determination of the metal/die interfacial heat transfer

IOP Conference Series Materials Science and Engineering

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Determination of the metaldie interfacial heattransfer coefficient of high pressure die cast B390alloyTo cite this article Yongyou Cao et al 2012 IOP Conf Ser Mater Sci Eng 33 012010

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Determination of the metaldie interfacial heat transfer

coefficient of high pressure die cast B390 alloy

Yongyou Cao12

Zhipeng Guo12

and Shoumei Xiong12

1 Department of Mechanical Engineering Tsinghua University Beijing 100084 China

2 State Key Laboratory of Automobile Safety and Energy Tsinghua University

Beijing 100084 China

E-mail smxiongtsinghuaeducn

Abstract High-pressure die cast B390 alloy was prepared on a 350 ton cold chamber die

casting machine The metaldie interfacial heat transfer coefficient of the alloy was investigated

Considering the filling process a ldquofingerrdquo-shaped casting was designed for the experiments

This casting consisted of five plates with different thicknesses (005 inch or 127 mm to 025

inch or 635 mm) as well as individual ingates and overflows Experiments under various

operation conditions were conducted and temperatures were measured at various specific

locations inside the die Based on the results the interfacial heat transfer coefficient and heat

flux were determined by solving the inverse heat transfer problem The influence of the mold-

filling sequence sensor locations as well as processing parameters including the casting

pressure die temperature and fastslow shot speeds on the heat transfer coefficient were

discussed

1 Introduction

High-pressure die casting (HPDC) is one of the most economical casting processes for mass producing

net-shaped parts Due to the excellent properties of die castings an increasing number of die casting

products are currently used in the automotive aerospace medical electronic and other industries

Techniques such as computer-assisted design and engineering which have rapidly developed in recent

years are applied in the modeling and simulation of the filling and solidification processes in HPDC

The use of these techniques significantly optimizes processes and saves costs However computer-

based techniques are only beneficial when the material properties as well as the boundary and initial

conditions used as inputs are correct [1]

The interfacial heat transfer coefficient (IHTC) characterizing

the thermal resistance between the metal and the mold is believed to be the one of most important

parameters during the solidification process for computer simulations [2-3]

Numerous studies [1-5]

on

determining the IHTC under various casting conditions have been conducted

In the current paper a die casting experiment was conducted using a ldquofingerrdquo-shaped casting of

B390 alloy The metaldie IHTC was determined according to the temperature readings obtained at

different locations inside the die by solving the inverse heat transfer problems The influence of the

mold filling sequence sensor locations as well as processing parameters including the casting

pressure die temperature and fastslow shot speeds on the heat transfer coefficient were discussed

2 Experiments

21 Finger-shaped casting

MCWASP XIII IOP PublishingIOP Conf Series Materials Science and Engineering 33 (2012) 012010 doi1010881757-899X331012010

Published under licence by IOP Publishing Ltd 1

A specially designed casting namely a finger-shaped casting was used in the current study As

shown in Figure 1 this casting has five plates with different thicknesses from T1 (005 inch or 127

mm) to T5 (025 inch or 635 mm) with an interval of 005 inch (or 127 mm) The biscuit of the

casting was designed with a diameter of 60 mm and a thickness of about 20 mm Each plate is 203 mm

long (along the metal filling direction) and 19 mm wide At the interface between the casting and die

of each plate one-dimensional heat transfer was assumed

Figure 1 Finger-shaped casting (a) configuration and (b) actual casting showing the location of

sensors

Commercial aluminum (Al) alloy B390 (Al-17Si-4Cu) was poured into a TOYO 350 ton cold

chamber high-pressure die casting machine The chemical compositions of the alloy and the die

material H13 steel is given in Table 1

Table 1 Chemical composition of B390 alloy (Al-17Si-4Cu) and H13 steel

Element wt Si Cu Mg Fe Zn Mn Ni Sn Al

B390 1654 463 058 068 082 014 0055 0060 Bal

Element wt C Mn Si S P Cr Mo V Fe

H13 0396 036 094 lt0005 lt0025 505 125 082 Bal

22 Die configuration and sensor installation

To gain a sufficiently rapid response time to follow the HPDC process and accurately measure the

temperatures inside the die a special temperature sensor unit (TSU) was designed As shown in Figure

2 at each distance (1 3 and 6 mm) from the front wall of the TSU two thermocouples were adjusted

The thermocouples were grounded sheathed K-type thermocouples with 05 mm outside diameter and

0045 mm wire diameter These thermocouples were inserted into 11 mm diameter holes and vacuum

nicro-brazed to the TSU body of H13 steel To investigate the influence of filling two TSUs were

located at both ends of each finger plate close to the gate (G) and overflow (F) as illustrated in Figure

