U.P.B. Sci. Bull., Series B, Vol. 78, Iss. 4, 016 ISSN 1454-1 STUDY REGARDING THE THERMAL PROPERTIES OF THE IRON OXIDES AND THEIR APPLICATION IN THE PROCESS OF THE HEAT TRANSFER FROM THE FURNACE HEARTH TO THE INGOT Beatrice Adriana CÂRLAN 1, Dan CONSTANTINESCU, Nicolae CONSTANTIN The iron oxides resulted from thermal processes have an important role in the analysis of the heat transfer particularities and in finding new methods of reducing the energy consumptions. Searching the specialty literature, there are not enough data regarding the thermal properties of the iron oxides. This is the main reason the authors have sampled the iron oxides and analyzed them in laboratory. The experimental values of the thermal properties of the iron oxides were then applied in a mathematical model in order to obtain a new parameter, the global coefficient of heat transfer, from the furnace hearth to the inferior surface of the steel ingot. Keywords: iron oxides, heat transfer, properties, experimental data 1. Introduction During thermal processes in metallurgy, it is important in many cases to know the exactly particularities of the heat transfer, in a complex system formed by materials with different properties. It may be included the heating in view of forming, thermal isolation structures or the complex material structures. [1] In the case of steel ingots heating, it can be taken into consideration the heat exchange by convection and radiation, or the heat transfer inside the material, by conductivity. The system may be composed by metal (the ingot), the metallic oxide (iron oxides), which may result from the previously thermal processes and the ceramic material (hearth of the aggregate) [] (Fig. 1). While the hearth temperature is higher than the ingot temperature, the sense of the thermal flow will be from the hearth to the ingot. It can be written [], [4]: 1 PhD student, Faculty of Materials Science and Engineering, University POLITEHNICA of Bucharest, Romania; corresponding author s e-mail: beatrice.carlan@yahoo.com; Prof., Dept. of Metallic Materials Processing and Eco-metallurgy, University POLITEHNICA of Bucharest, Romania, e-mail: danco@ines.ro; Prof., Dept. of Engineering and Management of Metallic Materials Obtaining, University POLITEHNICA of Bucharest, Romania, e-mail: nctin014@yahoo.com.
170 Beatrice Adriana Cârlan, Dan Constantinescu, Nicolae Constantin : thermal conductivity of the oxides; δ: thickness of the oxide layer; : thermal resistivity; k: global coefficient of heat transfer from the hearth to the ingot. It results: Because. (1) () () Fig. 1. The temperature in the system ingot-oxide-hearth (Source: D. Constantinescu et al, 01, [4]). The thermal properties of the iron oxides Having such an important role in the heating of the steel ingots, it is necessary to obtain data regarding the thermal properties of the iron oxides..1 Chemical composition and structure of the iron oxides On the purpose of determine the chemical composition of the iron oxides, the used method was the diffraction on powders, with the diffractometer X
Study regarding the thermal properties of the iron oxides and their application in the process 171 X Pert PRO MPD, PANalytical. After the laboratory analyses, there were obtained the results presented in Figs. and. Fig.. Iron oxides diffractograme for FeO+Fe O +Fe O 4 (Source: D. Constantinescu et al, 01, [4]) Fig.. Iron oxides chemical composition and ratio (Source: D. Constantinescu et al, 01, [4]). The thermal conductivity and thermal capacity of the iron oxides Analyzing the theoretical data of thermal conductivity (from specialty literature), there were deduced the values until the temperature of 1400 0 C, using the polynomial regression (Fig. 4) [5].
