1

Dependence of interfacial heat transfer

coefficient on casting surface temperature

during solidification of Al-Si alloy castings

cast in CO2 sand mold

Lazar Kovačević

Faculty of Technical Sciences, Trg Dositeja Obradovica 6, 21000 Novi Sad,

Serbia

e-mail: lazarkov@uns.ac.rs

Pal Terek

Faculty of Technical Sciences, Trg Dositeja Obradovica 6, 21000 Novi Sad,

Serbia

Aleksandar Miletić

Faculty of Technical Sciences, Trg Dositeja Obradovica 6, 21000 Novi Sad,

Serbia

Damir Kakaš

Faculty of Technical Sciences, Trg Dositeja Obradovica 6, 21000 Novi Sad,

Serbia

Abstract

Interfacial heat transfer coefficient at the metal-mold interface (IHTC) was estimated by an

iterative algorithm based on the function specification method. An Al-9 wt.%Si alloy plate casting

was made in a sand mold prepared by CO2 process. Thermal history obtained from the experiment

was used to solve an inverse heat conduction problem. Acquired transient IHTC values are then

given in function of the casting surface temperature at the interface. By comparing the obtained

results with previous findings, the influence of grain fineness number and consequently of mold

roughness on maximum IHTC values is revealed.

Keywords: crystallization of metals, inverse heat conduction, heat transfer

coefficient, mold roughness

Accepted Author Manuscript (AAM) A definitive version was subsequently published in Heat and Mass Transfer (2014) 50:1115-1124

DOI 10.1007/s00231-014-1326-0.

The final publication is available at link.springer.com

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List of symbols

A surface area (m2)

cp specific heat (Jkg-1

°C-1

)

FO Fourier number

h interfacial heat transfer coefficient (Wm-2

°C-1

)

k thermal conductivity (Wm-1

°C-1

)

M number of considered measurements

n iteration number

N number of cells in the mold subdomain

q heat flux at the metal-mold interface (Wm-2

)

Ra Average roughness (μm)

S objective function

T calculated temperature (°C)

V volume (m3)

x Cartesian coordinate (m)

X sensitivity coefficient

Y measured value of temperature (°C)

Δx cell width (m)

t thermocouple response time (s)

Greek symbols

Δτ time increment (s)

ρ density (kgm-3

)

τ time (s)

ε incremental value

Subscripts

CS casting surface

I, II and III mold subdomains

ini initial

3

liq liquidus temperature

m nodal point considered

m2, m3 and m4 nodal points corresponding to locations of

thermocouples TC2, TC3 and TC4 respectively

MS mold surface

r considered subdomain

sol solidus temperature

TC thermocouple

Superscripts

f number of future time steps for which the heat flux is

constant

p time step

j time step of internal regularization loop

4

1 Introduction

Increasing demand for highly competitive products in foundry manufacturing has

led to the development of computer aided engineering methods which reduce

cycle time and costs for producing high-quality castings. The goal is to provide

tools which simulate mold filling and solidification and are able to predict and

optimize shape, microstructure, mechanical properties and durability of cast

components [1-3]. Mathematical modeling is an incredible and reliable tool for

obtaining required information and preventing costs of experimental

investigations in order to increase the efficiency and improve the product quality

[4]. However, result of any numerical simulation is dependent on the accuracy of

input parameters and chosen boundary conditions. The cooling rate, which

controls solidification pattern and mechanical properties of the final part, is

mainly influenced by thermophysical properties of casting/mold material and

interfacial heat transfer coefficient at the metal-mold interface (IHTC) [5].

Material properties such as thermal conductivity, density, viscosity and specific

heat are usually readily available and independent from the shape of a casting.

Contrarily, IHTC depends greatly on the mold material, casting shape and process

parameters [5-14]. Therefore, it should be estimated for every casting process

individually. To further complicate the matter, IHTC is not a constant and changes

due to dynamic conditions at the metal-mold interface.

Most of the previous studies described the heat transfer as a function of time [5, 6,

10-13, 15, 16]. Such data can only be used for determining relative influence of

different parameters on the IHTC behavior [8]. Their applicability in numerical

simulations is usually limited to exactly the same mold configuration. Any

modification which includes changes in orientation of referred mold surface or the

time step when molten metal reaches the surface will make data almost useless.