1(b)

Figure 3 displays the 10 TSUs containing 60 thermocouples embedded inside the stationary die

until the front wall approached the cavity surface The cooling as well as heating lines were present in

the die at the distance of 25 mm from the parting face in order to control the mold temperature during

HPDC Real-time temperature data were then recorded using a data acquisition system manufactured

by the Integrated Measurement Corporation (Berlin Germany) with a sampling rate of 500 Hz


2

Figure 2 Configuration of the temperature

sensor unit

Figure 3 Graphical installations of temperature

sensor units (TSUs) and data acquisition system in

the cold-chamber die caster

Table 2 lists the thermal properties of B390 alloy and H13 steel The processing parameters

including the casting pressure (P) die temperature (Td) fast shot speed (vH) slow shot speed (vL) and

pouring temperature (TP) were varied in each set of experiment Others were fixed at the same

condition shown in Table 3 Nearly 240 shots were performed the first 20 shots were conducted to

preheat the dies to thermal equilibrium

Table 2 Thermal properties of related materials Table 3 Values of related processing parameters

Thermal properties B390 H13 Processing parameters Basic

condition Variable

Thermal conductance

λ (Wmiddotm-1

middotdegC-1

) 134 312 ndash 0013 T

a

Pouring temperature

TP (degC) 730 700 and 760

Specific heat

C (Jmiddotkg-1

middotdegC-1

) 963 478 ndash 0219 T

Die temperature

Td (degC) 50 150

Density ρ (kgmiddotm-3

) 2730 7730 ndash 024 T Casting pressure

P (MPa) 6998

10109 8381

6739 and

Mina

Solidus temperature TS (degC) 505 1471

Liquidus temperature

TL (degC) 650 1404

Slow shot speed

vL (mmiddots-1

) 02

01 03

04 and 08

Latent heat

Ls (Jmiddotkg-1

) 389000 209350

Fast shot speed

vH (mmiddots-1

) 175

125 15

2 and 25 a T stands for temperature (degC)

a Min stands for no intensification pressure

3 Results and discussion

31 Heat transfer estimation

Figure 4 shows a sample of the measured temperature profiles of the 30 cycles at the T4G position

under the basic condition The temperature profiles of the same position illustrate cyclic characteristics

in shape while the die casting phases were sequentially performed Given that these cycles were

performed under the same operation condition the results showed that the process was quite

reproducible The temperature curves measured at the same distance such as A1 and A2 or C1 and C2

almost overlapped The maximum difference between the two temperature profiles measured at the


3

same distance never exceeded 4 degC indicating that the heat transfer process can be reasonably

assumed to be one dimensional

Figure 4 Sequential temperatures of temperature sensor unit at the T4G position for 30 cycles

under the basic condition

The IHTC cannot be directly calculated using the measured die temperatures because the interfacial

heat flux density (IHFD) cannot be directly measured during casting and solidification However the

computer program used an inverse method [4-6]

based on the principle of Beck [7-8]

The average of

measured temperatures at 1 and 6 mm from the cavity surface (T1 and T6) were used to evaluate IHFD

IHTC and the die surface temperature The inversely calculated temperature at 3 mm from the cavity

surface namely T3c was compared to the average temperature at B1 and B2 measured at the same

distance to validate the inverse modeling Once the shot was performed the IHTC abruptly increased

until reaching the peak value maintained its value at a higher level and then sharply decreased

An analysis using the inverse method at the T4G position with respect to the last cycle of the

measured temperatures (T1 and T6) was subsequently performed as shown in Figure 4 The curves of

IHFD (q) and IHTC (h) as well as the die surface temperature casting center and surface

temperatures designated by Tds Tcc and Tcs were then obtained as shown in Figure 5 There was a

very good fit between the measured (T3m) and calculated (T3c) temperatures at 3 mm indicating that

the inverse estimation results were quite reliable

The casting surface temperature (Tcs) abruptly dropped after the shot was performed only taking 72

ms to drop below the liquidus temperature This result indicated that the molten alloy immediately lost

its superheat after it made contact with the die cavity surface and after a fast heat transfer at the

metaldie interface This phenomenon can be attributed to the prompt rise in the die surface

temperature (Tds) The casting surface temperature then continuously decreased indicating a much

smaller cooling rate as also evidenced in Figure 5 from the smaller slope of the curve

Corresponding to the rapid decrease in the casting surface temperature the IHTC abruptly

increased immediately after the shot was performed This abrupt increase was also associated with the

rapid increase in the IHFD until the peak value of 597 times 106 Wmiddotm

-2 was reached The IHTC kept

growing until reaching 2408 times 103 Wmiddotm

-2middotK

-1 when the IHTC started to fluctuate rising and falling

rapidly The abrupt decrease in the IHTC was due to the fact that the close contact previously achieved

between the casting and the die deteriorated This deterioration was probably caused by the lack of the


