7
Investigation of the slab heating characteristics in a reheating furnace with the formation and growth of scale on the slab surface Jung Hyun Jang a , Dong Eun Lee a , Man Young Kim a, * , Hyong Gon Kim b a Department of Aerospace Engineering, Chonbuk National University, Chonbuk 561-756, Republic of Korea b CAMSTech Co., Ltd., Chonbuk 561-844, Republic of Korea article info Article history: Received 12 September 2009 Received in revised form 6 May 2010 Accepted 6 May 2010 Available online 10 June 2010 Keywords: Steel slab Reheating furnace Scale Radiative heat transfer Transient conduction abstract In this work, the development of a mathematical heat transfer model for a walking-beam type reheating furnace is described and preliminary model predictions are presented. The model can predict the heat flux distribution within the furnace and the temperature distribution in the slab throughout the reheat- ing furnace process by considering the heat exchange between the slab and its surroundings, including the radiant heat transfer among the slabs, the skids, the hot combustion gases and the furnace wall as well as the gas convection heat transfer in the furnace. In addition, present model is designed to be able to predict the formation and growth of the scale layer on the slab in order to investigate its effect on the slab heating. A comparison is made between the predictions of the present model and the data from an in situ measurement in the furnace, and a reasonable agreement is found. The results of the present sim- ulation show that the effect of the scale layer on the slab heating is considerable. Ó 2010 Elsevier Ltd. All rights reserved. 1. Introduction The reheating furnace process, that is the midway step between the continuous casting process and the hot-rolling process, is com- monly used to raise the temperature of the slab, and, thereby, the plasticity of the slabs so that the subsequent hot-rolling process runs on wheels. Since the reheating furnace process should have lower energy consumption and combustion-generated pollutant emissions, the analysis of transient heating characteristics of the slab in the reheating furnace has attracted a great deal of interest during the past few decades. Furthermore, because the attainment of uniform temperature distributions inside the slab and the target temperature of the slab at the furnace exit determine the quality and productivity of the steel product, the reheating furnace process must be analyzed accurately and rapidly. However, experimental approach for analyzing a real reheating furnace process is greatly limited by the complex three dimensional structures and their influence on the furnace process. Therefore, models and methods to predict the furnace combustion and heat transfer processes are in high demand. These analytical studies can be classified into following two cat- egories. The first one [1–5] is to solve the full Navier–Stokes and energy conservation equations governing the hot gas flow and combustion process in the furnace, where the thermal radiation acts as an energy source term via the divergence of radiative heat flux. Although these full CFD analyses make it possible to accu- rately predict the thermal and combusting fluid characteristics in the furnace, they necessitate long computational time and result- ing much cost because of such difficulties as the treatment of so many governing equations and the complexity of the furnace structure as well as the uncertainty of the models. The second method [6–12], which is simple but can reasonably simulate the thermal behavior of the slab, focuses on the analysis of the radia- tive heat transfer in the furnace and the transient heat conduction within the slab. The model suggested in this work can be also cat- egorized as the second approach. Meanwhile, the reheating furnace is filled with hot-oxidizing combustion gases that mainly consist of H 2 O, CO 2 ,O 2 , and N 2 . The steel slabs are heated up by these gases. As the steel surface temperature rises, however, it reacts with the furnace gases result- ing in the formation of iron oxide layer that is generally termed scale. The thickness of the scale layer depends on slab residence time in the furnace, its surface temperature, temperature and aggressiveness of the furnace gas. The formation of scale causes physical loss of the slab. In addition, since the thermal conductivity of scale is very small compared to that of steel, the existence of scale on the slab can greatly affect the heat transfer behavior. How- ever, the previous works to predict thermal heating characteristics of the slab in a reheating furnace have not ever considered the existence of scale. 0017-9310/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2010.05.061 * Corresponding author. Address: Department of Aerospace Engineering, Chon- buk National University, 664-14 Duckjin-Dong, Duckjin-Gu, Jeonju, Chonbuk 561- 756, Republic of Korea. Tel.: +82 63 270 2473; fax: +82 63 270 2472. E-mail address: [email protected] (M.Y. Kim). International Journal of Heat and Mass Transfer 53 (2010) 4326–4332 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

