1 PROCESS MODELING AND SIMULATION OF AN ELECTRIC ARC FURNACE FOR COMPREHENSIVE CALCULATION OF ENERGY AND MASS TRANSFERS IN COMBINATION WITH A MODEL… [628545]

1 PROCESS MODELING AND SIMULATION OF AN ELECTRIC ARC
FURNACE FOR COMPREHENSIVE CALCULATION OF ENERGY AND
MASS TRANSFERS IN COMBINATION WITH A MODEL OF THE
DEDUSTING SYSTEM

T. Meier – RWTH Aachen University, Germany
A. Hassannia Kolagar, T. Echterhof, H. Pfeifer – RWTH Aachen University, Germany

The electric steelmaking through the electric arc furnace (EAF) is the second most important steel production
route in the world and the main process route for steel scrap recycling. As energy intensive process, the EAF
is in the focus of energetic optimization. Process models and simulations are able to contribute to a detailed
understanding of energy and mass transfers during the melting process and can be applied to investigate
new control strategies, waste heat recovery potentials or to assist the operator. Especially the EAF off-gas
offers development opportunities, due to its energy output of approximately 20 – 30 % of the entire energy
input and the possibility of process control through off-gas measurements. Th e following paper presents the
further development of a comprehensive process simulation model of an EAF, with fundamental
thermodynamic and physical equations in combination with a calculation model of the dedusting system.
Further chemical components wer e added and the gas radiation implemented to improve the gas phase
calculation. The results obtained from the EAF process model are utilized for subsequent computations in
the dedusting system model e.g. to predict waste heat recovery potentials, the load of the cooling system or
to analyze the post combustion process. The deterministic implementation of both models allows a fast and
easy adaptability to various EAFs and detailed investigation of energy distribution and mass transfers inside
the EAF . In future, the model can be applied for research on EAF designs and control strategies.

KEYWORDS: ELECTRIC ARC FURNACE – EAF – PROCESS MODELING – PROCESS SIMULATION –
DEDUSTING SYSTEM – GAS PHASE MODELING – OFF-GAS ENERGY

INTRODUCTION
The EAF off-gas with its energy output of up to 30 % of the total energy input is in focus of current and future
developments to further increase the energy and resource efficiency of the melting process in EAFs [1-4].
Here, waste heat recovery systems through steam generation and enhanced process control through off-gas
measurements are able to contribute to the optimization of the EAF process performance and to remain
competitive in times of rising energy costs and stricter environmental regulations. Comprehensive process
simulations of the melting process and the off-gas treatment system are capable to enhance the control of
the EAF and to deliver useful information for a better understanding of energy and mass transfers. EAF
process modeling and simulation has recently greatly expanded due to its diverse application possibility and
increased computational capacity. Several numerical models [5-13] were developed in order to improve the
melting pro cess or to enhance process control through soft sensing or to support the shop automation with
only limited consideration of the exhaust system.

A comprehensive, fast and easy adaptable model of the dedusting system is able to contribute to an
optimization of EAF control strategies, to reduce the energy output from the EAF and to improve waste heat
recovery when installed . Those capabilities are boosted when such a model is combined with an EAF
process simulation model with detailed gas phase simulation. The following paper presents such an
integrated application of an EAF process model with a modular calculation model of the dedusting system.
The presented EAF process model is further developed regarding the gas phase modeling. The described
model of the dedusting system is then used for subsequent off-gas calculations. Here, the post-combustion
process and the heat transfer to the cooling in a water cooled duct are simulated for two calculation cases:
an assumed controlled false air intake at the slip gap in contrast to an excessive false air intake. Hence, the
differences for the load of the cooling or higher steam generation possibilities are apparent.

2 1. EAF PROCESS MODEL ING

1.1. EAF MODEL DESCRIPTION
The EAF process model used for the presented resear ch is based on the model described by Logar , Dovžan
and Škrjanc , 2012 [8, 9, 14] . The deterministic model was developed in accordance with fundamental
physical laws, linked via first order differential equations, to be easy and fast adaptable to various EAFs. The
schematic overview about the structure of the process simulation model is given by Fig. 1 . The main thermal,
chemical and mass transfer phenomena occurring during the melting process are included, e.g. chemical
reactions, melting rates, energy distribution and heat transfer through radiation, conduction and convection.

