& Development
CHINA FOUNDRY Research
Vol.16 No.5 September 2019https://doi.org/10.1007/s41230-019-9065-y

Investigation on heat-transfer-coefficient between
aluminum alloy and organic/inorganic sand moldbased on inverse method*Jing-ying Sun1, Qi-chi Le1, Tong Wang1, Xu Zhao1, Wei-sen Shi2, Hong-wei Huo2, and Chiri Wang3
1. Key Laboratory of Electromagnetic Processing of Materials, Ministry of Education, Northeastern University, Shenyang 110819, China
2. BMW Brilliance Automotive Ltd., Shenyang 100044, China
3. ASK Chemicals (Zhenjiang) New Materials Technology Co, Ltd., Shanghai 200032, China

Abstract: A kind of cylinder sand mold was designed to investigate the heat-transfer-coefficients (HTCs)
between aluminum alloy and organic/inorganic binder bonded sand mold during the solidification processes.
Temperature during the solidification process was recorded and input into the simulation software. The inverse
model of MAGMA was used to calculate the HTC based on the actual temperature. Results show that thetemperature of the inorganic sand mold increased faster than the organic sand mold; while the temperature of
the casting part with the inorganic sand mold decreased faster. The optimal HTCs between Al and the organic/
inorganic sand mold are confirmed to be 300 to 700 and 1000 to 1800 W·m-2·K-1, respectively, along with thechange of solid-liquid phase line. The simulated temperature curves show the same trend as the measured ones.
The maximum deviation between the two temperature curves are 17.32 °C and 18.77 °C for castings by inorganicand organic sand molds.
Key words: heat-transfer-coefficient; aluminum alloy; organic; inorganic; inverse method
CLC numbers: TG221

Document code: AW

ith the continuous development of computer
simulation technology, improving the accuracy of
casting simulation process has become a critical challenge
for many researchers that needs to be overcome [1]. In
order to improve the accuracy of casting simulation,
the change of HTC, which is one of the most importantboundary conditions during the solidification process,must be known. Many researchers propose that theinverse method is a highly efficient way of calculating
HTC [2-4]. Based on the inverse method, the HTC value ofthe permanent-mold casting of Ti-6Al-4V was found to
decrease linearly from 2,000 to 1,500 W·m-2·K-1 between
the liquidus and the solidus [5]. The HTC of the squeeze
casting of AM60 magnesium alloy was also investigatedby extrapolation and numerical inverse methods, andthe results indicated that the heat flux and the HTCs
determined by the inverse method were more accurate
than by the extrapolated fitting method [6]. Recently,
Zhang A [7] studied the HTC between aluminum alloy and*Jing-ying Sun
Male, born in 1990, Ph.D. Research interests: aluminum alloy low pressure
die casting process and simulation.
E-mail: sunnyfish1990@126.com

Received: 2019-05-20; Accepted: 2019-08-06
336

Article ID: 1672-6421(2019)05-336-06

the sand mold in the low-pressure sand casting. Results
showed that the accuracy of HTC calculated using theinverse method was increased by 50% if the temperaturedependence of the thermo-physical parameters wasconsidered, rather than the normal constant treatment or
simple linear interpolation versus temperature.
With higher requirement of energy saving andenvironmental protection, the traditional organic sandcores are replaced by inorganic ones with a lower
carbon emission. More and more inorganic binder
bonded sand cores are gradually being used to produce
complex castings [8]. However, the difference of theheat-transfer behavior and HTC values between
organic and inorganic sand molds is not clear. In orderto ensure the accuracy of simulation, the difference of
HTC values between organic and inorganic sand moldcastings needs to be clarified.
In this study, the temperature changes of the A356
aluminum alloy in organic and inorganic sand molds
were measured during the solidification processes.
Based on the inverse method, the HTC values of theA356 aluminum alloy with organic and inorganic sandmolds were also calculated. To verify the accuracy ofthe calculation, the experimental temperature curves,
shrinkage morphologies and secondary dendrite arm

Research & Development CHINA FOUNDRY
Vol.16 No.5 September 2019spacing (SDAS) of the organic and inorganic sand castings werecompared with the simulation results.