4

required pressure transferred from inside as the solidification process proceeded An analysis of the

IHFD curve revealed that after the peak value was reached the heat flux exponentially decayed until

the value was at a much lower level

Figure 5 Typical results at the T4G position during the 30

th cycle under the basic condition T1 T6

and T3m denote the average measured temperatures at 1 6 and 3 mm from the cavity surface

respectively T3c is the inversely calculated temperature at 3 mm from the cavity surface Tds is the

die surface temperature Tcs is the casting surface temperature Tcc is the casting center temperature

q is the interfacial heat flux density h is the interfacial heat transfer coefficient

32 Influence of interfacial heat transfer

321 Casting geometry and sensor location Figure 6 details the related heat transfer curves of IHTC

and IHFD for all positions during the 30th cycle under the basic condition except for the T4F position

due to data recording failure The peak values of IHFD and IHTC are listed in Table 4 Similar trends

in the profiles of both IHTC and IHFD were found However upon careful considerations of the

different sensor locations and thicknesses obvious differences between the corresponding interfacial

heat transfer behaviors of the IHTC and IHFD curves (mainly the shape and peak) were observed

First the peak values of IHTC and IHFD varied with the different positions and casting thicknesses

The IHTC peak of T3G near the gate reached the peak value of 6429 times 103 Wmiddotm

-2middotK

-1 the second

peak value was 4282 times 103 Wmiddotm

-2middotK

-1 of T5G and the lowest peak was 1528 times 10

3 Wmiddotm

-2middotK

-1 of

T1G near the gate of the thinnest plate T1 Similar patterns existed in the IHFD

Second the high retention time of the IHTC varied with the different casting thicknesses Figure 6

clearly shows that this time gradually extends with increased casting thickness

Finally the mold filling sequence of each plate highly depended on the shape of the runner system

The different horizontal distance from each plate to the vertical runner and different size of each ingate

could directly influence the interfacial heat transfer behavior The interfacial heat transfer behavior of

T1F and T3G could be good examples for well explaining this point By comparing the heat transfer

profiles of the four positions in two plates (T1 and T3) to others different trends and special features

could be found For example due to the ingate nearest the vertical runner in T3G the headmost filling

during the fast shot phase caused the overheating of the alloy impacting the surface of the die cavity

This phenomenon created the distinguishing feature of the filling leading to the maximum IHTC As

for the thinnest plate T1 given the farthest distance to the vertical runner and the smallest ingate the

molten alloy abruptly sprayed into the cavity with the simulated velocity of around 110 mmiddots-1


5

compared with the average ingate velocity of 50 mmiddots-1

during the fast shot phase Then the metal jet

first hit the sensor surface of the die cavity near the overflow (T1F) instead of that near the gate

Consequently the IHFD near the overflow (T1F) reached its peak value 792 times 106 Wmiddotm

-2 higher and

76 ms earlier than that near the gate (T1G) even compared with other positions T1 plate was the

thinnest (only 005 inch or 127 mm) hence the quickly occurring solidification led to the slimmest

IHTC profile Helenius et al [9]

have similarly proposed that the peak value of the IHTC is greatly

dependent on the status of the contact between the molten alloy and the die surface where the

thermocouples are installed A high IHTC peak value is observed when the melt alloy directly hits the

location below which the thermocouples are adjusted during their initial contact

Figure 6 Profiles of IHTC and IHFD at all positions during the 30

th cycle under the basic condition

However if the effect of the mold filling is ignored the general trend of the IHTC peaks near the

gate is higher than that near the overflow The high retention time of the IHTC gradually extends with

increased casting thickness

Table 4 Values of qmax and hmax in Figure 6

Sensor locations

qmax values hmax values

Timeb (s)

q times 106

(Wmiddotm-2

) Time

b (s)

h times 103

(Wmiddotm-2

middotK-1

)

Near

overflow

(F)

T1F 2503248 792 2503272 2037

T2F 2503276 583 2503340 1681

T3F 2503328 621 2503508 2319

T4Fa - - - -

T5F 2503324 672 2503592 2597

Near gate

(G)

T1G 2503324 569 2503356 1528

T2G 2503328 561 2503444 1960

T3G 2503240 920 2503604 6429

T4G 2503348 597 2503824 2408

T5G 2503244 861 2503768 4282 a Data at the T4G position failed

b Time of prompt rise point of q and h was about 2503170 s as shown in Figure 6


6

Figure 7 shows the distribution of the IHTC and IHFD peaks at all positions of the finger-shaped

casting for 30 cycles under the basic condition except the T4F position Considering the particular

filling feature for plate T3 wherein the average of IHTC peaks was about 60 times 103 Wmiddotm