Fig. 1 – EAF process simulation model structure

Fig. 2 – Zones and phases of the EAF process simulation model
Within the simulation model and especially in the thermal and mass calculation module, the EAF is divided in
eight different zones and phases which are shown in Fig. 2. Each zone and phase is assumed to have a
homogeneous temperature and uniform physical properties. All relevant physical processes appearing
during the melting, e.g. thermal, chemical and mass transfer between these zones and phases are
considered in the according calculation modules. The offline simulation is performed within the software Data
moduleEnergy
distribution
module
Chemical
reaction
module
Input
mass
calculation
moduleThermal
and
mass
calculation
moduleSimulation
resultsEAF Model
Melting
geometry˜
1) Roof
2) Walls
3) Solid scrap
4) Liquid melt5) Solid slag
6) Liquid slag
7) Electrodes
8) Gas phase
2
1
2
38
5
67
41
2
3
4
5
6
7
8

3 MATLAB R2015a from MATHWORKS with a multi-step BDF/NDF solver with a variable step size to receive
fast and accurate results [15].

1.2. FURTHER DEVELOPMENT OF OFF-GAS MODELING
The ga
s phase originally consisted of the four gas components carbon monoxide (CO), carbon dioxide (CO 2),
oxygen (O 2) and nitrogen (N 2) and was implemented according to the EAF model from Bekker, Craig and
Pistorius, 1999 [5]. As water (H 2O) and hydrogen (H 2) can reach significant proportions of the off- gas, these
components need to be considered in the EAF process model for a later detailed modeling of the dedusting
system. Both components as well as natural gas in form of methane ( CH 4) are added to the process model
and included in the calculation of chemical reactions, heat transfer through gas radiation and mass transfer.
The rate of mass change due to extraction through off-gas removal and blow out through gaps and openings
is implemented according to already implemented gas components. The mass changes are defined the
same way as proposed by Bekker [5] and Logar [9] as well as the determination of the rate of change of the
relative pressure and energy distribution due to chemical reactions.

The sources of the chemical elements are the CH 4 injection and its combustion, the combustion of
hydrocarbons and the electrode cooling through water spray cooling . The modeling of the latter is realized
through the implementation of the electrode as an additional zone in the EAF model and its integration into
the heat transfer calculation module. Unless the spray water is not evaporated outside the EAF, it enters the
furnace vessel and takes part in further chemical reactions. In addition to combustion reactions, t he
implemented chemical reactions in the gas phase simulation are given by the following Equation (1) to (8).

Dominant overall reaction mechanisms are implemented via simple reaction kinetics calculation according to
Equation (9) and (10) to determine the rates of mass changes, while the rate of mass change for the
reversible equilibrium reactions (2) to (4) are calculated according to the forward and backward reaction
rates with Equation (11) [16, 17]. Here, C i describes the concentration of the component i = A, B, C, D and k
is the temperature dependent reaction rate constant.

  aA bB cC dD
(9)
    …ab
AB r k C C
(10)
    

11iill
f i b i
iir k C k C
(11)

The implemented equilibrium reactions are the heterogeneous and homogeneous water-gas reaction and
the Boudouard reaction. It is assumed, that these three chemical equilibrium reactions are dominant, due to
the amounts of carbon which are present inside the EAF. The reaction rate constants are implemented
temperature dependent and are calculated according to the Gibbs energy minimization.

The main heat transfer in the EAF takes place by thermal radiation due to the present temperature levels. By
enhancing the gas phase with water as a further element, the emissivity of the steam, carbon monoxide and
2 22C O CO (1)
22 C CO CO
(2)
22 C H O CO H  
(3)
2 2 2 CO H O CO H  
(4)
22 22CO O CO
(5)
4 2 2 2 3 2 4CH O CO H O  
(6)
2 2 222H O H O
(7)
2 2 2 22H O H O
(8)

4 methane are no longer negligible. The heat radiation of the gas is therefore implemented into the calculation
module of heat radiation . Emissivity and absorptivity of the gas components H 2O and CO are calculated
dependent on the actual composition and the gas temperature with a constant equal layer thickness.
Equation ( 12) shows the calculation of the irradiation [18]. Here, t  and  are the transmission and the
emission coefficients and  is the Stefan Boltzmann constant. The radiosity J and the radiative heat flow Q̇
for each surface are calculated with Equation ( 13) and (14) where E is the emission of each surface and
Egas the emission of the gas phase. The view factors VF are calculated for all surfaces inside the EAF and
the electrodes are implemented as an additional phase into the model.