For example, increase in casting modulus (volume to surface ratio) will prolong

solidification and cause a delay in IHTC drop due to air gap formation. Several

studies tried to overcome this problem by finding a correlation between IHTC and

air gap size [14, 17]. However, this approach requires coupling of flow, thermal

and stress analysis [18] which prolongs simulation time in most situations.

Furthermore, in order to measure air gap size accurately experimental casting

needs to be fairly large. In this way it is difficult to study and take into account

5

influence of some other important process parameters, for example absence of

convective flow in thin-walled castings. Another approach is to express IHTC as a

function of casting surface temperature [6, 8, 13]. Kim et al. [8] applied this

approach for horizontally solidifying aluminum in copper mold and distinguished

three separate regimes according to the physical state of a casting. In the liquid

state, IHTC is affected by roughness of a mold and wettability of the casting to the

mold surface. At the initial stage of solidification the IHTC suddenly drops to a

certain value. In the solid state IHTC depends only upon the thermal conductivity

and the thickness of the air gap. Thus, this approach offers the possibility to

express the IHTC irrespective of casting modulus since the timing of air gap

formation is now defined in relation to solidus and liquidus temperatures of the

casting surface. Recently Kovacevic et al. [19] developed correlation between

IHTC and casting surface temperature. The correlation decouples influences of

various process parameters and ties them to specific correlation variable. This

reduces number of experimental trials required to populate a comprehensive IHTC

database. Furthermore, there is a possibility to incorporate empirical or theoretical

relationships to calculate specific parameters. For example, one can use work of

Kim et al [8] to find IHTC value for different coatings and superheats between

liquid aluminum and copper mold. Additionally, it is reasonable to speculate that

the minimum value of IHTC during solidification of thick heavy castings in rigid

molds predominantly depends upon thermal resistance induced by contraction,

which can be calculated a priory. Therefore one can use mentioned correlation to

obtain a relatively accurate IHTC curve in cases for which there are no

experimental data.

Although previous studies have identified various factors which affect IHTC for

various shapes and positions of the castings wall, there is still a wide knowledge

gap. Recent studies have been usually focused on metal molds and there is almost

no published research that addresses behavior of IHTC in function of casting

surface temperature during solidification of an aluminum alloy in the CO2 sand

mold. Furthermore, previous investigations for flat vertical mold surfaces were

performed on castings which can be regarded as infinitely thick. The work

reported in this paper consists of experimental determination of the IHTC values

for a unidirectionally solidifying Al-9 wt % Si alloy plate casting in the CO2 sand

mold. After plotting the IHTC in function of the casting surface temperature a

6

previously proposed correlation [19] was applied to describe acquired relationship

numerically. Obtained results are then compared with the results from the

literature in order to find effect of sand grain size on IHTC.

2 Experimental setup

The molds used to determine IHTC in the present study were prepared by a CO2

process. Sodium silicate (Na2CO3) of 8% by weight was mixed with silica sand.

The grain fineness number of the used sand was 80. The molds were prepared by

regular hand molding technique and then hardened by using CO2 gas. They were

kept at the room temperature prior to the casting experiments.

Commercial Al-9 wt.% Si alloy was melted in an electric resistance crucible

furnace to temperature of 780°C and kept in molten state for approximately 15

hours prior to pouring. The pouring was performed by tilting the crucible and

allowing the molten metal to flow into the pouring basin. Temperature recordings

were started well before the metal was poured into the mold cavity.

Since sand is a good insulator itself, the use of insulation was not practical. Thus,

in order to promote directional horizontal solidification and one-dimensional heat

transfer, height and length were carefully chosen in relation to the thickness of the

casting. A schematic drawing of the experimental casting is shown in Fig. 1.