17 Beatrice Adriana Cârlan, Dan Constantinescu, Nicolae Constantin Thermal conductivity, kj/mhk 10,0 9,5 9,0 8,5 8,0 7,5 7,0 6,5 6,0 5,5 5,0 4,5 4,0,5,0,5,0 Y =-,19+0,0081 X-1,497E-0 X R: 0,9985 <0.0001 1,5 1,0 0,5 0,0 00 00 400 500 600 700 800 900 1000 1100 100 100 1400 Temperature, 0 C F6 PolyFit_F6 Fig. 4. Theoretical thermal conductivity for FeO+Fe O +Fe O 4, deduced by polynomial regression (Source: D. Constantinescu et al, 01, [4]) According to the theoretical data, it results that te value of the thermal conductivity on 80 0 C temperature is zero, but this is not corresponding to reality. Therefore, it intervened the need to perform some experimental analysis, to may establish the values of the iron oxides thermal conductivity (Fig. 5). 10 9 Thermal conductivity, kj/mhk 8 7 6 5 4 1 Y =1,1045+,818E-4 X+,798E-6 X R: 0,99999 <0.0001 F6 PolyFit_F6 0 100 00 00 400 500 600 700 800 900 1000 1100 100 100 1400 Temperature, 0 C Fig. 5. Experimental thermal conductivity for FeO+Fe O +Fe O 4 (Source: D. Constantinescu et al, 01, [4])
Study regarding the thermal properties of the iron oxides and their application in the process 17 In Fig. 6, there are presented some data for the thermal capacity and the thermal conductivity of the iron oxides, using data from the technical literature. [6], [7] Y1: Thermal capacity, kj/kg K 0,9 0,90 0,88 0,86 0,84 0,8 0,80 0,78 0,76 0,74 0,7 0,70 0,68 FeO Fe O 4 Fe O 0 00 400 600 800 1000 100 1400 1600 X: Temperature, o C 10 9 8 7 6 5 4 Y : Thermal conductivity, kj/mhk Fig. 6. Thermal capacity and conductivity of the oxide layer, using theoretical data (Source: D. Constantinescu, 011, [8]). The thermal resistivity of the iron oxides The thermal resistivity is the inverse of the thermal conductivity. It was determinated by calculus, depending of the thickness of the iron oxides layer (which was considered from 1 to 10mm) and temperature (from 700 to 1400 0 C). In table 1, there are presented values of the thermal resistivity, using theoretical thermal conductivity data, depending of the iron oxides layer thickness and in Fig. 7, it is the graphic representation of the thermal resistivity.
174 Beatrice Adriana Cârlan, Dan Constantinescu, Nicolae Constantin Table 1 Values of the thermal resistivity, using theoretical data, W/m K (Source: D. Constantinescu et al, 01, [4]) Thickness of the iron oxides layer Temperature δ 1 δ δ δ 4 δ 5 δ 6 δ 7 δ 8 δ 9 δ 10 0 C 1mm mm mm 4mm 5mm 6mm 7mm 8mm 9mm 10mm 700 871 45 90 18 174 145 14 109 97 87 800 1161 581 87 90 194 166 145 19 116 900 1451 76 484 6 90 4 07 181 161 145 1000 166 81 54 406 5 71 0 181 16 1100 1858 99 619 464 7 10 65 06 186 100 090 1045 697 5 418 48 99 61 09 100 1161 774 581 464 87 90 58 1400 554 177 851 69 511 46 65 19 84 55 r t, W/m K 600 400 00 000 1800 1600 1400 100 1000 800 600 400 00 0 600 700 800 900 1000 1100 100 100 1400 1500 Temperature, 0 C r 1 pentru =1mm r pentru =mm r pentru =mm r 4 pentru =4mm r 5 pentru =5mm r 6 pentru =6mm r 7 pentru =7mm r 8 pentru =8mm r 9 pentru =9mm r 10 pentru =10mm Fig. 7. Thermal resistivity of the iron oxides layer, using theoretical data (Source: D. Constantinescu et al, 01, [4]) In table, there are presented values of the thermal resistivity, using experimental thermal conductivity data, depending of the iron oxides layer thickness and in Fig. 8, it is the graphic representation of the thermal resistivity.