4
1[]n
k j gas k j
jG t J T VF (12)
 
   
1(1 ) (1 )n
k k k gas k j k j
jJ E E t J VF (13)
 









Q AJG (14)

2. EAF DEDUSTING SYSTEM MODELING
2.1. DEDUSTING SYSTEM MODEL DESCRIPTION
The off -gas from the EAF is removed via the dedusting system and mixed with leak air from the slip gap
between the EAF elbow and the hot gas duct. Despite of the significant environmental and energy issues,
limited research has been carried out on the modeling of the EAF dedusting system. Within this
comprehensive modeling, the model presented by Kirschen [19] and Velikorodov [20] is further developed
according to the comprehensive dedusting model described by Hofer [21]. The heat transfer in dedusting
systems was mathematically investigated and compared to off -gas measurements by Kir schen. Velikorodov
implemented the mathematical correlations in a dedusting system calculation model in order to better
understand the post combustion process and heat transfer and validated the model through measurements.

Fig. 3 – Schematic structure of the EAF dedusting system model
Fig. 3 schematically shows the modular set up of the dedusting system model. Dependent on the system to
be simulated, the arrangement can be adapted conveniently. This component -wise implementation allows
highest flexibility and fast adaptability. The dedusting system arrangement used for the following study
consists of a water cooled duct, a mixing chamber and a post combustion chamber. Here, the gas transport, Finger
shaft
PC
chamber
Water
cooled duct
EAF
Air
injection
Water
injection
Uncooled
duct
Mixing
chamber
Filter
Fan
Uncooled
duct
Input data from EAF process
model or measurementsImplemented
modulesFuture
implementations

5 adiabatic mixing with false air, heat transfer to the cooling and the post -combustion of CO, H 2 and CH 4 is
simulated.

2.2. WATER COOLED DUCT WITH POST -COMBUSTION
The modeling of the water cooled duct with post combustion, as one of the main parts of the dedusting
system, is based on the laws of conservation of mass and energy described by Equation ( 15) and (16). Here,
m ̇in and m ̇out are the input and output mass flow rate s of the off- gas, Ḣin and Ḣout are the input and output
enthalpy flows and Q̇ describes the total heat flow to the cooling. Further boundary condition s are determined
according to the geometry of the dedusting system and the cooling speci fication s.

 
 
in outdmmmdt (15)
 
 
in outdHHH Qdt (16)

The schematic overview about the modeling structure and the basic functioning of the water cooled duct
simulation module is shown by Fig. 4. The module calculates the gas temperature, the heat transfer and the
thermodynamic properties as illustrated in an iterative way.

Fig. 4 – Simulation s tructure of the wate r cooled duct module
The heat transfer between the off -gas and the cooling medium of the duct is determined with Equation ( 17)
to Equation ( 19). The heat flow Q̇ is calcul ated through the heat transfer coefficient K, the heat exchange
surface A and the logarithmic temperature ∆Tlog. Here, Tg and Tw are the gas and the water temperature
respectively and ∆Tin and ∆Tout denote the temperature difference between the gas and the water at the
input (in) and output (out) of the duct respectively [22].
As the overall heat exchange consists of several transfer phenomena, Equation ( 20) connects the
conductivities of the duct layers and the heat transfer coefficients from the gas through the duct to the
cooling medium. Here, D is the off- gas duct diameter, α
g and αw the gas side and cooling side heat transfer

6 coefficient s and φg and φw denote the gas side and the water side fouling factor . The heat conductivity of
the refractory and the steel are λz and λm and Sz and Sm are the corresponding layer thicknesses [22].

  
  
log Q KA T (17)
 gw TT T (18)
 
log
lnin out
in
outTTTT
T
(19)
       1
2 22 11ln ln ( )2 2 2 22z zm
gw
g z m z w zmKDS DS S DD D
D DS DS S
(20)
  1, ,2
g g kon g radf (21)

While the thicknesses and heat conductivities are assumed to be invariant, the total gas side heat transfer coeff icient is calculated with Equation ( 21) as a combination of convection α
g,kon and thermal radiation αg,rad,
taking into account a possible reduction factor of the active heat exchange surface f1. The conve ctive part is
mostly dominated by the volume flow rate, while the temperature, composition and dust load of the gas are
the most important influencing factors for the radiative heat transfer [21]. For the water side heat transfer
coefficient in the pipe , the coiled tubing approach is applied. In this approach, the second vortex flow caused
by the f low passed through the curvature of the tube, improve the heat transfer between the fluid and pipe
wall and also increases the pressure loss [22]. The off -gas is post-combust ed with the fal se air , entering the system at the slip gap. The chemical reactions
from Equation (4) , (7) and (22) are considered for the post-combustion process and the oxygen deficiency
coefficient and post-combustion efficiency coefficient are implemented into the model.