-2middotK

-1 the heat

transfer behavior was ignored in the following discussion As for the positions near the gate the peak

range of the IHTC was from 15 times 103 Wmiddotm

-2middotK

-1 to 42 times 10

3 Wmiddotm

-2middotK

-1 A thicker casting

corresponded to a higher average of IHTC peaks The average of IHTC peaks at the T5G position of

the thickest plate was about 42 times 103 Wmiddotm

-2middotK

-1 whereas that at T1G was about 15 times 10

3 Wmiddotm

-2middotK

-1

As for the positions near the overflow a similar pattern was found but the range of the averages was

from 16 times 103 Wmiddotm

-2middotK

-1 to 26times10

3 Wmiddotm

-2middotK

-1 which was lower than that near the gate The fastest

ingate velocity of the thinnest plate T1 severely vibrates the IHTC peaks at the T1F position This

vibration is greater than that on the peaks near the gate

Figure 7 All peak values of IHTC and IHFD at all positions for 30 cycles under the basic

condition T1 to T5 are the five plates from the thinnest to the thickest respectively

322 Initial die surface temperature After a great deal of data analysis of the finger-shaped casting

of B390 the following findings were obtained

(1) The casting pressure had nearly no effect on the IHTC peak value With increased

intensification pressure the distribution of IHTC peaks was more discrete because of the

molten alloy more sharply impacting the die surface

(2) The peak value of IHTC near the gate increased with increased slow shot speed especially

for the plate T5

(3) The peak value of IHTC near the gate mildly decreased with increased fast shot speed

During HPDC process the die temperature changes as the casting is sequentially performed and the

initial die surface temperature (the die surface temperature before injection) on other hand could

characterize the variation of the heat transfer between the metal and the die to some degree After the

thermal equilibrium inside the die was achieved the initial die surface temperatures at different

locations changed in a similar manner the initial die surface temperature gradually grew as the

castings were sequentially performed Considering previous research on metaldie interfacial heat

transfer behavior using the ldquosteprdquo shape casting for AM50 and ADC12 alloys Guo et al[5-6 10]

have

found that the influence of processing parameters on the IHTC was mainly on the peak value The

shape of the IHTC profile was not significantly affected The initial die surface temperature (TIDS) had


7

the dominant influence on the IHTC peak value (hmax) out of all the processing parameters By

correlation analysis the following relationship was found to have the best fit

2

max exp hA

h IDSh B T

(1)

Figure 8 IHFD peaks as a function of the initial die surface temperature under all conditions

Figure 9 IHTC peaks as a function of the initial die surface temperature under all conditions

Figures 8 and 9 illustrate the IHFD and IHTC peaks at 9 positions of 5 plates for about 240 cycles

under all conditions as a set of functions of the initial die surface temperature One of the prominent

characteristics was that all data followed a negative slope versus the initial die surface temperature


8

The other parameters did not show such a large influence including the casing pressure the slow and

fast shot speeds as well as the pouring temperature The peak values of the IHFD and IHTC were

dominated by the initial die surface temperature and changed according to

max

2ln ln lnq q IDS q

IDS

qA T B

T

(2)

max

2ln ln lnh h IDS h

IDS

hA T B

T

(3)

where Aq Bq Ah and Bq are the coefficients of fitting

Equations (2) and (3) show that the peak values of IHFD and IHTC decrease with increased initial

die surface temperature

The coefficients of the fitting the peak value of IHFD and IHTC varied with the sensor location

By considering the IHTC as a function of the temperature gap at the interface the effect of the

initial die surface temperature can be easily understood When the influence of the initial die surface

temperature on the IHTC is considered the explanation becomes easier However the possibility of

the initial temperature of the die influencing the temperature of the liquid metal at the interface is not

without merit and should therefore influence the surface tension As a consequence the micro-contact

conditions may change resulting in the modifications of the heat resistance and interfacial heat

transfer behavior According to the relationship between the peak value of IHTC and the initial die

surface temperature the proper peak value of IHTC could be used for solidification simulation as well

as the function of temperature or solidification fraction considering the casting thickness

4 Summary and conclusions

A detailed method for measuring the heat transfer of B390 alloy during HPDC has been established

using a finger-shaped casting The IHFD and IHTC have been successfully determined based on the

inverse method Based on the results the following conclusions are drawn

(1) The IHTC quickly increases right after the die casting shot until reaching the peak and then

slowly decreases The peak range of the IHTC between the B390 alloy and H13 steel is from

15 times 103 Wmiddotm

-2middotK

-1 to 80times10

3 Wmiddotm

-2middotK

-1

(2) The mold-filling sequence of each plate directly influences the interfacial heat transfer

behavior The general value of the IHTC peak near the gate (from 15 times 103 Wmiddotm

