ISSN 1067-8212, Russian Journal of Non-Ferrous Metals, 2016, Vol. 57, No. 7, pp. 686–694. © Allerton Press, Inc., 2016. Original Russian Text © V.E. Bazhenov, A.V. Koltygin, Yu.V. Tselovalnik, 2016, published in Izvestiya Vysshikh Uchebnykh Zavedenii, Tsvetnaya Metallurgiya, 2016, No. 5, pp. 42–51.
FOUNDRY
Determination of the Heat-Transfer Coefficient between the AK7ch (A356) Alloy Casting and No-Bake Mold V. E. Bazhenov*, A. V. Koltygin**, and Yu. V. Tselovalnik*** National University of Science and Technology MISiS, Moscow, 119049 Russia *e-mail:
[email protected] **e-mail:
[email protected] ***e-mail:
[email protected] Received June 5, 2015; in final form, July 7, 2015; accepted for publication July 9, 2015
Abstract—The heat-transfer coefficient h between a cylindrical cast made of AK7ch (A356) aluminum alloy and a no-bake mold based on a furan binder is determined via minimizing the error function, which reflects the difference between the experimental and calculated temperatures in the mold during pouring, solidification, and cooling. The heat-transfer coefficient is hL = 900 W/(m2 K) above the liquidus temperature (617°C) and hS = 600 W/(m2 K) below the alloy solidus temperature (556°C). The variation in the heat-transfer coefficient in ranges hL = 900–1200 W/(m2 K) (above the alloy liquidus temperature) and hS = 500–900 W/(m2 K) (below the solidus temperature) barely affects the error function, which remains at ~22°C. It is shown that it is admissible to use a simplified approach when constant h = 500 W/(m2 K) is specified, which leads to an error of 23.8°C. By the example of cylindrical casting, it is experimentally confirmed that the heat-transfer coefficient varies over the casting height according to the difference in the metallostatic pressure, which affects the casting solid skin during its solidification; this leads to a closer contact of metal and mold at the casting bottom. Keywords: computer simulation of casting processes, ProCast, interfacial heat-transfer coefficient (iHTC), no-bake sand mold (NBSM), thermal properties DOI: 10.3103/S1067821216070038
INTRODUCTION The broad extension of computer simulation (CS) systems of casting processes considerably simplified the prediction of the results of the application of casting technology in practice. The abundance of CS programs [1, 2] led the American Association of Computational Mechanics to begin verifying CAE systems (V&V process) in 1999 [3]. However, the adequacy of the CS results from various software products is not always identical to the results from casting of actual cast products. This fact is associated not only with the computer model implemented in a given program but also with the thermal properties of the materials and boundary conditions that are taken into account in the calculation. The multifactor character of the problem means that, in order to attain reliable CS results, they must be compared with experiments and the initial data applied in the model should be subsequently refined. In order to acquire adequate CS results, a series of boundary conditions should be determined, in addition to the thermal properties of the materials. The heat-transfer coefficient between the casting and mold h, or the interfacial heat-transfer coefficient (iHTC), is one of the most important characteristics. The h is not constant and depends on many parameters, such as the pressure (for example, during direct rolling [4]
and high pressure die casting [5, 6]); the gap between the surfaces of casting and mold, which appears during casting shrinkage and thermal mold expansion [2, 7]; mold surface roughness; the atmosphere in the casting–mold gap [8]; and the thickness and composition of the dye coating used [9]. For example, when casting AZ91D (ML5) magnesium alloy into a mold made of a no-bake sand mold (NBSM) based on furan resin, the heat-transfer coefficient is the largest in a range from the pouring temperature to the liquidus temperature. An air gap appears between the casting solid skin and mold during the solidification due to the linear shrinkage. This circumstance leads to an abrupt decrease in coefficient h. Its magnitude is almost invariable in a definite temperature range and remains constant [10]. The authors of [11] determined the heat-transfer coefficient when casting ASTM A890 Gr. 5A steel into the NBSM mold. In this case, a sufficiently high level of h remained down to 1000°C, which is much lower than the solidus temperature of aforementioned steel (1350°C). The h became almost constant below 1000°C. The high value of the heat-transfer coefficient at a temperature below the solidus temperature in the case of casting high-melting alloys is associated with the fact that, when the gap between the casting and the