1 Experimental procedure
K-type thermocouples (TC) were used to measure thetemperature of the casting and mold. Phoenix TM 10-channels
temperature recorder was used to record the temperature every
second for 1800 seconds. In order to ensure the accuracy oftemperature measurement and simplify the inverse calculation
model, a cylinder sand mold was designed. The mold and thelayout of the TCs are shown in Fig. 1. TC1 and TC2 wereused to measure the temperature of the casting and mold,respectively. The positions of the thermocouples should be as
close as possible to the interface of the casting and mold.

2 Inverse method
The inverse method was carried out to solve the HTC between
the casting and the sand mold. In order to make the program
run continuously and achieve the required solution accuracy,
the convergence criterion must be established. According to
the characteristics of the inverse method for HTC calculation,
the temperature deviation between the measured temperatureand the calculated temperature by each iteration is used as theconvergence criterion. The convergence criterion is as follows:
c

S

(1)

m
ij is the measured temperature of the measured pointscxj (j=1, …, Nm) change with the time, ti (i=1, …, Nt) ; ij
is

where

the calculated temperature accordingly; h = {h1 , h2 ,⋅ ⋅ ⋅, hN h } isthe unknown HTC; Nm is the number of thermocouples fortemperature measurement; Nt is the number of time points; Nhis the number of calculate HTC; σT is the error of measured
temperature; σk is the maximum allowable change in each
iteration; hk0 is the initial HTC.
When S(h) is minimized, h can be obtained. Take derivatives
on both sides:
t

m

m

1

c

l

l

ijl

(2)

l

T

where Xijl is the sensitive coefficient, and Xijl is expanded by
Taylor formula at hl position:c1cFig. 1: Experimental layout of mold and thermocouples

The chemical compositions of the A356 aluminum alloy
are shown in Table 1. The solidus and liquidus are 542 °C and
613 °C, respectively. The thermophysical parameters of thealuminum alloy and different sand molds are shown in Fig.
2. The pouring temperature is 700 °C, and sand molds werepreheated to 50 °C. Finally, the castings were cut longitudinallyfrom the middle section to compare the shrinkage morphologies
with simulation results. The microstructure was observed by
an optical microscope and the SDAS was measured to evaluate
the cooling rate of the castings by organic and inorganic sandmolds. Three values were achieved in each area, and the averagevalues were used for comparison.

c

1

7.23

Mg
0.36

Zn
0.007

Mn
0.0139

Sr
0.008

Fe
0.12

Where δh1 is the change of the previous iteration h1, and it
is used for calculating the sensitive coefficient. During thetemperature calculating process, the next iterative temperature( )Tijc h v +1 will also be linearized:
c
ij

c
ij

ijk

k

(4)

In the formula, the variation of the HTC Δhk will be achievedby the following equation:
h

lk

Al
Bal.

1

1

Table 1: Chemical compositions of A356 alloy studied (wt.%)
Si

(3)

t

lk

m

k

ijl

ijk
T

(5)

l

lk

(6)

l

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CHINA FOUNDRY Research
Vol.16 No.5 September 2019

(a)

(b)

(c)

(d)

(e)

(f)

Fig. 2: Thermophysical parameters of aluminum, and organic and inorganic binder bonded sand molds:(a) Al alloy - specific heat; (b) organic sand mold - specific heat; (c) inorganic sand mold - specificheat; (d) Al alloy - thermal conductivity; (e) organic sand mold - thermal conductivity; (f) inorganic
sand mold - thermal conductivity
t

m

l

T

m
ij

v
l

c
ij

ijl

(7)

l

l

where δlk is the Coronel mark.
The HTC between the casting and the mold can be achieved byusing inverse method. The detailed calculating processes are as follows:(1) Record the temperature curves of castings and molds
during the solidification process;(2) Assume the initial HTC,h, and setthe maximum number of iterations M;c(3) Achieve the temperature field of casting and mold, ij ,through numerical simulation;(4) Calculate the sensitive coefficient, Xij1, through Eq. (3);(5) Calculate and achieve Δh k through Eqs. (5)- (7).
Ifkk
Otherwise,
338

v
k

, the calculating program will stop and output h.
v
kk, and the program will go back tostep 3 and calculate again.
According to the correlative studies, when the temperature
was above the liquidus or below the solidus, the HTC remained
constant. It increased linearly when the temperature was
between the liquidus and the solidus [9-10]. Thus, the 4-point HTC
curve was set up with temperature change in MAGMA. Afterthe calculation, four additional output values were generated as
the standard of measurement between the simulation and theexperiment. These are as follows:• Delta gradient, which is the sum of the difference in the firstdeviation.
• Delta integral, which is the Riemann integral between themeasured and the simulated curves.
• Delta maximum, which is the maximum vertical (y-direction)
distance between the base points of the two curves.
• Delta quadratic, which is the sum of all square distances
between each individual base point (coordinate) in thecommon interval of both curves.