-2middotK

-1 to 42 times

103 Wmiddotm

-2middotK

-1) is higher than that near the overflow (ranging from 16 times 10

3 Wmiddotm

-2middotK

-1 to 26 times

103 Wmiddotm

-2middotK

-1) The high retention time of the IHTC gradually extends with increased casting

thickness

(3) The initial die surface temperature has the most dominant influence on the IHTC peak value

among all the processing parameters With increased initial die surface temperature the IHTC

peak decreases The coefficients of fitting the IHFD and IHTC peaks vary with the sensor

location

Acknowledgments

The current research was funded by the Ministry of Science and Technology (MOST) of China under

contract nos 2011ZX04001-71 2011BAE21B00 2011ZX04014-52 and 2010DFA72760 The die

casting experiments were conducted with the aid of engineers from TOYO Machinery Co Ltd

References

[1] Hamasaiid A Dour G Dargusch M Loulou T Davidson C and Savage G 2006 Heat transfer at

the castingdie interface in high pressure die casting - Experimental results and contribution

to modeling Modeling of Casting Welding and Advanced Solidification Processes - XI (Opio

France 28 May-2 June 2006) (TMS) ed C A Gandin and M Bellet pp 1205-1216


9

[2] Pehlke R D 1964 Unidirectional analysis of heat transfer during continuous casting Met Eng Q

4 42

[3] Pehlke R D and Berry J T 2002 Heat transfer at the moldmetal interface in permanent mold

casting of light alloys Proc from the 2nd Int Aluminum Casting Technology Symp

(Columbus USA 7-9 October) (ASM International) Ed M Tiryakioğlu and J Campbell pp

177-184

[4] Lau F Lee W B Xiong S M and Liu B C 1998 Study of the interfacial heat transfer between an

iron casting and a metallic mould J Mater Process Technol 79 25

[5] Guo Z P Xiong S M Liu B C Li M and Allison J 2008 Effect of process parameters casting

thickness and alloys on the interfacial heat-transfer coefficient in the high-pressure die-

casting process Metall Mater Trans A 39A 2896

[6] Guo Z P 2009 Study on metal ndash die interfacial heat transfer behaviour during high pressure die

casting process Doctor of Engineering (Beijing Tsinghua University)

[7] Beck J V Blackwell B and Haji-Sheikh A 1996 Comparison of some inverse heat conduction

methods using experimental data Int J Heat Mass Tran 39 3649

[8] Helenius R Lohne O Arnberg L and Laukli H I 2005 The heat transfer during filling of a high-

pressure die-casting shot sleeve Mater Sci Eng 413-414A 52

[9] Guo Z P Xiong S M Liu B C Li M and Allison J 2009 Understanding of the influence of

process parameters on the heat transfer behavior at the metaldie interface in high pressure

die casting process Sci in China Ser E-Tech Sci 52 172


10

Determination of the metaldie interfacial heat transfer

coefficient of high pressure die cast B390 alloy

Yongyou Cao12

Zhipeng Guo12

and Shoumei Xiong12

1 Department of Mechanical Engineering Tsinghua University Beijing 100084 China

2 State Key Laboratory of Automobile Safety and Energy Tsinghua University

Beijing 100084 China

E-mail smxiongtsinghuaeducn

Abstract High-pressure die cast B390 alloy was prepared on a 350 ton cold chamber die

casting machine The metaldie interfacial heat transfer coefficient of the alloy was investigated

Considering the filling process a ldquofingerrdquo-shaped casting was designed for the experiments

This casting consisted of five plates with different thicknesses (005 inch or 127 mm to 025

inch or 635 mm) as well as individual ingates and overflows Experiments under various

operation conditions were conducted and temperatures were measured at various specific

locations inside the die Based on the results the interfacial heat transfer coefficient and heat

flux were determined by solving the inverse heat transfer problem The influence of the mold-

filling sequence sensor locations as well as processing parameters including the casting

pressure die temperature and fastslow shot speeds on the heat transfer coefficient were

discussed

1 Introduction

High-pressure die casting (HPDC) is one of the most economical casting processes for mass producing

net-shaped parts Due to the excellent properties of die castings an increasing number of die casting

products are currently used in the automotive aerospace medical electronic and other industries

Techniques such as computer-assisted design and engineering which have rapidly developed in recent

years are applied in the modeling and simulation of the filling and solidification processes in HPDC

The use of these techniques significantly optimizes processes and saves costs However computer-

based techniques are only beneficial when the material properties as well as the boundary and initial

conditions used as inputs are correct [1]

The interfacial heat transfer coefficient (IHTC) characterizing

the thermal resistance between the metal and the mold is believed to be the one of most important

parameters during the solidification process for computer simulations [2-3]

