Study on interfacial heat transfer behavior of TA15 titanium alloy and die materials

Study on interfacial heat transfer behavior of TA15 titanium alloy and die materials

International Journal of Heat and Mass Transfer 108 (2017) 1573–1578 Contents lists available at ScienceDirect International Journal of Heat and Mas...

1MB Sizes 0 Downloads 14 Views

International Journal of Heat and Mass Transfer 108 (2017) 1573–1578

Contents lists available at ScienceDirect

International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

Study on interfacial heat transfer behavior of TA15 titanium alloy and die materials Meng Xu a, Rui Ling b, Zhihao Zhang a,⇑, Jianxin Xie a a b

Institute for Advanced Materials and Technology, University of Science and Technology Beijing, Beijing 100083, China School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, China

a r t i c l e

i n f o

Article history: Received 16 September 2016 Received in revised form 21 December 2016 Accepted 23 December 2016

Keywords: TA15 titanium alloy Die steel Interfacial heat transfer coefficient (IHTC) Glass lubricant

a b s t r a c t The curves of contact temperature-time between TA15 titanium alloy and H13 die steel with glass lubrication and without glass lubrication were obtained and the characteristics of the interface heat transfer were analyzed. The corresponding graph and empirical formula between the interfacial heat transfer coefficient (IHTC) and the temperatures of both the titanium alloy and the die steel were established. The results show that glass lubricant can reduce the interfacial heat transfer between the titanium alloy and the die steel effectively. When the initial temperatures of the titanium alloy and the die steel are respectively 700–800 °C and 340–400 °C, the temperature of the contact interface tends to be stable at the time of about 15 s under the condition of glass lubrication, which is about 50% longer than that without glass lubricant. The IHTC is increased from 125 W/(m2 °C) to 1000 W/(m2 °C) with the increase of the contact time under the condition of glass lubrication, while it is increased from 150 W/(m2 °C) to 1800 W/ (m2 °C) without glass lubrication. The empirical formula of IHTC obtained in this paper has high accuracy that the error between the simulated and experimental results is less than 10%. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Titanium alloy is the key material in aerospace, marine engineering, national defense and other fields due to many excellent properties, such as low density, good corrosion resistance, high strength and high temperature resistance [1–4]. Compared with the ferrous metals and other non-ferrous metals, titanium alloy has more unique physical, chemical and mechanical properties. Therefore, the plastic processing of titanium alloy has its own particularity [5], such as high processing temperature, narrow processing temperature range, high deformation resistance, poor surface quality and microstructural inhomogenity [6]. The processing yield, dimensional precision, surface quality, microstructure and properties of titanium alloy products have close relationship with temperatures of billet and die in the process of plastic processing [7]. For example, in the process of titanium alloy forging and extrusion, if the billet temperature, die temperature, forming rate and other parameters is incoordinate, it will lead to a large temperature difference between the surface of the billet and the center, causing the metal flow serious nonuniformity, and the products surface easy to crack [8]. In addition, the

⇑ Corresponding author. E-mail address: [email protected] (Z. Zhang). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.12.078 0017-9310/Ó 2016 Elsevier Ltd. All rights reserved.

die is prone to failure when the extrusion load is overload [7]. Therefore, how to effectively control the heat transfer process of billet and die is one of the key problems in the plastic processing of titanium alloy [9], and an accurate IHTC between titanium alloy and die is needed to be obtained. In heat transfer theory [10], the IHTC is a parameter which describes the heat transfer between interfaces and is often considered as a constant value in ideal conditions. However, an ideal condition is difficult to achieve in practice and the IHTC is influenced by many complicated factors [11]. Contact pressure and die temperature have great influence on interfacial heat transfer coefficient for press hardening applications [12]. In the process of interface heat transfer, the interface heat transfer coefficient varies according to different interface temperature and pressure [13]. Shojaefard and Goudarzi [14] have studied the heat transfer between stainless steel and aluminum based steady-state experiments. A study of the IHTC as a function of temperature and pressure was done by Malinowski et al. [15]. An investigation of die temperature changes and the heat transfer coefficient during hot forging of TC4 titanium alloy was carried out using experiments and a thermal-plastic coupled finite element analysis [9]. However, the studies on influence factors of the IHTC of TA15 titanium alloy plastic forming with lubrication are limited. In the formulation or optimization of extrusion, forging and other plastic forming process, if the heat transfer coefficient is set as a constant value, it usu-