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International Journal of Heat and Mass Transfer 53 (2010) 4326–4332

Contents lists available at ScienceDirect

International Journal of Heat and Mass Transfer

journal homepage: www.elsevier .com/locate / i jhmt

Investigation of the slab heating characteristics in a reheating furnace withthe formation and growth of scale on the slab surface

Jung Hyun Jang a, Dong Eun Lee a, Man Young Kim a,*, Hyong Gon Kim b

a Department of Aerospace Engineering, Chonbuk National University, Chonbuk 561-756, Republic of Koreab CAMSTech Co., Ltd., Chonbuk 561-844, Republic of Korea

a r t i c l e i n f o

Article history:Received 12 September 2009Received in revised form 6 May 2010Accepted 6 May 2010Available online 10 June 2010

Keywords:Steel slabReheating furnaceScaleRadiative heat transferTransient conduction

0017-9310/$ - see front matter � 2010 Elsevier Ltd. Adoi:10.1016/j.ijheatmasstransfer.2010.05.061

* Corresponding author. Address: Department of Abuk National University, 664-14 Duckjin-Dong, Duck756, Republic of Korea. Tel.: +82 63 270 2473; fax: +8

E-mail address: [email protected] (M.Y. Kim).

a b s t r a c t

In this work, the development of a mathematical heat transfer model for a walking-beam type reheatingfurnace is described and preliminary model predictions are presented. The model can predict the heatflux distribution within the furnace and the temperature distribution in the slab throughout the reheat-ing furnace process by considering the heat exchange between the slab and its surroundings, includingthe radiant heat transfer among the slabs, the skids, the hot combustion gases and the furnace wall aswell as the gas convection heat transfer in the furnace. In addition, present model is designed to be ableto predict the formation and growth of the scale layer on the slab in order to investigate its effect on theslab heating. A comparison is made between the predictions of the present model and the data from anin situ measurement in the furnace, and a reasonable agreement is found. The results of the present sim-ulation show that the effect of the scale layer on the slab heating is considerable.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

The reheating furnace process, that is the midway step betweenthe continuous casting process and the hot-rolling process, is com-monly used to raise the temperature of the slab, and, thereby, theplasticity of the slabs so that the subsequent hot-rolling processruns on wheels. Since the reheating furnace process should havelower energy consumption and combustion-generated pollutantemissions, the analysis of transient heating characteristics of theslab in the reheating furnace has attracted a great deal of interestduring the past few decades. Furthermore, because the attainmentof uniform temperature distributions inside the slab and the targettemperature of the slab at the furnace exit determine the qualityand productivity of the steel product, the reheating furnace processmust be analyzed accurately and rapidly. However, experimentalapproach for analyzing a real reheating furnace process is greatlylimited by the complex three dimensional structures and theirinfluence on the furnace process. Therefore, models and methodsto predict the furnace combustion and heat transfer processesare in high demand.

These analytical studies can be classified into following two cat-egories. The first one [1–5] is to solve the full Navier–Stokes and

ll rights reserved.

erospace Engineering, Chon-jin-Gu, Jeonju, Chonbuk 561-2 63 270 2472.

energy conservation equations governing the hot gas flow andcombustion process in the furnace, where the thermal radiationacts as an energy source term via the divergence of radiative heatflux. Although these full CFD analyses make it possible to accu-rately predict the thermal and combusting fluid characteristics inthe furnace, they necessitate long computational time and result-ing much cost because of such difficulties as the treatment of somany governing equations and the complexity of the furnacestructure as well as the uncertainty of the models. The secondmethod [6–12], which is simple but can reasonably simulate thethermal behavior of the slab, focuses on the analysis of the radia-tive heat transfer in the furnace and the transient heat conductionwithin the slab. The model suggested in this work can be also cat-egorized as the second approach.