Numerous studies [1-5]

on

determining the IHTC under various casting conditions have been conducted

In the current paper a die casting experiment was conducted using a ldquofingerrdquo-shaped casting of

B390 alloy The metaldie IHTC was determined according to the temperature readings obtained at

different locations inside the die by solving the inverse heat transfer problems The influence of the

mold filling sequence sensor locations as well as processing parameters including the casting

pressure die temperature and fastslow shot speeds on the heat transfer coefficient were discussed

2 Experiments

21 Finger-shaped casting


Published under licence by IOP Publishing Ltd 1








sensors






B390 1654 463 058 068 082 014 0055 0060 Bal


H13 0396 036 094 lt0005 lt0025 505 125 082 Bal









1(b)







2


sensor unit











condition Variable

Thermal conductance

λ (Wmiddotm-1

middotdegC-1

) 134 312 ndash 0013 T

a

Pouring temperature

TP (degC) 730 700 and 760

Specific heat

C (Jmiddotkg-1

middotdegC-1

) 963 478 ndash 0219 T

Die temperature

Td (degC) 50 150



P (MPa) 6998

10109 8381

6739 and

Mina



TL (degC) 650 1404

Slow shot speed

vL (mmiddots-1

) 02

01 03

04 and 08

Latent heat

Ls (Jmiddotkg-1

) 389000 209350

Fast shot speed

vH (mmiddots-1

) 175

125 15












3









The average of























-2middotK





4



















-2middotK

-1 the second


-2middotK


3 Wmiddotm

-2middotK

-1 of















5





-2 higher and














Sensor locations


Timeb (s)

q times 106

(Wmiddotm-2

) Time

b (s)

h times 103

(Wmiddotm-2

middotK-1

)

Near

overflow

(F)

T1F 2503248 792 2503272 2037

T2F 2503276 583 2503340 1681

T3F 2503328 621 2503508 2319

T4Fa - - - -

T5F 2503324 672 2503592 2597

Near gate

(G)

T1G 2503324 569 2503356 1528

T2G 2503328 561 2503444 1960

T3G 2503240 920 2503604 6429

T4G 2503348 597 2503824 2408




6




-2middotK

-1 the heat



-2middotK

-1 to 42 times 10

3 Wmiddotm

-2middotK




-2middotK


3 Wmiddotm

-2middotK

-1



-2middotK

-1 to 26times10

3 Wmiddotm

-2middotK












for the plate T5









have




7



2

max exp hA

h IDSh B T

(1)







8




max

2ln ln lnq q IDS q

IDS

qA T B

T

(2)

max

2ln ln lnh h IDS h

IDS

hA T B

T

(3)





















-2middotK

-1 to 80times10

3 Wmiddotm

-2middotK

-1



-2middotK

-1 to 42 times

103 Wmiddotm

-2middotK


3 Wmiddotm

-2middotK

-1 to 26 times

103 Wmiddotm

-2middotK


thickness




location

Acknowledgments




References






9


4 42




177-184
















10








sensors






B390 1654 463 058 068 082 014 0055 0060 Bal


H13 0396 036 094 lt0005 lt0025 505 125 082 Bal









1(b)







2


sensor unit











condition Variable

Thermal conductance

λ (Wmiddotm-1

middotdegC-1

) 134 312 ndash 0013 T

a

Pouring temperature

TP (degC) 730 700 and 760

Specific heat

C (Jmiddotkg-1

middotdegC-1

) 963 478 ndash 0219 T

Die temperature

Td (degC) 50 150



P (MPa) 6998

10109 8381

6739 and

Mina



TL (degC) 650 1404

Slow shot speed

vL (mmiddots-1

) 02

01 03

04 and 08

Latent heat

Ls (Jmiddotkg-1

) 389000 209350

Fast shot speed

vH (mmiddots-1

) 175

125 15












3









The average of























-2middotK





4



















-2middotK

-1 the second


-2middotK


3 Wmiddotm

-2middotK

-1 of















5





-2 higher and














Sensor locations


Timeb (s)

q times 106

(Wmiddotm-2

) Time

b (s)

h times 103

(Wmiddotm-2

middotK-1

)

Near

overflow

(F)

T1F 2503248 792 2503272 2037

T2F 2503276 583 2503340 1681

T3F 2503328 621 2503508 2319

T4Fa - - - -

T5F 2503324 672 2503592 2597

Near gate

(G)

T1G 2503324 569 2503356 1528

T2G 2503328 561 2503444 1960

T3G 2503240 920 2503604 6429

T4G 2503348 597 2503824 2408




6




-2middotK

-1 the heat



-2middotK

-1 to 42 times 10

3 Wmiddotm

-2middotK




-2middotK


3 Wmiddotm

-2middotK

-1



-2middotK

-1 to 26times10

3 Wmiddotm

-2middotK












for the plate T5









have




7



2

max exp hA

h IDSh B T

(1)