Research & Development CHINA FOUNDRY
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3 Results and discussion
3.1 Measured temperature
Figure 3 shows the temperature measurement results of the twokinds of sand castings. It can be seen that the temperature of
the inorganic sand mold increased faster than the organic mold,and the temperature of the casting in the inorganic sand molddecreased faster than the casting in the organic sand mold. By
observing the temperature of TC1, the temperature of both the
inorganic and organic molds show a plateau due to the identicalheat absorption and exothermic of the castings during thisperiod. In addition, the temperature plateau of the casting in theorganic sand mold is longer than that in the inorganic sand.

3.2 Calculated HTC
The HTC curves shown in Fig. 4 were generated automaticallyfrom MAGMA as optimal results. The HTC between the Al alloy
and the organic sand mold changed from 300 to 700 W·m-2·K-1
along with the solidus-liquidus. The HTC between the Al alloy andthe inorganic sand mold changed from 1,000-1,800 W·m-2·K-1
along with the solidus-liquidus. Heat transfer from the Al alloy
to the inorganic sand mold presented a larger value than theorganic sand mold. This phenomenon showed a good agreementwith the temperature comparison between organic and inorganic
sand molds.

(a)Fig. 3: Temperature curves of organic and inorganic sandcasting

3.3 Experimental verification
Based on the inversed HTC, the solidification process of theorganic and inorganic sand castings was calculated. Figure
5 shows the comparison of the simulated and measured
temperatures during the solidification process. Both organic andinorganic sand castings showed the same trend of temperaturechange for both the simulation and the experiment. The
maximum temperature deviation of the organic sand casting is17.32 °C, while that of the inorganic sand casting is 18.77 °C.
Table 2 lists all the output values which are used to evaluate thedifference between the simulation and the experiment.

(b)Fig. 4: Relationship of HTC with interface temperature for different sand molds: (a) Al-organic; (b) Al-inorganic

(a)

(b)

Fig. 5: Comparisons of simulated and experimental temperatures: (a) Organic sand casting;(b) Inorganic sand casting339

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Table 2: Output values of inverse model from MAGMA
Delta gradient

Delta integral

Delta maximum

Delta quadratic

Organic sand_TC1

86.97

12936.16

16.43

783936.56

Organic sand_TC2

89.29

25021.11

17.32

2211045.75

Inorganic sand_TC1

117.9717062.55

18.77

3310589.0

Inorganic sand_TC2

86.53

11752.03

17.9

1433232.5

Figure 6 shows the shrinkage morphologies of the castings
which showed a good correspondence with the simulation
results. The shrink depth of the inorganic casting showed adeeper shape. In order to evaluate the cooling rates of theorganic and inorganic sand castings, SDAS were measured
from middle to the edge of the castings. The microstructure andSDAS values are shown in Fig. 7. The average SDAS values ofthe organic casting are 80.4, 64.3, and 52.9 μm from the center
to the edge, while those of the inorganic casting are 65.7, 51.4,
and 45.9 μm, respectively. In summary, the SDAS values of the
inorganic casting are lower than that of the organic casting. It is
confirmed that the cooling rate of the inorganic casting is fasterthan the organic one.

Fig. 6: Comparison of shrinkage morphologies for experimental and simulated castings

4 Conclusions(1) During the solidification process, the temperature of the
inorganic sand mold increases faster than that of the organic
one. This can be explained by the greater thermal resistance ofthe organic sand mold.
(2) The optimal HTC between the Al alloy and the organic
sand mold is confirmed to be 300 to 700 W·m-2·K-1 along thesolidus-liquidus. Meanwhile, 1000 to 1800 W·m -2·K -1 was
340

exported as the optimal HTC between the Al alloy and theinorganic sand mold.
(3) Both organic and inorganic sand castings show thesame trend of temperature change for both the simulated andexperimental results. Shrinkage morphologies of the castingsshow a good correspondence with the simulation results.
SDAS measurement results proved that the cooling rate of the
inorganic casting is faster than the organic casting.

Research & Development CHINA FOUNDRY
Vol.16 No.5 September 2019

Fig. 7: Microstructures and SDAS of organic and inorganic sand castings

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