Meanwhile, the reheating furnace is filled with hot-oxidizingcombustion gases that mainly consist of H2O, CO2, O2, and N2.The steel slabs are heated up by these gases. As the steel surfacetemperature rises, however, it reacts with the furnace gases result-ing in the formation of iron oxide layer that is generally termedscale. The thickness of the scale layer depends on slab residencetime in the furnace, its surface temperature, temperature andaggressiveness of the furnace gas. The formation of scale causesphysical loss of the slab. In addition, since the thermal conductivityof scale is very small compared to that of steel, the existence ofscale on the slab can greatly affect the heat transfer behavior. How-ever, the previous works to predict thermal heating characteristicsof the slab in a reheating furnace have not ever considered theexistence of scale.

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Nomenclature

C specific heat, J/(kg K)I radiation intensity, W/m2

N/; Nh discretized number of each radiation direction~n unit normal vector on control surfaceqC

slab convective heat flux, W/m2

qRslab radiative heat flux, W/m2

qTslab total heat flux, W/m2

�r position vector~s unit direction vectorT Temperature, Kkp parabolic rate constant

R universal gas constant, J/(mol K)Q activation energy, J/mol

Greek symbolsq density of slab or scale, kg/m3

b0 extinction coefficient, =ja+rs, m�1

ja absorption coefficient, m�1

rs scattering coefficient, m�1

r Stefan–Boltzmann constant, =5.67 � 10�8 W/(m2 K4)U scattering phase function, sr�1

X solid angle, sr

J.H. Jang et al. / International Journal of Heat and Mass Transfer 53 (2010) 4326–4332 4327

Thus, the current work would suggest a mathematical heattransfer model to predict the formation and growth of the scale,and find the heat flux impinging on the slab surface and tempera-ture distribution inside the slab considering it. The furnace is mod-eled as radiating medium with spatially varying temperature andis filled with hot combustion gases that consist of H2O, CO2, O2,and N2, and have highly spectral radiative characteristics. Accord-ingly, the weighted sum of gray gas model (WSGGM) [13] is usedto consider the non-gray behavior of the combustion gases. Inthe following sections, after describing the methodology adoptedhere for the prediction of furnace processes within the reheatingfurnace, the formation and growth of scale and its effect on the

Non-firing Zone

Charging Zone

Preheating Zone H

Furnace Length

Slab

Furnace Wall

y

a

b

Furnace Wall

Slab

F M

Fig. 1. Geometry of the reheating furnace: (a)

heat transfer characteristics and thermal behavior of the slab areinvestigated. Finally, some concluding remarks are given.

2. Theoretical models

2.1. Reheating furnace process and furnace model

The walking-beam type reheating furnace modeled in this workis shown in Fig. 1. This furnace, currently run in the steel industry,has about 35 m in length and 11 m in width, and the highest fur-nace roof is about 5 m inside. There are five zones in the reheating

eating Zone Soaking Zone

= 39.2m

Burner

x

F F M

Symmetry Line

longitudinal and (b) transverse sections.

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O2

O2

O2O2

O2

O2

O2

O O

O2

O O

4328 J.H. Jang et al. / International Journal of Heat and Mass Transfer 53 (2010) 4326–4332

furnace as shown in Fig. 1(a); non-firing, charging, preheating,heating, and soaking zones. The fixed and moving skids are ar-ranged in the furnace as shown in Fig. 1(b), and the slabs are sup-ported and moved in the furnace by the fixed and moving beams,respectively. Namely, after the slab is supported and heated onthe fixed skids for a certain time, it is moved on the next fixedbeam by the cyclic movement of the moving skids, which consistsof sequential upward, forward, downward, and then backwardmovements. The slab is a high carbon steel, whose carbon contentis 0.35–0.55%. The slab is 1.1 m in width, 0.23 m in height and 8 min length. There are 29 slabs with 0.1 m interval between them inthe reheating furnace. The slab is assumed to be isothermal of26.8 �C when charged into the furnace and the slab residence timeis about 180 min. The thermophysical properties of the slab are gi-ven in Table 1. Those values shown Table 1 is obtained from thePOSCO technical R&D center. Although the temperatures and theconcentration distributions of the gases within a real furnace varyaccording to conditions of combustion and flow at each location,the mean temperature and mean mass fraction based on experi-mental data, listed in Tables 2 and 3, respectively, is used in thiswork. Furthermore, the temperatures of the furnace wall and skidsused are listed in Table 2.