8




max

2ln ln lnq q IDS q

IDS

qA T B

T

(2)

max

2ln ln lnh h IDS h

IDS

hA T B

T

(3)





















-2middotK

-1 to 80times10

3 Wmiddotm

-2middotK

-1



-2middotK

-1 to 42 times

103 Wmiddotm

-2middotK


3 Wmiddotm

-2middotK

-1 to 26 times

103 Wmiddotm

-2middotK


thickness




location

Acknowledgments




References






9


4 42




177-184
















10


sensor unit











condition Variable

Thermal conductance

λ (Wmiddotm-1

middotdegC-1

) 134 312 ndash 0013 T

a

Pouring temperature

TP (degC) 730 700 and 760

Specific heat

C (Jmiddotkg-1

middotdegC-1

) 963 478 ndash 0219 T

Die temperature

Td (degC) 50 150



P (MPa) 6998

10109 8381

6739 and

Mina



TL (degC) 650 1404

Slow shot speed

vL (mmiddots-1

) 02

01 03

04 and 08

Latent heat

Ls (Jmiddotkg-1

) 389000 209350

Fast shot speed

vH (mmiddots-1

) 175

125 15












3









The average of























-2middotK





4



















-2middotK

-1 the second


-2middotK


3 Wmiddotm

-2middotK

-1 of















5





-2 higher and














Sensor locations


Timeb (s)

q times 106

(Wmiddotm-2

) Time

b (s)

h times 103

(Wmiddotm-2

middotK-1

)

Near

overflow

(F)

T1F 2503248 792 2503272 2037

T2F 2503276 583 2503340 1681

T3F 2503328 621 2503508 2319

T4Fa - - - -

T5F 2503324 672 2503592 2597

Near gate

(G)

T1G 2503324 569 2503356 1528

T2G 2503328 561 2503444 1960

T3G 2503240 920 2503604 6429

T4G 2503348 597 2503824 2408




6




-2middotK

-1 the heat



-2middotK

-1 to 42 times 10

3 Wmiddotm

-2middotK




-2middotK


3 Wmiddotm

-2middotK

-1



-2middotK

-1 to 26times10

3 Wmiddotm

-2middotK












for the plate T5









have




7



2

max exp hA

h IDSh B T

(1)







8




max

2ln ln lnq q IDS q

IDS

qA T B

T

(2)

max

2ln ln lnh h IDS h

IDS

hA T B

T

(3)





















-2middotK

-1 to 80times10

3 Wmiddotm

-2middotK

-1



-2middotK

-1 to 42 times

103 Wmiddotm

-2middotK


3 Wmiddotm

-2middotK

-1 to 26 times

103 Wmiddotm

-2middotK


thickness




location

Acknowledgments




References






9


4 42




177-184
















10









The average of























-2middotK





4



















-2middotK

-1 the second


-2middotK


3 Wmiddotm

-2middotK

-1 of















5





-2 higher and














Sensor locations


Timeb (s)

q times 106

(Wmiddotm-2

) Time

b (s)

h times 103

(Wmiddotm-2

middotK-1

)

Near

overflow

(F)

T1F 2503248 792 2503272 2037

T2F 2503276 583 2503340 1681

T3F 2503328 621 2503508 2319

T4Fa - - - -

T5F 2503324 672 2503592 2597

Near gate

(G)

T1G 2503324 569 2503356 1528

T2G 2503328 561 2503444 1960

T3G 2503240 920 2503604 6429

T4G 2503348 597 2503824 2408




6




-2middotK

-1 the heat



-2middotK

-1 to 42 times 10

3 Wmiddotm

-2middotK




-2middotK


3 Wmiddotm

-2middotK

-1



-2middotK

-1 to 26times10

3 Wmiddotm

-2middotK












for the plate T5









have




7



2

max exp hA

h IDSh B T

(1)







8




max

2ln ln lnq q IDS q

IDS

qA T B

T

(2)

max

2ln ln lnh h IDS h

IDS

hA T B

T

(3)





















-2middotK

-1 to 80times10

3 Wmiddotm

-2middotK

-1



-2middotK

-1 to 42 times

103 Wmiddotm

-2middotK


3 Wmiddotm

-2middotK

-1 to 26 times

103 Wmiddotm

-2middotK


thickness




location

Acknowledgments




References






9


4 42




177-184
















10



















-2middotK

-1 the second


-2middotK


3 Wmiddotm

-2middotK

-1 of















5





-2 higher and














Sensor locations


Timeb (s)

q times 106

(Wmiddotm-2

) Time

b (s)

h times 103

(Wmiddotm-2

middotK-1

)