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mold forms, heat is largely transferred by radiation. A similar dependence is observed when casting into metallic molds [12]. The simplest method to determine the heat-transfer coefficient was used in [13]. The authors compared the experimental solidification time of the aluminum alloy casting in a sand mold with the solidification time calculated at various values of the heat-transfer coefficient. In this manner, the value (h = 500 W/(m2 K)) that is most often used in calculations was found. The use of a constant heat-transfer coefficient for calculations continuing below the alloy solidus temperature (for example, when calculating stresses in a casting [14]) is incorrect. Values of h are most often found to be time-dependent [4, 7, 10, 11, 15–17] and temperature-dependent [5, 10, 11]. In order to determine the heat-transfer coefficient from experimental data the inversion method and other computational methods are used [4, 6, 10, 11]. The main criterion, which allows us to evaluate the difference between the experimental and calculated results, is the error function Err. This function is generally described by the following equation [11]: n
Err =
∑ (t
− te ) , 2
c
(1)
i =1
where tc and te are the calculated and experimental temperature in the mold and a casting, °C, respectively; and n is the number of measurements. The goal of this study was to determine the heattransfer coefficient during the fabrication of a cylindrical casting of the A356 alloy in an NBSM mold to improve the adequacy of simulation results in the ProCast program. EXPERIMENTAL Smelting of Alloy, Casting Process, and Temperature Recording during Casting Solidification As the charge materials, we used the commercial AK7ch (A356) alloy (GOST (State Standard) 1583–93) and magnesium Mg90 (99.9 wt % Mg) (GOST 804–93) to compensate the magnesium loss during smelting. The alloy was prepared in a high-frequency induction furnace in a clay graphite crucible. The alloy was poured into a mold at 690°C. A cylindrical casting 50– 56 mm in diameter and 150 mm in height was fabricated. To fabricate the mold, quartz sand 2K1O302 (0.2 mm), Furtolit Q105 furan resin, and Härter SR 85 catalyst (Furtnebach GmbH, Austria) were used.
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Fig. 1. Mold in assembly with mounted thermocouples.
Resin in the amount of 15 g (1.5 wt %) and catalyst in the amount of 6 g (0.6 wt %) were added to 1 kg of sand. Molding was performed layer by layer in four flasks. After molding the bottom flask, four thermocouples were mounted over the parting line with the second flask, etc. The mold was arranged on a plate made of aluminum alloy. The appearance of the assembled mold is shown in Fig. 1. Thermocouples were arranged at three height levels (Fig. 2): the bottom level—thermocouples T1, T2, T3, and T4; the medium level—thermocouples T5, T6, T7, and T8; and the top level—thermocouples T9, T10, T11, and T12. Thermocouples T1, T5, and T9 were arranged on the surface of the working mold cavity. The distance between the levels by height was 40 mm and the distance between the thermocouples of one level along the horizontal was 10 mm. Readings of chromel–alumel thermocouples were recorded with a frequency of 1 second using a BTM4208SD 12-channel temperature recorder (Lutron, Israel). The alloy composition was determined using an ARL-4460 multichannel optical emission spectrometer (Thermo Fisher Scientific, United States).
Simulation of Casting Pouring and Solidification Casting pouring and solidification was simulated in the ProCast program, version 2013.5 (ESI Group, France). The simulation parameters are presented in
Table 1. Parameters of simulation of casting filling and solidification Alloy temperature, °C
Mold characteristics filling time, s
initial temperature, °C
solidus
liquidus
pouring
8
25
556
617
690
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I
II
developed by CompuTherm LLC (United States) and contained in the ProCast program. The alloy density was calculated in the Thermo-Calc program (Thermo-Calc Software, Sweden) using the corresponding TCAL1 thermodynamic database. The thermal characteristics of the mold (NBSM based on a furan binder) were taken from [18]. The computational mesh consisted of ≈615000 elements.
III
9 10 11 12
40 mm
10 mm
56 7 8
1 2 3 4
20 mm
IV
Fig. 2. Arrangement diagram of thermocouples in the mold. I is the casting, II is the mold, III are the flasks, and IV is the plate.