Meanwhile, the presence of the skid structure considerably dis-torts heat transfer to the slab surfaces, both as a result of radiativeshielding of the slab bottom surface and conduction of energyacross the slab/skid contact area. It is reported that conductionheat loss to the skid is found to be two orders of magnitude lessthan the reduction in radiative heat transfer to the slab and thenthe dominant factor in the formation of skidmarks is the radiativeshielding by skid structures [6]. On the basis of the fact, it is as-sumed that conduction heat loss to the skid is negligible. There-upon, although the fixed skids are contact with the slab bottomsurface in the real furnace, it is assumed that there is an intervalof 0.005 m between the slab and fixed skid.

Table 1Thermal properties of steel slab and wustite.

Temperature (�C) Conductivity(W/m K)

Specific heat(J/kg K)

Density(kg/m3)

Slab30 26.89 299.0 7778400 25.44 401.6600 22.70 512.0800 20.89 542.81000 23.69 478.9

Wustite [FeO]– 3.20 725.0 7750

Table 2Temperature conditions used in this work (�C).

Zone Tg,upper Tg,lower Tg,skid

Non-firing 950 930 730Charging 950 930 730Preheating 1000 980 780Heating 1200 1170 970Soaking 1180 1160 960

Table 3Concentration distribution of the furnace combustion gases.

Furnace gas

H2O CO2 O2 N2

0.111 0.177 0.015 0.697

2.2. High temperature oxidation of metal

The reheating furnace is filled with hot-oxidizing combustiongases consisting of H2O, CO2, O2, and N2. In such a high tempera-ture environments, a metal easily reacts with the combustion gasesthrough the processes of (a) a initial oxygen adsorption, (b) achemical reaction to form a surface oxide and oxide nucleation,(c) a growth of continuous oxide film, and (d) a cavity/micro-crack/porosity formation within the film shown as shown inFig. 2. As a result, an oxide layer consists of wustite, magnetiteand hematite as shown in Fig. 3, forms on the slab surface. Thiscan best be illustrated by the well known Ellingham/Richardsondiagram [14]. Wustite, FeO, is the innermost phase of the scalewhich forms next to the metal and is the most iron rich. Magnetite,Fe3O4, is the intermediate phase. Hematite, Fe2O3, is the outer-most layer of the scale and has the highest oxygen content. How-ever, at temperatures higher than approximately 600 �C, the per-cent composition of the three oxides, wustite, magnetite andhematite are about 96%, 4% and 1%, respectively [15,16]. Therefore,in this work, it is assumed that the scale layer consists of only onecomponent, wustite. The thermal properties of wustite by Torresand Colas [17] are listed in Table 1. As shown in Table 1, sincethe thermal conductivity of wustite is very small compared to thatof slab, it is expected that the existence of the wustite on the slabsurface can affect the heat transfer behavior.

Meanwhile, in most cases, the rate of scale growth at high tem-perature follows a parabolic regime. In this case, the thickness ofscale can be represented as follows:

MetalMetal MetalMetal

Metal

O-2 e-

O2

M+2 OMetal

O-2 e-

O2

M+2 OMetal

O2

M+2 OMetal

O2

M+2 O

(a) adsorption (b) nucleation and growth

(d) cavity, microcrack, and porosity formation

(c) film growth

Fig. 2. Schematic representation of the oxide film formation in gaseous environ-ments at high temperature environments: (a) adsorption, (c) nucleation andgrowth, (c) film growth, and (d) cavity, microcrack, and porosity formation.

Oxidizing atmosphere, 2O

Hematite, 2Fe 3O

Magnetite, 3Fe 4O

Wustite, FeO

Steel, Fe

Fig. 3. Illustrative example of the typical scale layers on the slab surface exposed tooxidizing environment.