1574

M. Xu et al. / International Journal of Heat and Mass Transfer 108 (2017) 1573–1578

Nomenclature A hc k Q Tc TH13 TTA15

contact surface area (m2) interfacial heat transfer coefficient (W/(m2 °C)) slope of temperature T variation with the heat transfer distance X (temperature gradient, dT/dX) heat flux (W) temperature of interface contact surface (°C) interface temperature of H13 steel (°C) interface temperature of TA15 alloy (°C)

ally leads to large errors. Therefore, it is necessary to determine the change of the IHTC with the temperatures of the die and alloy billet. In this paper, taking the extrusion of TA15 titanium alloy with glass lubrication as simulation object, the heat transfer process between die and titanium alloy with glass lubrication and without glass lubrication were studied, and the curves of the contact surface temperature with the change of contact time were measured. Based on the calculation of IHTC, the IHTC between the titanium alloy and the die steel was obtained, and the corresponding relationship graph and function equation of the IHTC with the temperatures of the titanium alloy and the die steel were established. Furthermore, the above function was verified by comparing the numerical simulation results and the experimental results.

2. Experimental methods The experimental materials are TA15 titanium alloy and H13 die steel. According to the extrusion characteristics of titanium alloy, the simulation device of interface heat transfer experiment was designed as Fig. 1. The diameter of both die steel and titanium alloy was U20 mm. For the accuracy of temperature measurement

MTS Testing Machine

Die Steel

Computer

1 2

Lubricant

3

5 6

Subscripts exp exponential function sin Sine function

and subsequent calculated temperature gradient, 3 blind holes with a diameter of U1 mm and a depth of 10 mm were made at an interval of 5 mm, and the first hole started at a distance of 1 mm from the end of die steel and titanium alloy. The exposed K thermocouple was selected as the temperature sensor in order to reduce the response time, and was fixed by ultrafine MgO powder in the blind hole in order to keep good contact with the apex. The thermocouple was connected with a multi-channel signal processing module, and the temperature data was collected by a multi-channel data acquisition card. The thickness of lubricant coating is about 1 mm in the extrusion process of the titanium alloy. In this paper, therefore, the glass lubricant powder was coated directly on the end face of the die steel and the thickness of the powder glass lubricant between titanium alloy and die steel was 1 mm (the thickness of loose lubricant). The glass lubricant is supplied by Beijing Tian Lichuang Science and Technology of Glass Develop Co.,Ltd. The main composition of the lubricant is shown in Table 1. This paper mainly studies the relationship between the interface temperature and the heat transfer coefficient. After adding the glass lubricant, a resistance type heating furnace was used to heat the cylindrical specimen to a predetermined temperature. Because the glass lubricant is filled into interface gap at the high temperature, the heat transfer medium is the glass heat transfer medium instead of the air. At this point, the interface heat transfer coefficient changes with the temperature of the interface, so the pressure is set to a certain value. The pressure was applied through a MTS material testing machine. According to our previous experiments, the pressure applied in the experiment was about 12 MPa, because the higher pressure would lead to the deformation of samples at high-temperature and the lower pressure couldn’t make the lubricant compact. According to the data measured by the interfacial heat transfer experiment, the contact heat transfer coefficient can be calculated by Eq. (1):

hc ¼ Q =ðDT c  AÞ

Heat Furnace 4

Greek symbol D difference function k thermal conductivity (W/(m °C)) p circumference ratio

Data Acquisition card

Titanium Alloy

where Q is the heat flux (W); DTc is the temperature difference between two ends of contact interface (°C); A is the contact surface area (m2). From the Eq. (1), the IHTC can be obtained when the DTc and Q were measured. DTc is the temperature difference between position 3 and 4 of the experimental device in Fig. 1. Heat flux Q can be calculated according to the Fourier law [10]:

Q ¼kAk

Fig. 1. Schematic illustration of interface heat transfer experimental equipment.

ð1Þ

ð2Þ

where k is the thermal conductivity (W/(m °C)), and its value comes from the related textbooks [10]; k is the slope of temperature T variation with the heat transfer distance X (temperature gradient, dT/dX). In this paper, the temperature data of position 1 2, 3 or 4, 5, 6 is used to obtain more accurate data.