Table 1. The mold filling time was determined by timekeeping. The temperature dependences of thermal conductivity, enthalpy, density, solid phase fraction, and liquidus and solidus alloy temperatures were calculated using the thermodynamic base for the computation of thermal properties of aluminum alloys
ANALYSIS OF RESULTS The composition of the alloy according to the results of chemical analysis is presented in Table 2. The fabricated alloy corresponds to the AK7ch (A356) grade by the composition, excluding small excesses of magnesium, iron, and copper, which are not of a fundamental character. The temperature dependences of thermal conductivity (λ), heat capacity (c), and density (ρ) of the AK7ch alloy as calculated in the ProCast program are shown in Fig. 3. The properties of the A356 alloy (analog of the AK7ch alloy) according to the data [19–21] are also shown there. We can see (Fig. 3a) that the alloy thermal conductivity calculated in the ProCast program (curve 1) is rather close to the data found in [20] (curve 2). Dependence 3 [21] is substantially different; it is evidently not quite correct, since it does not show an abrupt variation in thermal conductivity associated with crystallization/melting. The values of heat capacity in [19] and [21] (4 and 3 in Fig. 3b, respectively) agree well with the results of calculation in the ProCast program. We failed to find the experimental temperature dependence for the density of the A356 alloy; therefore, we compared the calculated values found in the ProCast program (curve 1 in Fig. 3c) and the Thermo-Calc program (curve 5). It is seen that they almost coincide. We used the thermal properties of a NBSM mold based on furan resin for the simulation [18]. Figure 4 shows the temperature dependences of the thermal conductivity, heat capacity, and density of the phenol NBSM (curve 1), furan NBSM (curve 2), and quartz sand (curve 3) taken from [11, 18, 19], respectively. Dependences λ(t) (Fig. 4a) of materials under consideration are close. Their temperature dependences are also almost identical (Fig. 4b). The authors of [11] found two peaks in line c(t) for a NBSM based on a
Table 2. Composition of the alloy, wt % Alloying elements
Impurities, no larger
Alloy
Obtained AK7ch (A356)
Al
Si
Mg
Bal.
6.01
0.58
Bal.
6.0–8.0
Mn
Cu
Zn
Ti
Ni
Results of chemical analysis 0.07 0.57 0.30
0.20
0.02
0.02
0.30
0.15
–
0.25–0.45
Fe
GOST 1583–93 0.50 0.50
0.20
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(а)
λ, W/m K 250
(b)
c, kJ/kg K 1.5
200
1
1.3 2
689
1 4
150
1.1 3
100
0.9 3
50 0
200
400
600
800 t, °C
0.7 0
200
400
600
800 t, °C
600
800 t, °C
(c)
ρ, g/cm3 2.8 5 2.7 3
1
2.6
2.5
2.4
2.3 0
200
400
Fig. 3. (a) Thermal conductivity, (b) heat capacity, and (c) density of the AK7ch (A356) alloy (Table 2) against the temperature. (1) ProCast, (2) [20], (3) 21, and (4) [19], and (5) Thermo-Calc.
phenol binder that correspond to the heat effects of water evaporation (~100°C) and thermal destruction of resin (~320°C). These effects are usually excluded from the curve of heat capacity. The graphic temperature dependence of density for the NBSM based on a phenol binder (curve 2 in Fig. 4c) is presented only in [18]. We recorded the temperature fields in a mold to τ = 1500 s from the beginning of pouring. Upon reaching this time (by the results of simulation), the mold surface, which was in contact with the flask, was heated. RUSSIAN JOURNAL OF NON-FERROUS METALS
This fact means that further variation of the temperature field begins to be affected by the heat-transfer coefficients between the mold and aluminum flasks, as well as between the mold and aluminum plate. It is rather complicated to determine several heat-transfer coefficients for various interfaces simultaneously. The primary analysis of recording temperature fields in the mold showed that the value of temperature recorded by thermocouple T2 differs from the calculated value by 80–100°C on average. This phenomenon may be
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(а)
λ, W/m K 1.0
(b)
c, kJ/kg K 1.5
1.3 0.8
1
2 1
1.1
0.6
3 2
0.4
0.2 0
0.9
3
200
0.7
400
600
800 t, °C
0.5 0
200
400
600
800 t, °C
(c)
ρ, g/cm3 1.44
1.42
2
1.40
1.38
1.36 0
200
400
600
800 t, °C
Fig. 4. (a) Thermal conductivity, (b) heat capacity and (c) density of materials against the temperature. (1) NBSM based on phenol binder [11], (2) NBSM based on furan binder [18], and (3) quartz sand.