Study regarding the thermal properties of the iron oxides and their application in the process 175 Values of the thermal resistivity, using theoretical data, W/m K Thickness of the iron oxides layer Table Temperature δ 1 δ δ δ 4 δ 5 δ 6 δ 7 δ 8 δ 9 δ 10 0 C 1mm mm mm 4mm 5mm 6mm 7mm 8mm 9mm 10mm 700 890 445 96 178 148 17 111 98 89 800 100 515 4 57 06 171 147 18 114 10 900 110 605 40 0 4 01 17 151 14 11 1000 1400 700 466 50 80 00 175 155 140 1100 1610 805 56 40 68 0 01 178 161 100 1848 90 61 460 68 06 6 0 04 184 100 080 1040 69 50 416 46 97 60 1 08 1400 0 1165 776 58 466 88 91 58 r t, W/m K 400 00 000 1800 1600 1400 100 1000 800 r 1 pentru grosime de 1mm r pentru grosime de mm r pentru grosime de mm r 4 pentru grosime de 4mm r 5 pentru grosime de 5mm r 6 pentru grosime de 6mm r 7 pentru grosime de 7mm r 8 pentru grosime de 8mm r 9 pentru grosime de 9mm r 10 pentru grosime de 10mm 600 400 00 0 600 700 800 900 1000 1100 100 100 1400 1500 Temperature, 0 C Fig. 8. Thermal resistivity of the iron oxides layer, using experimental data
176 Beatrice Adriana Cârlan, Dan Constantinescu, Nicolae Constantin. The evaluation of the global coefficient of heat transfer If it is considered that on the contact surface between the furnace hearth and the steel ingot, the sense of the thermal flow will be from the hearth to the ingot (Fig. 1), than: 1 1 a1 (for thesteelingot) (4) y a y (for theiron oxides layer) (5) a y (for the furnace hearth) (6) θ 1, θ, θ : temperatures of the three components of the system; τ: time; a=λ/cρ: thermal diffusivity. The temperature in the middle of the oxide layer is presented in eq. 7: S m y v const. (7) The temperature fluctuation in the oxide layer is transferred almost linear: y m (8) The heat transferred from the hearth, by a surface element, ds, in the time dτ, in the point y=0 is presented in equation 9. d Q dsd rt m dsd y (9) Replacing, it is obtained:
Study regarding the thermal properties of the iron oxides and their application in the process 177 r t (10) The relative coefficient of heat transfer is noted with χ (equation 11): r t (11) To calculate the relative coefficient of heat transfer it was chosen as refractory material of the furnace hearth, the chamotte. In Fig. 9 it is presented the relative coefficient of heat transfer, χ, calculated using the theoretical values of thermal resistivity, depending on the thickness of the oxide layer (which fluctuates between 1 and 10mm), in the temperature interval 700-1400 0 C. Relative coefficient of heat transfer, m -1 1600 1400 100 1000 800 600 400 00 0 0 1 4 5 6 7 8 9 1mm mm mm 4mm 5mm 6mm 7mm 8mm 9mm 10mm Data for furnace hearth 1-700 0 C; -800 0 C; -900 0 C; 4-1000 0 C; 5-1100 0 C; 6-100 0 C; 7-100 0 C; 8-1400 0 C Fig. 9. Relative coefficient of heat transfer (using theoretical data of thermal resistivity)
178 Beatrice Adriana Cârlan, Dan Constantinescu, Nicolae Constantin In Fig. 10 it is presented the relative coefficient of heat transfer, χ, calculated using experimental values of thermal resistivity, depending on the thickness of the oxide layer (which fluctuates between 1 and 10mm), in the temperature interval 700-1400 0 C. Relative coefficient of heat transfer, X 1500 1400 100 100 1100 1000 900 800 700 600 500 400 00 00 100 1mm mm mm 4mm 5mm 6mm 7mm 8mm 9mm 10mm 0 1 4 5 6 7 8 9 Data for furnace hearth 1-700 0 C; -800 0 C; -900 0 C; 4-1000 0 C; 5-1100 0 C; 6-100 0 C; 7-100 0 C; 8-1400 0 C Fig. 10. Relative coefficient of heat transfer (using experimental data of thermal resistivity) Applying a function proposed by P. Frank and R. Mises, [9] the form of the function for the analysed case will be: e a v m a dsd m 1 where Φ is the symbol for Gauss function (equation 1). ( ) 0 e d d Q e C dsd dq ds C v S 1 c C v S e C d 1 o (1) (1) (14) (15)