1575

M. Xu et al. / International Journal of Heat and Mass Transfer 108 (2017) 1573–1578 Table 1 The composition of glass lubricant (wt.%). SiO2

Al2O3

B2O3

Na2O

CaO

MgO

BaO

ZnO

LiO

40

4

25

15

5

3

5

2

1

Substituting Eq. (2) into Eq. (1), the IHTC can be expressed as Eq. (3):

hc ¼ ðk  kÞ=DT c

ð3Þ

The calculated heat transfer coefficient and the corresponding temperatures of the titanium alloy and die steel were summarized in the graph. Then the three-dimensional coordinates were taken into the MATLAB software for surface fitting to obtain the corresponding empirical formula of the IHTC and the temperatures of the titanium alloy and die steel. Finally, the temperature field data was got by taking the corresponding empirical formula into Deform simulation software for heat transfer calculation. The simulated temperature field data and the corresponding experimental data are compared to verify the accuracy of the corresponding empirical formula of the heat transfer coefficient and the temperatures of the titanium alloy and die steel 3. Results and discussion 3.1. Interface heat transfer characteristics between TA15 titanium alloy and H13 die steel The heat transfer between the titanium alloy and die steel was studied under the conditions that the interface temperature of TA15 was 700–800 °C and the interface temperature of H13 was 340–400 °C. Multiple experiments were carried out with glass lubricant. Meanwhile, in order to compare the heat transfer behavior under the condition without lubrication, another heat transfer experiment of the direct contact between the titanium alloy and the die steel was added. The temperature-time variation curves of the TA15 titanium alloy and H13 die steel are shown in Fig. 2. The curves 1–6 represent the temperature changes of the position 1–6 in Fig. 1, respectively, and the curves 3 and 4 are the temperature changes of the contact surface. The starting point of heat transfer is the change point of the slope of the curve, and the ending point is about the intersection point of the two tangent lines. Fig. 2(a) is a group of interface heat transfer experimental curves with the glass lubricant. The temperature changes of the 6 measured points can be seen from the Fig. 2(a). When the interfaces contact, only the temperature change of the contact surface is the most intense (curves 3 and 4) and the interface heat transfer process is between the two dotted lines, which indicates that the

3.2. Determination of IHTC between TA15 titanium alloy and H13 die steel According to the temperature-time data obtained from the multi groups of experiments (2 groups of typical data in Fig. 2), the IHTC of the titanium alloy and the die steel were calculated by Eqs. (1) and (2). The temperature-time data of the TA15 titanium alloy and the H13 die steel at the contact surface and the corresponding IHTC were summarized in Fig. 3. The temperature curves in the figure correspond to the left longitudinal axis, and the IHTC curve corresponds to the right longitudinal axis. Curves 1 and 2 are the temperature change of the die steel and the titanium alloy, respectively, and the curve 3 is the change of IHTC . As shown in Fig. 3(a), when the interface temperature of the TA15 alloy and the H13 steel is 770 °C and 380 °C, respectively, the IHTC is increased from 125 W/(m2 °C) to 1000 W/(m2 °C) in the process of heat transfer with lubricant. However, the IHTC is gradually increased from 150 W/(m2 °C) to 1800 W/(m2 °C) without lubricant, as shown in Fig. 3(b). The numerical value of heat transfer coefficient hC is related to the values of k, DTc and k, as shown in Eq. (3). The k can be set to a fixed value due to its small change in the temperature range, and DTc and k are variables. According to the data in Fig. 2(a), the DTc is gradually decreased from 380 °C to 145 °C and the k is gradually increased from 7 °C/ mm to 18 °C/mm with the temperature change of the contact interface, and then the value of k/DTc is gradually increased, which indicates that the IHTC hc = (kk)/DTc is gradually increased with time under the lubricant condition. Similarly, in the condition of no lubrication, the IHTC hc = (kk)/DTc is increased with time, because the DTc is decreased from 380 °C to 50 °C and k is increased from 8 °C/mm to 21 °C/mm with the temperature change

(b)

(a)

800

6

700

5

TA15

4

600 Heat transfer

H13

500

3 2 1

Temperature/

Temperature/

temperature of the contact interface tends to be stable after about 15 s. Fig. 2(b) is the interfacial heat transfer curve without lubricant. The time in which the interfacial temperature reaches a stable value decreases to about 10 s. Therefore, the thermal resistance of the interface is increased by adding glass lubricant. Because of the glass lubricant in the contact interface, the actual contact area of the specimen and the number of hot runners at the interface is reduced. Moreover, the thermal resistance of the glass is larger than that of the metal, so the IHTC between the titanium alloy and the die steel is reduced.