caused by the fact that the thermocouple is shifted relative to the position specified in the calculation for the molding process. For this reason, thermocouple T2 was excluded from further analysis. It was noted above that the magnitude of the heattransfer coefficient between the casting and mold varies during solidification. Until the alloy is in the liquid state, good contact between metal and mold is observed and the heat-transfer coefficient is high. In
the course of solidification, a gap is formed between the solid skin and inner mold surface (due to linear casting shrinkage during cooling and thermal expansion of the mold upon heating), and the heat-transfer coefficient decreases. In this study, we simulated mold filling and casting solidification at various values of heat-transfer coefficient h specified in the form of the plot presented in Fig. 5. We selected the values of hL from 400 to
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cient varied linearly from hL to hS in the crystallization range. Based on the experimental results and simulation results for each combination of hL and hS, we calculated the error function tErr according to the formula derived from expression (1):
h, W/m2 K
hL
⎡ 11 1500 i, j t Err = ⎢ t c − t ei, j ⎢⎣ j =1 i =1
∑∑(
tL
556
t, °C
617
Fig. 5. Schematic plot of the temperature dependence of the heat-transfer coefficient.
1200 W/(m2 K) with a step of 100 W/(m2 K) above the liquidus temperature (617°C) and the values of hS from 100 to 900 W/(m2 K) with the same step while the solidus temperature (556°C). The heat-transfer coeffi(a)
hL, W/m2 K 800
⎦
(11 ⋅ 1500),
(b)
hL, W/m2 K 1200
700
2⎤
) ⎥⎥
23 1100
24
600
25
400 100
200
300
400
500 hS, W/m2 K
900 500
21.7
21.75
21.8
21.85
21.9
20.05 22.0
27
32
31
28 29 30
21.95
1000
26 500
600
700
800 900 hS, W/m2 K
Fig. 6. Calculated values of tErr (°C) for ranges of (a) hL = 400–800, hS = 100–500 W/(m2 K) and (b) hL = 900–1200, hS = 500– 900 W/(m2 K). RUSSIAN JOURNAL OF NON-FERROUS METALS
(2)
where t ci, j , t ei, j are the calculated and experimental temperatures, respectively, in time instant i (from 1 to 1500 s) for thermocouple j (from 1 to 11). The error function reflects the average difference between the experimental and calculated values of temperature (in °C) in the mold. This quantity is clearer than the error function Err calculated according to Eq. (1). The calculated values of tErr (°C) for regions of values of hL from 400 to 800 W/(m2 K) an hS from 100 to 500 W/(m2 K) are shown in Fig. 6a. We can see that the error decreases upon increasing hL and hS, and the desired heat-transfer coefficient is higher. Figure 6b shows the results of the calculation of tErr (°C) for hL = 900–1200 W/(m2 K) and hS = 500–900 W/(m2 K). In the range of these values of the heat-transfer coefficient, the error function is almost invariable and lies within the limits of 21.6–22.1°C. This circumstance can be caused by a small shift in the arrangement of thermocouples in the performance of the experiment
hS tS
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t, °C 600
t, °C 600
(а)
500
(b)
T5c
500 T5e
T1c
400
400
300
T1 T3e
200
T6e
e
300
T3c
T7e
T6c
200 T7c
100
100 T4e
T4c
T4
0
e
T8c
0 0
300
700
1100
1500 τ, s
t, °C 600
0
300
700
1100
1500 τ, s
(c)
500
T9c
400
T10c
T9e
300 T11e
200
T10e T11c
100 T12e
T12c
0 0
300
700
1100
1500 τ, s
Fig. 7. Experimental T e (solid lines) and calculated T c (dashed lines) cooling curves for thermocouples T1–T12 (excluding T2) at hL = 900 and hS = 600 W/(m2 K).
relative to the calculated points in a model or by an insignificant difference in thermal properties of materials used in modeling and experiments. The value of the error function is not identical both for thermocouples arranged at various levels (by height) and for thermocouples established at one level but arranged at various distances from the casting surface. Readings of thermocouples arranged immediately at the contact interface of metal with the mold (T1, T5, and T9) are the most important, and the min-
imal value of the error function was found for them at hL = 900 and hS = 600 W/(m2 K). Figure 7 shows the experimental T e (solid lines) and calculated T c (dashed lines) cooling curves for thermocouples T1–T12 (excluding T2) at hL = 900 and hS = 600 W/(m2 K). We can see that the calculated cooling curves for thermocouples at the bottom level T3, T4 (Fig. 7a) and medium level T7, T8 (Fig. 7b), which are arranged at a distance of 20 and 30 mm from the casting–mold interface, considerably differ from
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in the top part, and the heat-transfer coefficient in the top casting part is smaller than in the bottom part. The use of thermal properties of the AK7ch (A356) alloy and a NBSM mold based on furan binder, which were taken from the database of the ProCast program, allowed us to calculate the reliable temperature distribution in the mold. The calculated cooling curves according to readings of 11 thermocouples differ from the experimental cooling curves by no more than 22°C. Herewith, the values of the heat-transfer coefficient giving such a result lie in a rather broad range. For a more exact coincidence of the experimental and calculated cooling curves, we should use the experimental thermal properties of the alloy and mold material.