Fig. 1 Model of experimental plate casting with thermocouple positioning

Considering that solution of an inverse heat conduction problem (IHCP) is highly

sensitive to the temperature measurements, special attention was given to

selection and fixing of thermocouples. To reduce measurement error

7

thermocouples are usually placed parallel to the isotherms. However, in sand

molds this requirement is very difficult to achieve since the presence of

thermocouples severely undermines the strength of surrounding sand and causes

penetration of molten metal into the thermocouple leads [20]. Thermocouples are

thus positioned perpendicular to the isotherms. In order to minimize heat

conduction error through the thermocouple leads and to obtain accurate IHTC

estimation thermocouple wires with minute diameter of 0.0799 mm (Omega TT-

K-40-SLE) were used. Another potentially significant source of error can be

thermocouple response time [21, 22]. The final welded thermocouple junction was

a 0.2 mm diameter sphere. For such miniature thermocouples the manufacturer

gives extremely rapid hot water response time of 15 ms. However this figure is

checked by manually calculating the response time:

TC TC pTC

TC TC

V ct

h A

(1)

By assuming that heat transfer between solidified casting and the thermocouple is

similar to the lowest IHTC between the casting and the mold (corresponding to

approx. 600 Wm-2

K-1

), response time of used thermocouples can be calculated to

a value of 0.2s. Response time of the thermocouple located in the casting and in

contact with molten metal will be even shorter. Therefore, for chosen acquisition

speed of 2Hz, thermocouple response time should not introduce significant

measurable error.

In order to obtain accurate results from the IHCP algorithm (especially at the

initial solidification stages), the mold thermocouples have to be positioned as

close to the casting as possible. In our investigations the first thermocouple is

always positioned 1 to 2 mm from the casting wall. In such close proximity to the

casting thermal gradients are at the maximum and error of thermocouple

placement should be minimal in order to obtain reliable estimates. Even in

precisely machined permanent molds, exact positioning of the thermocouples is

not possible and constitutes an unavoidable source of error. In sand molds this

problem is amplified. During molding process sand is placed over carefully

positioned thermocouples and loose sand grains can easily displace the mold

thermocouples. In order to minimize thermocouple bead placement error, relative

position of every thermocouple was measured two times: after their placement

8

during molding and after molds cooled to a room temperature following the

pouring. More details on the casting procedure can be found elsewhere [19].

MarSurf PS1 stylus profilometer was used to measure the mold surface roughness

in order to determine its effect on the IHTC values. Unfortunately, direct

measurement of mold surface roughness is unfeasible without damaging the mold,

since the profilometer stylus would need to be placed in 10 to 20 mm wide mold

cavity. Therefore, measurements were carried out on separately molded flat

samples made from the same sand batches used in casting experiments.

3 Estimation of IHTC

3.1 The direct problem

The heat transfer during the experiment was assumed as one-dimensional transient

heat conduction described by:

p

Tk T c

x x

(2)

The initial and boundary conditions were described by following equations:

,0 iniT x T x (3)

0

0,

x

Tk T q

x

(4)

4 4,T x Y (5)

The above equations were discretized using the finite volume method, as shown in

Fig. 2. Considering that the thermocouple positions were determined after

mounting, mold was divided in three subdomains, one between each mold

thermocouple. Interior cell widths in each subdomain were determined by

following equations:

2

1I

I

xx

N

(6)

9

3 2

1II

II

x xx

N

(7)

4 3

1III

III

x xx

N

(8)

where x2, x3 and x4 are distances from the interface of the second, third and fourth

thermocouple respectively. In this investigation all three subdomains were

discretized by 4 cells (NI=NII=NIII=4). The importance of non-uniform grid

discretization during IHTC determination for sand casting process should be

emphasized. As already stated, thermocouples are easily displaced during the

molding. Therefore, their exact positions cannot be predetermined, and vary from

one pouring to another. By utilizing fixed grid technique, exact matching of

computational nodes and thermocouple positions is hardly achievable. This leads

to an increase in thermocouple positioning error. By overlapping positions of

computational nodes and thermocouples through Equations (6) – (8) overall

estimation error can be reduced.

