A Study on the 2-D Temperature Distribution of the

Strip due to Induction Heater

Jong-Hyun Lee1, Jin-Taek Kim

1, Sung-Hyuk Lim

2, Do-Gyun Jung

2,

Hyeong-Jin Kim2, Byung-Joon Baek

1*

1 School of Mechanical System Engineering, Chonbuk National University,

Jeonju, 561-756, Korea 2 Technical Research Center, Hyundai Steel Company, Dangjin,

Chunnam, 343-823, Korea.

Abstract. Lowering the temperature drop of the hot strip in hot rolling process

results in the increased rolling load and qulaity deterioration. The induction

heating is the competitive way to heat the cooled bar. In this study, a two-

dimensional thermal analysis has been performed to predict the temperature

distribution along the width direction passing through the induction heater. In

addition, correction coefficient for the amount of the cooling, Setting Power

efficiency of the Induction Heater and heating efficiency is proposed to improve

the prediction value.

Keywords: Reheating facility, Roughing mill, Finishing mill, Induction heater

1 Introduction

Hot rolling process consists of heating the bar for a suitable material for deformation

temperature in the reheating furnace, forming some standard bar in Roughing mill,

Finishing mill, cooling in run out table (ROT) process and down coiling.

The hot strip passing through the Roughing mill and Finishing mill cooled down due

to the heat transfer to the cold environment. Lowering the bar temperature results in the

increased rolling load and a twist or wave occurs in the strip. Therefore, extra heating is

needed to compensate the heat loss. The induction heating is the competitive way to

heat the cooled bar. Rudnev [1,2] reported a comprehensive study of induction heating

prior to hot working. A few case studies are also provided to illustrate the capabilities

of numerical simulation. The ability to model the induction heating process is very

important to control and to optimize the processing parameter. The mechanism of the

energy transformation in induction heating with magnetic flux concentrator is carried

out in [3].

In this study, a two-dimensional thermal analysis has been performed to predict the

temperature distribution along the width direction passing through the induction heater.

In addition, correction coefficient for the amount of the cooling, Setting Power

efficiency of the Induction Heater and heating efficiency is proposed to improve the

prediction value.

Advanced Science and Technology Letters Vol.90 (Mechanical Engineering 2015), pp.1-5

http://dx.doi.org/10.14257/astl.2015.90.01

ISSN: 2287-1233 ASTL Copyright © 2015 SERSC

2 Induction Heater Model

Fig. 1 shows the process of rolling equipment from Roughing mill to Finishing mill

with bar heater and edge to increase the bar temperature. The bar is heated by induction

heating and cooled down passing through the area exposed to air by convection and

radiation heat transfer.

Fig. 1 Diagram of hot rolling process

3 Governing Equation

A two-dimensional heat transfer model is used to approximately predict the

temperature of the bar. The two-dimensional heat transfer model consists of the

following equations by selecting the width of the x-coordinate direction of the material,

the thickness direction in the y-direction.

∂2T

∂x2 +∂2T

∂y2 +q̇

k=

1

∂T

∂t (1)

Here �̇� represents a heat generation rate of the bar. Heat generation rate is applied to

hot bar by the induction heater. The equation is expressed in equation (2) by using the

induced current equation, the efficiency of the induction heater, input power, size and

depth of penetration depth of material.[4,5]

�̇�(𝑥) = 𝑓(𝑄, 𝜎, 𝐻, 𝑤) ∙ 𝐽(𝑥)2

= 𝑄

𝐻∙𝑤∙𝑣∙𝑡𝐼𝐻∙

𝑒−2𝑥

𝛿 −2𝑒−𝐻

𝛿 +𝑒2(𝑥−𝐻)

𝛿

𝛿−2𝐻∙𝑒−𝐻

𝛿 −𝛿∙𝑒−2𝐻

𝛿

(2)

4 Results and Discussion

Fig. 2 illustrates the comparison of the results of present study and that of literature [6].

One-dimensional temperature distribution in the thickness direction is analyzed in this

case. The temperature difference between present result and that of literature shows is 3

oC at surface, 1 oC at 1/4 point of the thickness and is 1 oC at center of the bar cross

section. It was found that the maximum deviation is within 3% error. This temperature

difference can be occurred because of differences in physical properties that is not

same with the value used in the reference paper.

Advanced Science and Technology Letters Vol.90 (Mechanical Engineering 2015)

2 Copyright © 2015 SERSC

Fig. 3 shows the results obtained by using the commercial software of STAR-CCM+ to

validate our code developed using MATLAB. It can be seen that the temperature rises

significantly at the surface by the effect of induction heating and penetrates into the

depth of the thickness of the bar. It is found out that this temperature distribution is

agrees fairly well with MATLAB code and experimental results, which validates the

methodology that is adopted in this study.

.

Fig.2 Comparison of temperature distribution. Fig.3 Temperature from STAR-CCM+.