42 2222 CH O CO H O (22)
The concept of a post -combustion length calculation with two linear temperature profile s over the post
combustion length is assumed for the progress of the post -combustion. The temperature profile s enable fast
iterative calculation of the heat transfer. The necessary false air intake at the slip gap for the post –
combus tion influences the combustion process significantly and is determined through an approximation,
due to the complex flow conditions. One practical way is the application of the Bernoulli's equation [21] and
another one is the calculation according to a nitrogen balance [20] . The following results are achieved by the
assumption of an excessive a nd uncontrolled false air intake of four times the off-gas volume flow rate . This
case is roughly chosen according to current EAF and dedusting system operation as measurements from
Velikorodov are illustrating [20].

3. RESULTS AND DISCUSSION
This section illustrates the gas phase simulation results of the EAF process model and the dedusting system
calculation model. The process simulation was performed with measured input data from an industrial scale
EAF with an approximate tapping weight of 140 t, which are charged into the furnace via two scrap baskets.
The EAF off-gas simulation results for the temperature , composition and mass flow are used for further
calculation in the dedusting system model. There , a water cooled duct with CO, H
2 and CH 4 post-combustion
is simulated. The assumed duct has a diameter of 3.6 m and a length of 20 m.

3.1. EAF PROCESS SIMULATION
Relevant results from the EAF process model for further calculations in the dedusting system model are the
off-gas temperature, the volume flow rate at standard temperature and pressure (STP) and the off -gas

7 composition. Fig. 5 shows the simulation results for the off-gas temperature in comparison to the measured
data and the simulated off-gas composition while the comparisons of the simulated and measured mole
fractions of CO and H 2 in the off-gas a re illustrated in Fig. 6 .

Fig. 5 – Simulated and measured EAF off-gas temperature (left) and simulated composition (right) for a single heat

Fig. 6 – Com
parison of simulated and measured EAF off-gas composition for CO (left) and H 2 (right) for a single heat
The charging of the scrap baskets is visible at 8 00 s simulated process time, where the new starting
temperature of the gas is set to 500 K . The differences between measured and simulated values are at
maximum approximately 200 K while the shape of the curves is already similar. Here, the differences
between the simulation of a homogeneous gas phase and the measurement at the fourth hole of the furnace,
where post combustion effects are increasing the temperature locally, have to be considered while
0200400600800100012001400160018002000
0 1000 2000 3000Temperature [ C]
Time [s]T_gas_meas.
T_gas
0,00,10,20,30,40,50,60,70,80,91,0
0 1000 2000 3000Composition [mol-fraction]
Time [s]X_CO X_H2
X_CH4 X_CO21.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0,00,10,20,30,40,50,60,70,80,91,0
0 1000 2000 3000Composition [mol-fraction]
Time [s]X_CO_sim.
X_CO_meas.1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0,00,10,20,30,40,50,60,70,80,91,0
0 1000 2000 3000Composition [mol-fraction]
Time [s]X_H2_sim.
X_H2_meas.1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0

8 comparing the results. The simulated off-gas composition gives an overview about the main off-gas
components during the process simulation. The remaining off-gas components O 2, N2 and H2O are left out
as O 2 and H 2O are reaching mole fractions between 0.00 a nd 0.05 and N 2 forms the remaining fraction to a
sum of o ne.

At the beginning of the melting process of each scrap basket, H 2 mole fractions of more than 30 % are visible.
The injection of natural gas through gas burners as additional chemical energy input leads to the formation of
H2O, which takes part in further reaction mechanisms like water gas shift reaction and thus leading to an
increase of H 2. Furthermore, combustible materials like oil, plastics and paint are charged into the furnace
and are leading to an increased presen ce of H 2 in the off-gas. Another product from the heterogeneous
water gas reaction is CO. Together with injected carbon and charged coal and the incomplete oxidation o f
those, the mole fraction of CO in the off-gas reaches values up to 70 %. The simulated results of b oth
components of the gas phase are showing good results compared to the measured data. The shape of the
curves is similar and the magnitude is in the same range.