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J.H. Jang et al. / International Journal of Heat and Mass Transfer 53 (2010) 4326–4332 4329

x2 ¼ kpt ð1Þ

where x is the scale thickness, kp is parabolic rate constant, and t isthe oxidation time. The parabolic rate constant is exponentiallydependent on temperature, expressed as:

kp ¼ k0e�Q=RT ð2Þ

where kp is a constant, Q is the activation energy of iron oxidation, Ris the gas constant, and T is absolute temperature. The current workused the parabolic rate constant, expressed as [18]:

kp ¼ 6:1e�169;452=RT ð3Þ

0 5 10 15 20 25 30 350

200

400

600

800

1000

1200

Tem

pera

ture

(o C)

z (m)

Experiment

Tg (upper zone)

Tg (lower zone)

Tcenterline, W.Scale

Tcenterline, W/O.Scale

Fig. 4. Comparison of the predicted and experimental results of the centerlinetemperature of the slab.

2.3. Governing equations

The two dimensional transient heat conduction equation to pre-dict the temperature distribution within the slab including thescale is,

qC@T@t¼ @

@xk@T@x

� �þ @

@yk@T@y

� �ð4Þ

where q, C, and k represent density, specific heat, and conductivityof the slab or the scale, respectively. The boundary condition of Eq.(4) is the total heat flux on the slab or scale surface, qT

slab, which canbe obtained from the sum of the convective and radiative heat fluxas following,

qTslab ¼ qC

slab þ qRslab ð5Þ

where qCslab and qR

slab are the convective and radiative heat flux,respectively. The convective heat transfer between the furnace gasand the solid surface is evaluated by using the equation,

qCslab ¼ HcðTgas � TslabÞ ð6Þ

where Hc is the gas convective heat transfer coefficient at the sur-face of the slab of 7.8 W/m2 K [8]. Also, Tgas and Tslab are the temper-atures of the furnace gas and the slab surface, respectively.

The radiative heat flux on the slab or scale surface is calculatedfrom the following equation,

qRslab ¼

ZX¼4p

Ið~rw;~sÞð~s �~nwÞdX ð7Þ

where Ið~rw;~sÞ is the radiation intensity at the slab surface ~rw anddirections~s. ~nw is the outward unit normal vector at the slab sur-face, and X is the solid angle. For a radiative active medium, theradiation intensity at any position ~r along a path ~s through anabsorbing, emitting and scattering medium can be given by the fol-lowing radiative transfer equation (RTE),

1b0

dIð~r;~sÞds

¼ �Ið~r;~sÞ þ ð1�x0ÞIbð~rÞ þx0

4p

ZX0¼4p

Ið~r;~sÞUð~s0 !~sÞdX0

ð8Þ

where b0 = ja + rs is the extinction coefficient, ja is absorption coef-ficient, rs is scattering coefficient, x0 = rs/b0 is the scattering albe-do, and Uð~s0 !~sÞ is the scattering phase function of radiativetransfer form the incoming direction ~s0 to the scattering direction~s. Ibð~rÞ is the blackbody radiation of the medium. This equation, ifthe temperature of the medium, Ibð~rÞ, and the boundary conditionsfor intensity are given, provides a distribution of the radiationintensity in the medium. For a diffusely emitting and reflecting wallwith temperature Tw, the outgoing intensity at the which is theboundary condition of Eq. (8) can be expressed as the summationof the emitted and reflected ones like,

Ið~rw;~sÞ ¼ ewIbwð~rwÞ þ1� ew

p

Z~s0 �~nw<0

Ið~rw;~s0Þj~s0 �~nwjdX0 ð9Þ

where ew is the wall emissivity and Ibw ¼ rT4w=p is the blackbody

intensity of the wall.

2.4. Solution method

As mentioned in the previous, the model developed in this workconsists of coupled two parts, i.e., the radiation model and the heatconduction model. At certain time step, the radiation model solvesthe RTE using the slab surface temperature that resulted from theconduction model at the previous time step. And then, the conduc-tion model solves the heat conduction equation using the radiativeheat flux on the slab surface that resulted from the radiation modelat current time step. The above process is repeated every time step.As a result, the slab temperature could be calculated at each loca-tion in the furnace.