Study regarding the thermal properties of the iron oxides and their application in the process 179 Comparing () with (15), the global coefficient of heat transfer will be defined: dq k v s c ds (16) C C k e 1 C d c 0 (17) b c a (coefficient of heat penetration) (18) The final form of the coefficient k is presented in equation 19. k 0 b c c c [Jm - K -1 ] (19) In Fig. 11 it is presented the global coefficient of heat transfer, calculated for a chamotte furnace hearth, depending on the stationary time of the steel ingot on the hearth (which fluctuates between 10 and 100 hours). Global coefficient for heat transfer, J/m K 0,65 0,60 0,55 0,50 0,45 0,40 0,5 0,0 0,5 0,0 0,15,=10h,=0h,=0h,=40h,=50h,=60h =70h,=80h,=90h,=100h 600 700 800 900 1000 1100 100 100 1400 1500 Temperature, 0 C Fig. 11. Global coefficient of heat transfer (using as refractory material for hearth the chamotte)
180 Beatrice Adriana Cârlan, Dan Constantinescu, Nicolae Constantin Therefore, the global coeficient of the heat transfer, k, is dependent only on the coefficient of heat penetration, b and the stationary time of the steel ingot on the furnace hearth. Along with the increasing of the contact duration, τ c, the coefficient of heat transfer, k, is decreasing. 4. Conclusions Because in the technical literature are not too many data regarding the thermal properties of the iron oxides, the authors have sampled it and analyzed in laboratory. The main goal was to compare the theoretical with the experimental data, but also to apply it in mathematical models, in order to determine new methods of reducing the energy consumptions. The analyzed mathematical model has in view the establishing of the global coefficient of heat transfer, k, from the furnace hearth to the inferior surface of the steel ingot. The thermal sense of the coefficient k is similar with the global coefficient of heat transfer by radiation and convection, from the burned gases to the free surfaces of the ingot. The k coefficient depends of the thermal parameters of the hearth material and steel ingot, separated from the hearth with a metallic oxide layer. R E F E R E N C E S [1] Brunklaus J. Henry, Cuptoare industrial (Industrial furnaces), Edtura Tehnica, Bucharest, 1977. [] Dan Constantinescu, A heat transfer model regarding the contact zone of a heavy ingot with the heating furnaces hearth, in Metalurgia International, vol. 16, April 011, pp. 141. [] Dan Constantinescu, Cristian Predescu, Paul Tudor, Mirela Sohaciu, Avram Nicolae, Termotehnica metalurgica (Metallurgical Heat Engineering), Editura Printech, Bucharest, 00, ISBN-97-65-7-9. [4] Dan Constantinescu, Andrei Berbecaru, Mihai Brânzei, Beatrice Adriana Cârlan, George Coman, Preliminary study concerning the role of the thermo-physical factors during the heating processes of the heavy ingots for forging, in Metalurgia International, Special Issue no., vol. 18, February 01, pp. 158. [5] Raznjevik Kuzman, Tabele si diagrame termodinamice (Heat engineering tables and diagrams), Editura Tehnica, Bucharest, 1978. [6] W. Heiligenstaedt, Thermique appliqué aux fours industriels, Ed. Dunod, Paris, 1971. [7] Hütte, Manualul Inginerului (Engineer Book), Editura Tehnica, Bucharest, 1995, ISBN 97-1-091-4. [8] Dan Constantinescu, Mathematical model for complex heat transfer between metal and refractory aggregate material, METAL 011, May, p. 148, ISBN 978-80-8794--. [9] O. Pawelski, Berechnung der Wärme durchgangszah für Wärmwalzen und Schmieden, Archiv für Eisenhüttenwesen, BRD, 40, nr. 10, p. 81-88.