3.2. DEDUSTING SYSTEM CALCULATION
The ac
hieved off-gas results from the EAF process simulation are further used in the dedusting system
calculation model to determine off-gas temperatures and the heat flow to the cooling media for two different
false air intakes at the slip gap. The achieved results for the temperature at the end of the cooled duct and
heat flow are shown in Fig. 7 . The blue line shows the results for a false air intake of two times the off-gas
volume flow rate (LAx2), presenting a controlled post combustion, and the green curve for a false air intake
of four times the off-gas volume flow rate (LAx4), presenting current post combustion with an excessive ai r
ingress.

Fig. 7 – Output Temperature (Out) at the end of the cooled duct (left) and heat flow to the cooling medium (right)
After charging each scrap basket, the temperature level at the end of the duct increases significantly due to
the amount of CO and H 2 present in the off- gas. The latent enthalpy of CO and H 2 is transformed to thermal
enthalpy through post-combustion of these elements with false air from the slip gap . Here, the first
calculation case with two times false air ingress at the slip gap leads to higher temperature levels than the
second calculation case with four times false air ingress . The losses are related to the mixing, where the
highest exergy losses of the whole post combustion process in the dedusting system are occurring [23].
02004006008001000120014001600
0 1000 2000 3000Temperature [ C]
Time [s]T_Out_LAx2
T_Out_LAx4
T_EAF_gas
0510152025
0 1000 2000 3000Heat flow [MW]
Time [s]Qdot_LAx2
Qdot_LAx4

9
The differences between the temperature levels of the two cases are resulting in differences for the heat
flows to the cooling. Maximum heat flows of more than 20 MW are possible for the first calculation case
within the assumed duct while the second case leads to maximum heat flows of approximately 10 MW. For a
better comparability, the heat flows can be integrated to total energies which can be averaged over the entire
process time. For the first calculation case with two times false air ingress, a total energy of 88 kWh/t is
transferred to the cooling, leading to an average heat flow of 15 MW. The second calculation case results in
a total energy transfer of 46 kWh/t which correlates to an average heat flow of approximately 8 MW. On the
one hand, these results are leading to the consequence of a higher load to the cooling system for the first
calculation case. On the other hand, if a heat recovery system is installed, more energy can be recovered for
the first calculation case and e.g. more steam c an be generated with a more controlled post combustion
process in the dedusting system.

4. CONCLUSION
Further developments and model enhancements of the described EAF process simulation model and the
calculation model of the dedusting system are described within this paper. In particular, the EAF model is
improved with a more detailed gas phase simulation, leading to more accurate off-gas predictions for further
calculations in the dedusting system model. Therefore, further chemical elements were implemented into the
gas phase and further chemical reactions are considered. In addition, thermal radiation of the gas phase is
included in the total heat transfer module as a consequence of the temperature levels of the gas phase in
combination with the present CO, H 2O and CH 4 levels. Regarding the dedusting system model, a
comprehensive approach for the post-combustion of CO, H 2 and CH 4 and updated heat transfer calculations
are implemented as further model developments.

The simulation results for the EAF gas phase are well corresponding to the measured off-gas data from the
EAF. With some further developments on the gas phase temperature simulation, the model will be capable
to reproduce the measured off-gas composition and energy output through the off-gas for single heats with
slight parameter adaptions. Once the EAF model is parameterized to a single industrial scale EAF, averaged
results for a set of heats are achievable. The obtained results are applicable in the calculation model of the
dedusting system to further optimize process control strategies, to investigate other modes of operation or to
analyze off-gas energy output and waste heat recovery potentials. Furthermore, such a combination of
process models can be applied for training genetic algorithms without long lasting and expensive off-gas
measurements to support off-gas measurements in non-harsh conditions and back calculations [13].

The presented results are providing an insight into the opportunities of a coupled modeling of the EAF and its
dedusting system. Both models and especially the dedusting system model need to be further validated
through measurements. Nevertheless, the amount of energy leaving the melting process through the off-gas
shows the optimization potential. In the future, the investigation of waste heat recovery installations is
intended to support decision processes or to improve steam generation in the dedusting system. Here, the
results of the two calculation cases are showing the effect of a nearly controlled false air intake for post-
combustion in the dedusting system in contrast to an excessive false air intake.