The transient heat conduction equation expressed in Eq. (4) isdiscretized by using the finite volume method (FVM) [19]. A cen-tral differencing scheme is used for the diffusion terms in the x-and y-directions, while the unsteady term is treated implicitly.The resulting dicretized system is then solved iteratively by usingthe TDMA (tridiagonal matrix algorithm) algorithm until the tem-perature field in the slab satisfies the following convergencecriterion:

maxðjTni;j � Tn�1

i;j j=Tni;jÞ 6 10�6 ð10Þ

where Tn�1i;j is the previous value of Tn

i;j in the same time level.Meanwhile, the RTE expressed in Eq. (8) must be analyzed in or-

der to compute the radiative heat flux on the slab or scale surfaceas shown in Eq. (7). In this work, the finite volume method (FVM)for radiation suggested by Chui and Raithby [20], and developed byChai et al. [21] and Baek et al. [22] is adopted to discretize the RTE.More detailed information on the FVM can be easily found in theliterature [10,20–22].

3. Results and discussion

The reheating furnace heat transfer model developed in thiswork was used to investigate several aspects of furnace behavior,especially focusing on the prediction of the scale formation andits effects on the heating characteristics and thermal behavior ofthe slab.

As mentioned previously, in order to consider the non-graycharacteristics of the combustion gases, the WSGGM, which postu-lates that total emissivity and absorptivity may be represented bythe sum of gray gas emissivities weighted with a temperaturedependent factor, is used, and further information on the model

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0 20 40 60 80 100 120 140 160 1800.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0

200

400

600

800

1000

1200

Scal

e Th

ickn

ess

(mm

)

Time (min)

Sth(upper surface)

Sth(lower surface)

Tg (upper zone)

Tg (lower zone)

Tem

pera

ture

(o C)

Fig. 5. Scale growth on the top and bottom surfaces of the slab.

4330 J.H. Jang et al. / International Journal of Heat and Mass Transfer 53 (2010) 4326–4332

is easily found in Smith et al. [13] On the other hand, it is assumedthat there is no scattering, i.e., rs = 0, and the emissivity of the fur-nace wall is 0.8 and the emissivities of the skid structure, slab andscale are set to 0.5. In fact, the exact surface emissivity of the scalelayer has not been reported, and it is only expected to be equal toor slightly higher than the surface emissivity of the slab. In this

Fig. 6. Distribution of the heat flux vector on the slab and temperature contours in the scaslab (charging zone), (c) 13th slab (preheating zone), (d) 22nd slab (heating zone), and

work, therefore, it is assumed that the emissivity of the scale isequal to one of the slab. Also, because of its symmetry, a half ofthe furnace is modeled in order to reduce computing time. The spa-tial mesh systems used in this study is (Nx � Ny) = (156 � 151) andangular systems of (Nh � Nu) = (4 � 12) for 2p sr.

Firstly, in order to validate the model developed in this work,the results from the present model are compared with the experi-mental data provided by POSCO. Fig. 4 shows the longitudinal tem-perature profile of the centerline temperature of the slab. Asshown, the temperature of the slab with scale is overall higher thanone of the slab without scale. And, it can be seen from the figurethat the temperature difference gradually decreases as the slab isheated and is 10 �C at the exit of the furnace. Also, at comparisonwith experimental data, the result considering the scale effect isa better agreement with the experimental data than the resultnot considering the scale effect. This means that the formation/growth of scale is one of the important matters which must be con-sidered in order to more exactly investigate the thermal behaviorof the slab in the reheating furnace.

The reheating furnace is filled with hot-oxidizing combustiongases and the slabs are heated up by these gases. In addition, thesegases react with the steel slabs resulting in the formation of ironoxide layer that is generally termed scale. As above mentioned,scale growth rate of most metals at high temperature follows the

le and slab without (left) and with (right) scale: (a) 1st slab (non-firing zone), (b) 8th(e) 29th slab (soaking zone).

