; Molian, P. A. Thermochemical modeling in CO2 laser cutting of carbon steel. J. Mater. Sci. 1994, 29 (21), 56075611. (15) Hlavacek, V.; Pranda, P. High-speed Chemical Drill. U.S. Patent Application, 2001. (16) Kubaschewski, O.; Hopkins, B. E. Oxidation of Metals and Alloys; Butterworth: London, 1962. (17) Kofstad, P. High-Temperature Oxidation of Metals; Wiley: New York, 1966. (18) Kirschfeld, L. The Combustibility of Metals in Oxygen. I. The Combustion Rate of Iron Wires in Quiescent Oxygen. Angew. Chem. 1959, 71, 663-667. (19) Hlavacek V.; Pranda P.; Wang H. Continuous Hot Rod. U.S. Patent pending, 2003.
Received for review September 16, 2003 Revised manuscript received February 5, 2004 Accepted February 10, 2004 IE030729R