TA15 Heat transfer

H13

400 0

5

10

15

20

Time/s

25 30

35

40

Time/s

Fig. 2. Measured temperature changes of the titanium alloy and the die steel with contact time: (a) with lubricant; (b) without lubricant.

M. Xu et al. / International Journal of Heat and Mass Transfer 108 (2017) 1573–1578

1 2

H13 TA15

3

hc

(a) 3 2

1250

750 500

1

250 0

5 10 15 20 25 30 35 40

(b)

1000

hc(W/m2· )

Heat transfer

Temperature/

800 750 700 650 600 550 500 450 400 350

hc(W/m2· )

Temperature/

1576

Heat transfer

0

Time/s

Time/s

Fig. 3. The temperature and IHTC changes of contact surface between the titanium alloy and the die steel with contact time: (a) with lubricant; (b) without lubricant.

of the contact interface (Fig. 2(b)). The heat transfer coefficient without lubricant is larger than that with lubricant, because the decrease amplitude of DTc and increase amplitude of k is larger. According to the above experimental data with lubricant, the temperatures of the titanium alloy and the die steel as well as the corresponding heat transfer coefficient are summarized in Fig. 4 . The IHTC is gradually increased from 200 W/(m2 °C)to 1300 W/(m2 °C) with the increase of the die steel temperature and the decrease of the titanium alloy temperature, as shown in Fig. 4. This result can provide a basal data for the hot working process and the simulation process of titanium alloy. For example, the change of the IHTC is very small in the process of rapid extrusion and rolling, due to the small change of the interface temperature. Therefore, the fixed value of IHTC can meet the requirement of numerical simulation in engineering application. However, the IHTC varies in a great range when the change of the interface temperature is large, and the fixed value of the IHTC leads to large error during the numerical simulation. Therefore, the heat transfer coefficient must be set to a variable with the interface temperature. After importing the data from Fig. 4 into MATLAB software by Excel and fitting by the sftool in MATLAB, the relationship of the IHTC between the temperatures of the titanium alloy and the die steel can be expressed as Eq. (4):

hc ¼ 778:6  6:436 sinð0:3674p  T H13  T TA15 Þ þ 0:634expðð0:1114T TA15 Þ2 Þ

ð4Þ

where hc is the IHTC (W/(m2 °C)); TH13 is the interface temperature of H13 steel (°C); TTA15 is the interface temperature of TA15 alloy (°C). Eq. (4) described the IHTC between the surface temperature of the titanium alloy and die steel well, which has a broad applicability for the numerical simulation and a good guidance in selecting the heat transfer boundary conditions of titanium alloy hot working. 3.3. Verification of IHTC between TA15 titanium alloy and H13 die steel The finite element simulation technology of plastic processing has become more and more mature. The accuracy of simulation is determined by the accurate plastic constitutive relation, the heat transfer boundary condition, the friction boundary condition and so on. In order to verify the accuracy of IHTC in Eq. (4), the heat transfer behavior of the TA15 titanium alloy and H13 die steel was simulated by Deform software. The model of interface heat transfer between the titanium alloy and die steel is shown in Fig. 5. The front end of the sample exposed in air was used as the research object in order to facilitate the analysis. The expression of heat transfer coefficient Eq. (4) was taken into Deform software for simulation calculation of heat transfer, and the initial temperatures of the die steel and titanium alloy were 380 °C and 770 °C, respectively. The gradient distribution of simulation temperature in the heat transfer process is shown in Fig. 6. The central temperature in the sample is greater than the edge temperature due to air heat

740 200 250

720 700

Titanium temperature/

Constant Heat Source

300 350 400 450

500

680

550

600

660 640 620 600

650 700

750 800 850 900 950 1000 1050 1100 1150 1200 1250 1300

Air Radiation Heat Transfer Coefficient h=20 W/( m2• )

Die steel (start at 380 )

Glass Lubricant

Titanium Alloy (start at 770

Air Radiation Heat Transfer Coefficient h=20 W/( m2• )

)

580 400

420

440

460

480

500

520

540

Die temperature/ Fig. 4. Relationship of interface temperature and IHTC between the TA15 titanium alloy and the H13 die steel.