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J.H. Jang et al. / International Journal of Heat and Mass Transfer 53 (2010) 4326–4332 4331

parabolic regime of Eq. (1). Fig. 5 shows growth of the scale layeron the top and bottom surface of the slab. As shown, since the tem-perature is relatively low from non-firing zone to preheating zone,the growth rate is low. On the other hand, the growth rate of thescale increases since the heating zone where the temperature isrelatively high. Also, it can be seen from the figure that becauseof the temperature difference between the upper and lower zoneof the furnace, the scale layer formed on the top slab surface isthicker than the scale layer formed on the bottom slab surface.At the furnace exit the thicknesses of scale on the top and bottomslab surfaces are 1.75 mm and 1.55 mm, respectively.

As listed in Table 1, the thermal conductivity of scale is verysmall compared to one of steel, while the specific heat of scale issomewhat large. As a result, the existence of scale formed on theslab surface can greatly affect the heat transfer behavior. Namely,due to the very small heat conductivity of scale, it should preventthe heat energy, which is transferred from the surroundings to theslab surface, from conducting into the inside of the slab. And thesurface of scale should be slowly heated due to its large specificheat. Fig. 6 shows the heat flux distribution on the surface andthe temperature distribution inside the scale and slab in each zoneof the furnace according to existence and non-existence of thescale. It can be seen that although more heat energy is transferredto the surface in a case of considering the scale layer, the surfacetemperature rises slowly due to the specific heat of the scale. Also,due to the thermal conductivity of the scale, the temperature gra-dient within the slab in that case is more severe, especially nearsurface.

In order to more closely examine these effects of the scale, thescale surface temperature, the temperature of the interface

0 5 10 15 20 25 30 350

200

400

600

800

1000

1200

Tscale, W.Scale

Tinterface, W.Scale

Tslab, W/O.Scale

Tem

pera

ture

(o C)

z (m)

Tg (upper zone)

Tg (lower zone)

0 5 10 15 20 25 30 350

200

400

600

800

1000

1200 Tg (upper zone)

Tg (lower zone)

Tem

pera

ture

(o C)

z (m)

Tscale, W.Scale

Tinterface, W.Scale

Tslab, W/O.Scale

a

b

Fig. 7. Predicted temperature profiles on the top (a) and bottom (b) surface of theslab.

between the scale and slab and the slab surface and the surfacetemperature of the slab without the scale layer is illustrated inFig. 7. Similarly, the temperature of the scale surface is lower thanthat of the slab without scale throughout the furnace. However, thetemperature difference is prominent in the entrance region of thefurnace and decreases gradually as the slab approaches the exit re-gion of furnace.

4. Conclusions

In this work, the development of a mathematical heat transfermodel for a walking-beam type reheating furnace is described.The model includes firstly a sub-model for consideration of thescale effect on the thermal behavior of the slab as well as a sub-model for analysis of radiative heat transfer, which is extremelyimportant in a high temperature environment such as a reheatingfurnace. The model adopted in this work can predict the growth ofthe scale based on the given longitudinal furnace gas temperature.And then, considering the scale on the slab surface, the model pre-dicts the radiative and convective heat fluxes on the slab surface,and finally the temperature distribution in the slab throughoutthe furnace. Using the model, the effect on the thermal behaviorin the reheating furnace is investigated in this work, and the fol-lowing conclusions can be drawn.

1. The result predicted from the present model is in a good agree-ment with the experimental data from POSCO. This means thepresent model is reasonable.

2. The growth rate of the scale increases as the temperature of thefurnace gas increases. For a specific case studied in this work,scale thicknesses on the top and bottom slab surfaces are1.75 mm and 1.55 mm, respectively, at the furnace exit.

3. The scale layer formed on the slab surface makes the heatingrate of the slab slow and the temperature gradient within theslab increase. As a result, the temperature of the slab with scaleis lower 10 �C than without scale at the exit of the reheatingfurnace.

Acknowledgements

This work was supported by the Korea Research FoundationGrant by the Korean Government (MOEHRD, Basic Research Pro-motion Fund) (KRF-2008-331-D00103). Also, the authors gratefullyacknowledge the interest and support exerted by the POSCO,Korea.

References

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