d, mm 60
2
58
693
1 56
54
52
50 0
40
80
120
160 l, mm
Fig. 8. Diameters (d) of the casting obtained experimentally (1) and of the pattern by which the mold cavity was molded (2), depending on their height (l).
the experimental. The calculated and experimental cooling curves for thermocouples of the bottom and medium levels arranged at the casting–mold interface (T1, T5, and T6) almost coincide. An inverse pattern is observed for the top-level thermocouples T9–T12 (Fig. 7c). Larger deviations of the calculated cooling curves from the experimental ones are observed for thermocouples approached the casting–mold interface (T9, T10). The deviations of the calculated and experimental curves for thermocouples arranged at a distance of 20 mm (T11) and 30 mm (T12) are considerably smaller. The heat-transfer coefficient varies over the casting height, because the metallostatic pressure and plasticity of the solidified casting skin affect the air gap between metal and mold [22]. Figure 8 shows the results of measurements of diameters of the casting fabricated in the experiment and of the casting pattern, by which the mold cavity was molded, depending on the height. We can see that the casting and pattern diameters almost coincide in the bottom part, which is associated with the fact that the forming solid skin in the casting is pressed to the mold wall under the effect of the metallostatic pressure (which is maximal in the bottom casting part). The difference between the pattern and casting diameters in the top casting part is considerably larger, because the metallostatic pressure is considerably lower. Consequently, the gap between the casting and the mold during solidification is larger RUSSIAN JOURNAL OF NON-FERROUS METALS
CONCLUSIONS By means of comparing the experimental and calculated cooling curves, we determined the heat-transfer coefficient upon the fabrication of a cylindrical casting 50 mm in diameter made of AK7ch (A356) aluminum alloy in a mold made of NBSM based on furan binder. We found the following results. (1) Using the thermal properties of the mold (taken from [18]) and alloy (calculated with the help of the thermodynamic database of the ProCast program), the heat-transfer coefficients between the casting and the mold were determined in ranges above the liquidus temperature hL = 900 W/(m2 K) and below solidus temperature hS = 600 W/(m2 K). These coefficients provide the value of the error function, which reflects the difference between the experimental and calculated temperatures in the mold no larger than 22°C. (2) It is established that the variation in the heattransfer coefficient in limits hL = 900–1200 W/(m2 K) and hS = 500–900 W/(m2 K) when simulating casting into NBSM molds barely affects the average value of the error function, which remains equal ~22°C. (3) It is found that the heat-transfer coefficient varies over the casting height, which is associated with the variation in the metallostatic pressure that affects the forming metal skin during the solidification. It is confirmed that, in order to obtain simulation results identical to the those of the experiment, it is possible to use the calculated thermal characteristics of the alloy and mold properties from [18]. REFERENCES 1. Tikhomirov, M.D., Comparsion of thermal problems in “Poligon” and “ProCast” simulation software of casting processes, in: Komp’yuternoe modelirovanie liteinykh protsessov (Computer Simulation of Casting Processes: Collected Works), vol. 2, St. Petersburg: Tsentr. Nauch.-Issl. Inst. Mater., 1996, p. 22. 2. Tikhomirov, M.D., Simulation of Thermal and Shrinkage Processes during the Solidification of Castings of
Vol. 57
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3.
4. 5.
6.
7.
8.
9.
10.
11.