Constant Heat Source Fig. 5. Simulation model of interface heat transfer between titanium alloy and die steel.

1577

M. Xu et al. / International Journal of Heat and Mass Transfer 108 (2017) 1573–1578

(a)

(b)

(d)

(c)

A=383 B=412

Die Steel

Die Steel

Die Steel

Die Steel

C=435 D=461 P=622 Q=638 R=654 S=670 T=685 U=701

Titanium Alloy

Titanium Alloy

Titanium Alloy

Titanium Alloy

V=717 W=733 X=749

Fig. 6. Simulated temperature distribution between the H13 die steel and the TA15 titanium alloy: (a) 5 s; (b) 10 s; (c) 15 s; (d) 20 s.

transfer on the model surface, so the central temperature was used in the analysis of heat transfer process. The temperature variation of the H13 die steel and TA15 titanium alloy is shown Fig. 6(a–d). When the heat transfer is carried out to 5 s, the contact surface temperature of the die steel is increased from 380 °C to 412 °C, and the contact surface temperature of the titanium alloy is decreased from 770 °C to 717 °C (Fig. 6(a)). When the heat transfer is carried out to 15 s, the contact surface temperature of the die steel is increased to about 461 °C and the contact surface temperature of the titanium alloy is decreased to about 638 °C (Fig. 6(c)). However, when the time is further prolonged to 20 s, the temperature field is similar to that of 15 s, the temperature of the die steel is slightly greater than 461 °C and the temperature of the titanium alloy is slightly decreased to about 622 °C, which indicates that the temperature is basically stable after heat transfer time above 15 s. The temperature measured in the experiment is the center temperature of contact surface, therefore, it also takes the temperature field data at the center of the contact surface as the simulation value in the simulation process of the heat transfer. The interface temperature-time curves obtained from both the simulation of Fig. 6 and the experiment were summed up in a graph, as shown in Fig. 7(a). The curves tend to be the horizontal state after 15 s,

which indicates that the heat transfer at the interface is basically stable at about 15 s. The temperature deviation between the simulated values and the experimental values is less than 10%. Similarly, in order to make the results more convincing, another heat transfer experiment as well as related simulation is carried out, and the results are summarized in Fig. 7(b). The temperature deviation between the simulated values and the experimental values is less than 10%. It indicates that the interfacial heat transfer behavior in the experiment is consistent with that in the simulation process and verifies the high accuracy of heat transfer coefficient in Eq. (4). The systematic uncertainty mainly includes the experimental temperature measurement error, the calculating error of the interface heat transfer coefficient and the deform simulation error. In the process of the experiment, measurement results error is mainly affected by the precision of the thermocouple and the selection of the temperature measuring point, therefore, the center point of the sample is selected as the measured point for the accuracy of the experiment. The heat transfer coefficient is calculated by heat transfer equation, and 3 temperature measurement points are set up. k(dT/dX) is obtained by multiple sets of calculated mean values for the accuracy, and then the heat flux (Q) is obtained from the formula Q = kAk. A certain error between the results of deform

(b)

(a)

Simulated Value Experimental Value

Temperature/

Titanium Alloy

Temperature/

Simulated Value Experimental Value

Titanium Alloy

Die Steel

Die Steel

Time/s

Time/s

Fig. 7. Comparison of simulated and experimental values in interfacial heat transfer process: (a) Contrast with raw data; (b) Contrast with new data.