Two dimensional MATLAB code was developed based on the algorithm tested by

previous 1-D code. Fig. 4 shows the temperature distribution across the width direction

of the cold bar. The bar at temperature of 22 oC enters the bar heater and heated to the

target temperature through the heater. The temperature increases from center to the

surface due to the effect of skin depth of the induction current. It is noted that the

temperature keeps nearly uniform across the width direction, while significant drops

near the edge area. It represents the need of extra heating by edge heater of the hot mill

process. It was also compared with experimental data measured by CA type

thermocouples at several locations of the stainless steel. Table 1 shows the quantitative

comparison of simulated temperature and measured temperature. The temperature rise

by induction heating is 32 oC and maximum temperature difference occurs at surface of

the bar with 2.8 % deviation.

Fig. 5 shows the thermal image of the hot strip taken by the IR camera (FLIR

SC2500, FLIR). The thermo-graphic data are analyzed using the software FLIR Altair.

The image illustrates the surface temperature of the hot strip moving through the actual

hot rolling process. Temperature to be increases is ∇T =20 oC. The inlet temperature of

the hot bar entering bar heater increases from 1150 oC to 1170

oC at the exit of the bar

heater.

Table 1. Comparison with measured temperature.

Surface

P=8

1/4

P=16

1/2

P=24

Cold bar test (oC) 53.9 32.0 22.5

Temperature calculated (oC) 56.3 32.2 22.1

Temperature difference (oC) -2.8 -0.8 0.4

Advanced Science and Technology Letters Vol.90 (Mechanical Engineering 2015)

Copyright © 2015 SERSC 3

Fig.4. Temperature distribution with measured temperature.

Fig. 5 Temperature rising 20 oC on the head.

Fig. 6 shows the surface temperature distribution of hot strip heated by 2 bar heaters.

The temperature increases uniformly) across the width direction with setting

temperature value (∆T = 40 oC, ∆T = 20 oC) while passing through the 2 heaters.

However, temperature drop near edge area cannot be avoided due to the cooling of the

side surface. This edge effect occurs at 13% length of the width. It was also compared

with experimental data measured by IR camera. It represents fairly good agreement

between numerical and experimental results.

(a) ∆T = 40 oC (b) ∆T = 0 oC

Fig. 6 Temperature distribution of hot strip across the width direction.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8950

1000

1050

1100

1150

1200

BH1(Inlet

BH2(Outlet)

IR(Outlet)

IR(OutletLeft)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.81000

1050

1100

1150

1200

1250

BH1(Inlet

BH2(Outlet)

IR(Outlet)

IR(OutletLeft)

Advanced Science and Technology Letters Vol.90 (Mechanical Engineering 2015)

4 Copyright © 2015 SERSC

5 Conclusion

Numerical simulation has been performed to investigate the temperature distribution of the

bar in hot mill process. The domain of hot mill process from Roughing mill to Finishing

mill is transformed to time dependent problem passing through the position of the bar. The

temperature was modified using the experimental data to improve the accuracy of the

predicted value.

The skin depth of the bar is predicted to investigate induction current affected area. A

significant decrease in temperature is found from the surface to center of the bar. . Heating

efficiency of the real model in the width direction were predicted by applying internal heat

generation distribution about the Cold bar test, and Cold bar test for temperature rise

amounts were calculated by back calculation method then, heating rate of surface in the

width direction was calculated and verified.

The temperature increases uniformly across the width direction with setting

temperature value while passing through the heaters. However, temperature drop near

edge area cannot be avoided due to the cooling of the side surface. This edge effect

occurs at 13% length of the width.

Acknowledgments. The authors like to express their sincere gratitude to

HYUNDAI STEEL COMPANY for their financial support, thank the Rolling

Technology Development Team for their helpful mill data and discussion.

References

1. D.U. Furrer and S.L Semiatin : Simulation of Induction Heating Prior to Hot

Working and Coating, ASM Handbook, Volume 22B, Metals Process Simulation.

(2010)

2. Rudnev, V. I., Loveless, D., Schweigert, K., Dickson, P., and Rugg, M., :

Efficiency and Temperature Considerations in Induction Re-Heating of Bar, Rod

and Slab, Industrial Heating, pp.39-43 (2000)

3. Feng Li, Xue Kun Li, Tian Xing Zhu, Qian Zhe Zhao, Yi Ming Kevin Rong :

Modeling and Simulation of Induction Heating with Magnetic Flux Concentrator,

Applied Mechanics and Materials, pp.268-270, 983 (2012)

4. K.F. Wang, S. Chandrasekar, and H.T.Y. Yang : Finite-Element Simulation of

Moving Induction Heat Treatment, Journal of Materials Engineering and

Performance, Volume 4, Issue 4, pp.460~473 (1995)

5. Martin Fisk : Simulation of Induction Heating in Manufacturing, Licentiate thesis

(2008:42)

6. Kim, H. J. : A Numerical Study on Temperature Profiles of Steel Plates Heated by

Induction Heater, KSME 2003 Conference , pp.1412~1416 (2003)

Advanced Science and Technology Letters Vol.90 (Mechanical Engineering 2015)

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