Near

overflow

(F)

T1F 2503248 792 2503272 2037

T2F 2503276 583 2503340 1681

T3F 2503328 621 2503508 2319

T4Fa - - - -

T5F 2503324 672 2503592 2597

Near gate

(G)

T1G 2503324 569 2503356 1528

T2G 2503328 561 2503444 1960

T3G 2503240 920 2503604 6429

T4G 2503348 597 2503824 2408




6




-2middotK

-1 the heat



-2middotK

-1 to 42 times 10

3 Wmiddotm

-2middotK




-2middotK


3 Wmiddotm

-2middotK

-1



-2middotK

-1 to 26times10

3 Wmiddotm

-2middotK












for the plate T5









have




7



2

max exp hA

h IDSh B T

(1)







8




max

2ln ln lnq q IDS q

IDS

qA T B

T

(2)

max

2ln ln lnh h IDS h

IDS

hA T B

T

(3)





















-2middotK

-1 to 80times10

3 Wmiddotm

-2middotK

-1



-2middotK

-1 to 42 times

103 Wmiddotm

-2middotK


3 Wmiddotm

-2middotK

-1 to 26 times

103 Wmiddotm

-2middotK


thickness




location

Acknowledgments




References






9


4 42




177-184
















10





-2 higher and














Sensor locations


Timeb (s)

q times 106

(Wmiddotm-2

) Time

b (s)

h times 103

(Wmiddotm-2

middotK-1

)

Near

overflow

(F)

T1F 2503248 792 2503272 2037

T2F 2503276 583 2503340 1681

T3F 2503328 621 2503508 2319

T4Fa - - - -

T5F 2503324 672 2503592 2597

Near gate

(G)

T1G 2503324 569 2503356 1528

T2G 2503328 561 2503444 1960

T3G 2503240 920 2503604 6429

T4G 2503348 597 2503824 2408




6




-2middotK

-1 the heat



-2middotK

-1 to 42 times 10

3 Wmiddotm

-2middotK




-2middotK


3 Wmiddotm

-2middotK

-1



-2middotK

-1 to 26times10

3 Wmiddotm

-2middotK












for the plate T5









have




7



2

max exp hA

h IDSh B T

(1)







8




max

2ln ln lnq q IDS q

IDS

qA T B

T

(2)

max

2ln ln lnh h IDS h

IDS

hA T B

T

(3)





















-2middotK

-1 to 80times10

3 Wmiddotm

-2middotK

-1



-2middotK

-1 to 42 times

103 Wmiddotm

-2middotK


3 Wmiddotm

-2middotK

-1 to 26 times

103 Wmiddotm

-2middotK


thickness




location

Acknowledgments




References






9


4 42




177-184
















10




-2middotK

-1 the heat



-2middotK

-1 to 42 times 10

3 Wmiddotm

-2middotK




-2middotK


3 Wmiddotm

-2middotK

-1



-2middotK

-1 to 26times10

3 Wmiddotm

-2middotK












for the plate T5









have




7



2

max exp hA

h IDSh B T

(1)







8




max

2ln ln lnq q IDS q

IDS

qA T B

T

(2)

max

2ln ln lnh h IDS h

IDS

hA T B

T

(3)





















-2middotK

-1 to 80times10

3 Wmiddotm

-2middotK

-1



-2middotK

-1 to 42 times

103 Wmiddotm

-2middotK


3 Wmiddotm

-2middotK

-1 to 26 times

103 Wmiddotm

-2middotK


thickness




location

Acknowledgments




References






9


4 42




177-184
















10



2

max exp hA

h IDSh B T

(1)







8




max

2ln ln lnq q IDS q

IDS

qA T B

T

(2)

max

2ln ln lnh h IDS h

IDS

hA T B

T

(3)





















-2middotK

-1 to 80times10

3 Wmiddotm

-2middotK

-1



-2middotK

-1 to 42 times

103 Wmiddotm

-2middotK


3 Wmiddotm

-2middotK

-1 to 26 times

103 Wmiddotm

-2middotK


thickness




location

Acknowledgments




References






9


4 42




177-184
















10




max

2ln ln lnq q IDS q

IDS

qA T B

T

(2)

max

2ln ln lnh h IDS h

IDS

hA T B

T

(3)





















-2middotK

-1 to 80times10

3 Wmiddotm

-2middotK

-1



-2middotK

-1 to 42 times

103 Wmiddotm

-2middotK


3 Wmiddotm

-2middotK

-1 to 26 times

103 Wmiddotm

-2middotK


thickness




location

Acknowledgments




References






9


4 42




177-184
















10


4 42




177-184
















10

determination of the metal/die interfacial heat transfer

Documents