1578

M. Xu et al. / International Journal of Heat and Mass Transfer 108 (2017) 1573–1578

simulation and the actual experiment results is inevitable because the simulation process is a simplified process of the actual experiment, which is induced by the simulation software. 4. Conclusions (1) Glass lubricant can effectively reduce the interfacial heat transfer between the titanium alloy and the die steel. When the initial temperatures of the titanium alloy and the die steel are respectively 700–800 °C and 340–400 °C, the temperature of the contact interface tends to be stable at a time of about 15 s under the condition of glass lubrication, which is about 50% longer than that of without glass lubricant. (2) When the initial temperature of the titanium alloy and the die steel are 700–800 °C and 340–400 °C, respectively, the IHTC is increased from 125 W/(m2 °C) to 1000 W/(m2 °C) with the increase of the contact time under the condition of glass lubrication, while it is increased from 150 W/ (m2 °C) to 1800 W/(m2 °C) without glass lubrication. (3) The corresponding relation graph and empirical formula between the interfacial heat transfer coefficient (IHTC) and the temperatures of both the titanium alloy and the die steel were obtained, and the empirical formula was established as follow:

hc ¼ 778:6  6:436 sinð0:3674p  T H13  T TA15 Þ þ 0:634expðð0:1114T TA15 Þ2 Þ (4) The formula of IHTC has high accuracy that the error between the simulation and experimental results is less than 10% in this paper. Acknowledgments This work was supported by the National Key Research and Development Program of China under contract number 2016YFB0300900.

References [1] M.H. Rausch, A. Leipertz, A.P. Fröba, Dropwise condensation of steam on ion implanted titanium surfaces, Int. J. Heat Mass Transf. 53 (1–3) (2010) 423–430. [2] L. Li, K. Yu, K. Zhang, Y. Liu, Study of Ti–6Al–4V alloy spectral emissivity characteristics during thermal oxidation process, Int. J. Heat Mass Transf. 101 (2016) 699–706. [3] Zhichao Sun, H. Yang, Microstructure and mechanical properties of TA15 titanium alloy under multi-step local loading forming, Mater. Sci. Eng., A 523 (1) (2009) 184–192. [4] X.G. Fan, H. Yang, P.F. Gao, R. Zuo, P.H. Lei, The role of dynamic and post dynamic recrystallization on microstructure refinement in primary working of a coarse grained two-phase titanium alloy, J. Mater. Process. Technol. 234 (2016) 290–299. [5] W. Pachla, M. Kulczyk, S. Przybysz, J. Skiba, K. Wojciechowski, M. Przybysz, et al., Effect of severe plastic deformation realized by hydrostatic extrusion and rotary swaging on the properties of CP Ti grade 2, J. Mater. Process. Technol. 221 (2015) 255–268. [6] W. Peng, W. Zeng, Q. Wang, Q. Zhao, H. Yu, Effect of processing parameters on hot deformation behavior and microstructural evolution during hot compression of as-cast Ti60 titanium alloy, Mater. Sci. Eng., A 552.2 (2014) 384–391. [7] D. Damodaran, R. Shivpuri, Prediction and control of part distortion during the hot extrusion of titanium alloys, J. Mater. Process. Technol. 150 (1–2) (2004) 70–75. [8] J.X. Xie, J.A. Liu, Theory and Technology of Metal Extrusion, Metallurgical Industry Press, Beijing, 2012. [9] Z.M. Hu, J.W. Brooks, T.A. Dean, The interfacial heat transfer coefficient in hot die forging of titanium alloy, ARCHIVE Proceedings of the Institution of Mechanical Engineers Part C J.Mech.Eng.Sci. 1989-1996 (vols 203–210) 212 (1998) 485–496. [10] S.M. Yang, W.Q. Tao, Heat Transfer Theory, Higher Education Press, Beijing, 2006. [11] Y. Chang, X. Tang, K. Zhao, P. Hu, Y. Wu, Investigation of the factors influencing the interfacial heat transfer coefficient in hot stamping, J. Mater. Process. Technol. 228 (2014). [12] J. Mendiguren, R. Ortubay, E.S.D. Argandoña, Experimental characterization of the heat transfer coefficient under different close loop controlled pressures and die temperatures, Appl. Therm. Eng. 99 (2016) 813–824. [13] M. Merklein, J. Lechler, T. Stoehr, Investigations on the thermal behavior of ultra high strength boron manganese steels within hot stamping, Int. J. Mater. Form. 2 (2) (2009) 259–262. [14] M.H. Shojaefard, K. Goudarzi Goudarzi, The numerical estimation of thermal contact resistance in contacting surfaces, Am. J. Appl. Sci. 5 (11) (2008) 1566– 1571. [15] Z. Malinowski, J.G. Lenard, M. Davies, E A study of the heat-transfer coefficient as a function of temperature and pressure, J. Mater. Process. Technol. 41 (2) (1994) 125–142.