Even though the models are not extensively validated yet, the calculated heat transfer to the cooling
illustrates the amount of energy leaving the melting process through the off- gas and exhibits the optimization
potential. In the future it is intended, to predict the potential of a waste heat recovery installation to support
decision processes if a steam generation is taken into consideration for process optimization. In addition, the
results of the two calculation cases show the effect of a nearly controlled false air intake for post-combustion
in the dedusting system in contrast to an excessive false air intake. Here, higher amounts of generated
steam could lead to faster amortization times and thus, making waste heat recovery profitable.

10 REFERENCES

[1] C. FRÖHLING, P. HEMMLING, J. KEMPKEN and W.H. EMLING, AISTech, Atlanta (Georgia, USA) (2012), pp.
81-86.
[2] A. HAMPEL, A. FLEISCHANDERL, G. ENICKL, F. ZAUNER, T. STEINPARZER and M. HAIDER, AISTech,
Indianapolis (Indiana, USA) (2011), pp. 1047-1061.
[3] M. MEYN, R. NORTHEMANN and C. FRÖHLING, SEAISI ASEAN, Nusa Dua (India) (2012), pp. 1-8.
[4] D.J. ZULIANI, V. SCIPOLO and C. BORN, Millenium Steel. Millennium Steel Publishing, London (2010), pp. 54-
61.
[5] J.G. BEKKER, I.K. CRAIG and P.C. PISTORIUS, ISIJ Int. 1, (1999), pp. 23-32.
[6] J.M.M. FERNANDEZ, V.A. CABAL, V.R. MONTEQUIN and J.V. BALSERA, Eng. Appl. Artif. Intel. 7, (2008), pp.
1001-1012.
[7] V. LOGAR, D. DOVZAN and I. SKRJANC, ISIJ Int. 3, (2011), pp. 382-391.
[8] V. LOGAR, D. DOVZAN and I. SKRJANC, ISIJ Int. 3, (2012), pp. 402-412.
[9] V. LOGAR, D. DOVZAN and I. SKRJANC, ISIJ Int. 3, (2012), pp. 413-423.
[10] R.D.M. MACROSTY and C.L.E. SWARTZ, Ind. Eng. Chem. Res. 21, (2005), pp. 8067-8083.
[11] R.D. MORALES, H. RODRIGUEZ-HERNANDEZ and A.N. CONEJO, ISIJ Int. 5, (2001), pp. 426-435.
[12] P. NYSSEN, C. OJEDA, J.C. BAUMERT, M. PICCO, J.C. THIBAUT, S. SUN, S. WATERFALL, M. RANGER
and M. LOWRY, SteelSim METEC, Düsseldorf (2011), pp. 1- 9.
[13] A.H. KOLAGAR, T. MEIER, T. ECHTERHOF and H. PFEIFER, International Journal of Engineering Systems
Modelling and Simulation 4, (2015), pp. 244-255.
[14] V. LOGAR and I. SKRJANC, ISIJ Int. 7, (2012), pp. 1225-1232.
[15] T. MEIER, V. LOGAR, T. ECHTERHOF, I. ŠKRJANC and H. PFEIFER, steel research international, (2015), pp.
n/a-n/a.
[16] R.J. KEE, M.E. COLTRIN and P. GLARBORG, Chemically reacting flow: theory and practice. Wiley, Hoboken,
New Jersey (2003).
[17] R.J. KEE, M.E. COLTRIN and P. GLARBORG, Chemically reacting flow: theory and practice. Wiley, Hoboken,
New Jersey (2005).
[18] J.R. HOWELL, R. SIEGEL and M.P. MENGUC, Thermal radiation heat transfer. CRC Press, Boca Raton
(2011).
[19] M. KIRSCHEN, V. VELIKORODOV and H. PFEIFER, Energy 14, (2006), pp. 2926-2939.
[20] V. VELIKORODOV, Der Einfluss der Entstaubung auf den spezifischen elektrischen Energieeinsatz des
Lichtbogenofens (2009).
[21] M. HOFER, Instationäre, nichtlineare Modellierung und Simulation gasdurchströmter Apparate in
Abgasbehandlungsanlagen von Elektrostahlwerken (1997).
[22] VDI E.V., VDI-Waermeatlas. Springer, Berlin (2006).
[23] K. GANDT, T. MEIER, T. ECHTERHOF and H. PFEIFER, submitted and accepted to: Ironmaking and
Steelmaking: Processes, Products and Applications, (2016), pp. n/a-n/a.