Icmae 2014

Advanced Materials Research Vol. 1016 (2014) pp 342-346 Online available since 2014/Aug/28 at www.scientific.net © (2014) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMR.1016.342

Experimental and Numerical Analysis Applied on Steel Bars Cooling Paul Campos Santana Silva1,a, Paulo Henrique Terenzi Seixas1,b, Caroline Rodrigues1,c, Leonardo Fonseca1,d and Rudolf Huebner1,e 1

DEMEC / UFMG – Av. Antônio Carlos, 6627 – Pampulha – CEP: 31.270-901 – BH/MG – Brazil a

paulsilva@ufmg.br, bpauloterenzi@hotmail.com, ccarolrodri201@gmail.com, d leofonseca@yahoo.com.br and erudolf@ufmg.br

Keywords: Mathematical model, cooling, steel bar and heat treatment.

Abstract. AISI 1020 steel bars cooling have been investigated aiming to obtain their cooling rate during heat treatment. Hot steel bars just taken out of the furnace are piled over other ones that were taken out of the furnace earlier. A mathematical model has been created and implemented using the software EES, Engineering Equation Solver. An experiment was conducted to validate the mathematical model. The experiment consists in three loads of three bars each with a time interval of 5 minutes between them. The initial temperature of each bar was 150oC. The mathematical model can obtain the thermal profile of each bar and the average and maximum deviation when confronted with experimental data were about 8% and 20% respectively.

Introduction Steels are widely used in several mechanical engineering applications due their availability, their developed mining and refining techniques, its low cost and high mechanical properties versatility by heat treatment [1]. Heat treatment consists in heating or cooling the material in a controlled way aiming changing their properties by controlling the austenitic transformation [2].

Temperature, cooling rate and soaking time are some important parameters to evaluate during the thermal treatment. The final mechanical properties are result of the austenite transformation [3].

A mathematical model has been created to obtain the cooling thermal profile of AISI 1020 steel bar. This code was created using EES, Engineering Equation Solver, which is a calculator where it is allowed write the equations without manipulating them and there are AISI 1020 properties on its library. Uniform temperature has been considerate for each bar. The total control volume has been divided in nine small control volumes [4], each bar is your own control volume boundary.

An experiment has been done to validate the mathematical model.

Methodology The experiment consists in four thermocouples placed on the center of selected bars recording the temperature every 30 seconds. A comparison has been done between the experimental and the mathematical model to obtain the deviation of the model.

Experimental setup The experiment consists in obtain the thermal profile of nine piled bars. The bars have been piled three by three. They are distributed in three rows and three columns.

A resistive electric oven was used in this experiment with chamber dimensions of 200 x 170 x 300 mm. The chamber is thermally insulated by low density fiber. The heating resistors are inside the walls and the roof.

The process of heating the bar up 150 °C and approximate to homogenous temperature takes 90 minutes. The heating rate was set as 150 °C / hour, and then the oven reaches the target temperature around 50 minutes and other 40 minutes are necessary to obtain a homogeneous temperature.

Fig. 1 illustrated the evolution of the experiment configuration. When the bars reaches an uniform temperature around 150 °C, first, stage 1, three of them are removed from the oven and placed over All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP, www.ttp.net. (ID: 187.20.23.103-29/08/14,04:06:38)

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the wood support being the first row and two thermocouple are placed on the first two bars for obtain the thermal profile. Second, stage 2, five minutes later the first load, another three bars are removed from the oven and placed over the first three bars being the second row and one thermocouple is placed on the first bar of the second row. Finally, stage 3, five minutes later from the second load, the last three bars are placed over the six bars being the third row and one thermocouple is placed on the first bar of the third row and all thermocouple register the temperature until the experiment completes 45 minutes.

Figure 1. Stages 1, 2 and 3 of the experiment.

The thermocouples were placed in the middle of the three axes in each bar. The data logger was set to take the bar temperature every 30 seconds. There is a thermo hygrometer to register the temperature, humidity and pressure of the environment.

Mathematical model The mathematical model has been developed considering heat transfer by radiation and convection.

The conduction was neglected because of an assumption that there is no deformation between the bars, and then there is just a single line of contact.

Some assumptions were made to simplify the mathematical model such as considering the bars as diffuse and gray surface, uniform temperature for each bar based on the Biot number.

A gray surface may be defined as one of which emissivity and absortivity are independent of wavelength over the spectral region of the irradiation and the surface emission. Practically speaking, a diffuse and gray surface is one which emissivity and absortivity are directional and wavelength independent.

The Biot number consists in an assumption of uniform temperature when the resistance to conduction within the solid is much smaller than resistance to convection across the fluid boundary layer. Typical Biot number as criteria is 0.1. The Biot number is evaluated by the Eq. 1. Then, the mathematical model assumes uniform temperature for each bar [5].

(1) Where is the sum of heat transfer coefficient by radiation and convection, W/m /K, is the characteristic length, m, and k is the conductivity, W/m/K. The Fig. 2, present the tag for mentioning each bar as well the environment.

2

Figure 2- Tags of bars and environment

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The Eq. 2, 3, 4 and 5 represents the energy balance for each bar at stage 1, 2 and 3.