BAZHENOV et al. High-Strength Aluminum Alloys and the Development of the Computer Analysis Model of Casting Technology, Extended Abstract of Cand. Sci. (Eng.) Dissertation, St. Petersburg: St. Petersburg Gos. Politekh. Univ., 2004. Borovkov, A.I., Burdakov, S.F., Klyavin, O.I., Mel’nikova, M.P., Mikhailov, A.A., Nemov, A.S., Pal’mov, V.A., and Silina, E.N., Komp’yuternyi inzhiniring (Computer Engineering), St. Petersburg: St. Petersburg Politekh. Univ., 2012. Wang, D., Zhou, C., Xu, G., and Huaiyuan, A., Heat transfer behavior of top side-pouring twin-roll casting, J. Mater. Proc. Technol., 2014, vol. 214, pp. 1275–1284. Griffiths, W.D. and Kawai, K., The effect of increased pressure on interfacial heat transfer in the aluminium gravity die casting process, J. Mater. Sci., 2010, vol. 45, no. 9, pp. 2330–2339. Sun, Z., Hu, H., and Niu, X., Determination of heat transfer coefficients by extrapolation and numerical inverse methods in squeeze casting of magnesium alloy AM60, J. Mater. Process. Technol., 2011, vol. 211, pp. 1432–1440. Nishida, Y., Droste, W., and Engler, S., The air-gap formation process at the casting-mold interface and the heat transfer mechanism through the gap, Metall. Mater. Trans. B, 1986, vol. 17B, pp. 833–844. Bouchard, D., Leboeuf, S., Nadeau, J.P., Guthrie, R.I.L., and Isac, M., Dynamic wetting and heat transfer at the initiation of aluminum solidification on copper substrates, J. Mater. Sci., 2009, vol. 44, no. 8, pp. 1923– 1933. Lu, S.-L., Xiao, F.-R., Zhang, S.-J., Mao, Y.-W., and Liao, B., Simulation study on the centrifugal casting wet-type cylinder liner based on ProCAST, Appl. Therm. Eng., 2014, vol. 73, pp. 512–521. Chen, L., Wang, Y., Peng, L., Fu, P., and Jiang, H., Study on the interfacial heat transfer coefficient between az91d magnesium alloy and silica sand, Exp. Therm. Fluid Sci., 2014, vol. 54, pp. 196–203. Palumbo, G., Piglionico, V., Piccininni, A., Guglielmi, P., Sorgente, D., and Tricarico, L., Determination of interfacial heat transfer coefficients in a sand mould casting process using an optimised inverse analysis, Appl. Therm. Eng., 2015, vol. 78, pp. 682–694.
12. Zhang, L., Li, L., Ju, H., and Zhu, B., Inverse identification of interfacial heat transfer coefficient between the casting and metal mold using neural network, Energy Conv. Manag., 2010, vol. 51, pp. 1898–1904. 13. Sutaria, M., Gada, V.H., Sharma, A., and Ravi, B., Computation of feed-paths for casting solidification using level-set-method, J. Mater. Process. Technol., 2012, vol. 212, pp. 1236–1249. 14. Baghani, A., Davami, P., Varahram, N., and Shabani, M.O., Investigation on the effect of mold constraints and cooling rate on residual stress during the sandcasting process of 1086 steel by employing a thermomechanical model, Metall. Mater. Trans. B, 2014, vol. 45, pp. 1157–1169. 15. Bertelli, F., Cheung, N., and Garcia, A., Inward solidification of cylinders: reversal in the growth rate and microstructure evolution, Appl. Therm. Eng., 2013, vol. 61, pp. 577–582. 16. Martorano, M.A. and Capocchi, J.D.T., Heat transfer coefficient at the metal-mould interface in the unidirectional solidification of Cu-8%Sn alloys, Int. J. Heat Mass Transfer, 2000, vol. 43, pp. 2541–2552. 17. Griffiths, W.D., A model of the interfacial heat-transfer coefficient during unidirectional solidification of an aluminum alloy, Metall. Mater. Trans. B, 2000, vol. 31B, no. 2, pp. 285–295. 18. Midea, T. and Shah, J.V., Mold material thermophysical data, AFS Trans., 2002, vol. 110, pp. 121–136. 19. Yu, K.-O., Modeling for Casting and Solidification Processing, New York: CRC, 2001. 20. Bakhtiyarov, S.I., Overfelt, R.A., and Teodorescu, S.G., Electrical and thermal conductivity of A319 and A356 aluminum alloys, J. Mater. Sci., 2001, vol. 36, pp. 4643–4648. 21. Bencomo, A.I., Bisbal, R.I., and Morales, R., Simulation of the aluminum alloy A356 solidification cast in cylindrical permanent molds, Revista Materia, 2008, vol. 13, no. 2, pp. 294–303. 22. El-Mahallawy, N.A. and Assar, A.M., Metal-mould heat transfer coefficient using end-chill experiments, J. Mater. Sci. Lett., 1988, vol. 7, pp. 205–208.
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