(2) Where m is bar’s mass, is the specific heat, has been approximated by , and is the heat transfer coefficient by convection and radiation respectively, A is the area and is the view factor.

Where i=1, 2 and 3 and j=0, 1, 2 and 3 to the stage 1.

Where i=1, 2, 3, 4, 5 and 6 and j=0, 1, 2, 3, 4, 5 and 6 to the stage 2.

Where i=1, 2, 3, 4, 5, 6, 7, 8 and 9 and j=0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 to the stage 3.

(3) (4) (5) -8

2

4

Where is the emissivity, is the Stefan Boltzmann constant, 5.67 E W/m /K , is the dimensionless number Nusselt, is the dimensionless number Raylaigth, is the gravity, is the volumetric thermal expansion coefficient, is the diameter, is the kinematic viscosity and is the thermal diffusivity. Nusselt number is defined as shown in the Eq. 6 for Rayleigh number up to 10E12 [6].

(6) For two parallel cylinder with equals radius, r, separated by a distance, s, the radiation view factor, , is defined by Eq. 7 [7]. Considering the bar 5, it is easily observed all radiation is transfer by neighboring bars then the diagonal radiation view factor is defined by Eq. 8.

(7) (8) Results An infrared thermal camera, was used to evaluated a bar’s emissivity. Into the software ThermaCAM Researcher Professional has been used with an insulating with known emissivity aiming to obtain the bar emissivity [8]. The result obtained for the bar emissivity was 0.91.

Fig. 3, Fig. 4, and Fig. 5 presents the comparison between experiments and mathematical model results for the bars 1, 4 and 7.

Figure 3. Comparison between experiment and mathematical model for bar 1

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Figure 4. Comparison between experiment and mathematical model for bar 4

Figure 5. Comparison between experiment and mathematical model for bar 7 The percentage deviation follows the Eq. 9. Table 1 shows a summary of the five results with the average and maximum percentage deviation of five experiments.

(9) Table 1 presents the summary of the results of each experiment where T1, T4 and T7 represent the thermocouple on bar 1, 4 and 7 respectively.

Table 1. Summary of the results of the experiments Experiment 1 2 3 4 5

Deviation Average Maximum Average Maximum Average Maximum Average Maximum Average Maximum

T1 12% 17% 5% 10% 13% 20% 13% 20% 8% 15%

T4 3% 10% 7% 19% 12% 18% 9% 15% 5% 13%

T7 7% 14% 7% 17% 4% 11% 4% 10% 11% 16%

Discussion and Conclusion The Fig. 3 and 4 show a discontinuity on the experiment temperature profile due to second and third loading, the same behavior was detected by the mathematical model. The temperature of mathematical model and experiment beginning with the same value, Fig. 3 indicates a gain of energy when the second and third loading enter to the system, which reveal, although small, the presence of diffusive process.

The same behavior is presented on Fig.4 and the gain of energy is observed when the third row is loaded. Near to the end of the experiments the experimental temperature is lower than mathematical

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model temperature, one possible explanation is the equation used to evaluate the heat transfer coefficient into the cavities or the view factor used in radiation calculation.

The mathematical model does not take advantage of the finite volume techniques and it is observed on the accuracy. However the code is cheap and can be implemented in any software calculator. Furthermore, the average and maximum deviation encountered were about 8% and 20% respectively, which is similar to the heating process results encountered for billets heating of an industrial process [9].

References [1] W.D. Callister: Materials science and engineering, edited by John Wiley & Sons, New York, NY (2007).

[2] A.L.V.C. Silva and P.R. Mei: Aços e ligas especiais, edited by Edgard Blücher, São Paulo (2008) [3] M. Kutz: Mechanical Engineering Handbook, edited by John Wiley & Sons, New York, NY (1998).

[4] C.S. Assunção: Glendon Siderúrgico: Análise termodinâmica e modelagem matemática simplificada (Master Thesis), Universidade Federal de Minas Gerais (2006).

[5] T.L. Bergman, A.S. Lavine, F.P Incropera and D.P DeWitt: Fundamentals of heat and mass transfer, edited by John Wiley & Sons, New York, NY (2011).

[6] S.W. Churchill and H.H. Chu: Correlating equations for laminar and turbulent free convection from a horizontal cylinder, International Journal of Heat and Mass Transfer, volume 18, 9, 1049-1053 (1975).

[7] R. Siegel and J.R. Howell: Thermal radiation heat transfer, edited by Taylor & Francis, New York, NY (2002).

[8] M. Mario: Uso da Termografia Como Ferramenta Não Destrutiva Para Avaliação de Manifestações Patológicas Ocultas, Information on http://www.lume.ufrgs.br/bitstream/handle/10183/34409/000789733.pdf?sequence=1 (2011).

[9] C.V. Magalhães: Modelagem matemática do aquecimento de carga em forno siderúrgicos (Master Thesis), Universidade Federal de Minas Gerais (2000).

Mechanical and Aerospace Engineering V 10.4028/www.scientific.net/AMR.1016

Experimental and Numerical Analysis Applied on Steel Bars Cooling 10.4028/www.scientific.net/AMR.1016.342