Fig. 2 Computational grid with thermocouple positions

After applying energy balance method and approximating time derivative using

fully implicit method, Equation (2) can be rewritten as:

1

1 1 1 21 2 2

pp p p p p pr rr m r m m p

x FoFo T Fo T T q

k

(9)

for surface cell (m=1, r=1),

1 1 1 1

1 11 2p p p p p p p

r m r m r m mFo T Fo T Fo T T

(10)

10

for interior cells,

1 1 11

1 11 1 1

2 2 21

p p pp p p p

m m m mp p p

p I I II p I II p II I II

k k kT T T T

c x x x c x x c x x x

(11)

for boundary cell between subdomains I and II (m=NI),

1 1 11

1 11 1 1

2 2 21

p p pp p p p

m m m mp p p

p II II III p II III p III II III

k k kT T T T

c x x x c x x c x x x

(12)

for boundary cell between subdomains II and III (m=NI+NII –1), and

4

p p

mT Y (13)

for the last cell (m=NI+NII+NIII –2). For is the Fourier number of the subdomain r

and is defined by:

11

21

pp

r p

p r

kFo

c x

(14)

If the values of heat flux at the metal-mold interface are known, transient

temperature field in the mold can be calculated by solving equation system

defined by Equations (9) – (14) for each time increment. In the present study,

equation system was solved by a matrix inversion method.

The thermophysical properties of the sand were taken as functions of temperature

and are shown in Table 1. Although temperature dependent thermal properties

increase the accuracy of the model they make the system nonlinear. This usually

requires adding additional iteration loop. However, most thermal properties are

known only within ±5% at best. It is not particularly effective to develop highly

sophisticated techniques to precisely handle temperature dependent thermal

properties that are known imprecisely [23]. Additionally, a change of temperature

inside mold is slow due to poor thermal diffusivity of the sand and relatively small

time steps used. Thus, in presented scheme, the problem is solved as quasi-linear

by using thermal properties evaluated at the previous time step, as shown in

Equations (9) – (14).

11

Table 1 Thermophysical properties of the sand mold [24]

Properties Values

Density (kg/m3) 1600

Specific heat capacity (J/kgK) 0.1540.407( 273)T

Thermal conductivity (W/mK) 2 5 21.26 0.169 10 0.105 10T T

Following the methodology proposed by Dour et al. [25] the accuracy of IHTC

estimation can be calculated to a value of approx. ±25% [19].

3.2 Iterative procedure

The heat flow across a metal-mold interface can be characterized by a

macroscopic averaged IHTC given by:

( )( )

( ) ( )CS MS

qh

T T

(15)

For current experimental setup this equation can be rewritten as:

1

pp

p p

m

qh

Y T

(16)

where m=1. Therefore, estimation of the IHTC consists of estimating an unknown

boundary heat flux using measured thermal histories at known locations inside the

heat conducting solid. Such problems are known as IHCP and are inherently ill

posed. They are extremely sensitive to measurement errors and are generally

solved by minimizing an objective function with some stabilization technique

used in the estimation procedure. In the present study, an algorithm based on the

sequential function specification method was used to minimize objective function

(S) defined as:

2 2

2 2 3 3

1 1

M Mp p p p

m m

p p

S Y T Y T

(17)

Heat flux value is treated as a piecewise function of time and heat flux

components are sequentially estimated at each time step. In order to stabilize the

solution, measured temperatures from several future time steps are considered

during estimation of the “current” heat flux.

12

At the start of the estimation, suitable initial value of heat flux (qini) is assumed

and the initial temperature field of the mold is determined from experimental

measurements. First measurements from thermocouples TC2, TC3 and TC4 are

used as initial temperatures of the cells located at boundaries between two mold

subdomains. Temperatures of the interior cells are then calculated by linear

interpolation. In this way, assumption of constant initial mold temperature is

avoided. The value of the heat flux is assumed to be constant for f=6 subsequent

future time steps for which the temperature field of the mold is calculated. The

assumed heat flux value is then changed by a small value (εq) and new

temperature fields corresponding to (q+εq) are determined. Using these values,

sensitivity coefficients and correction of assumed value of heat flux are obtained

by following equations:

1 1

1

p j p p p j p

m mp j

m p

T q q T qX

q

(18)

1 1 1 1 1 1

2 2 2 3 3 3

1 1

2 21 1

2 3

1

f fp j p j p j p j p j p j

m m m m

j jp

fp j p j

m m

j

Y T X Y T X

q

X X

(19)

The corrected heat flux of the same time step, used in the next cycle of

calculation, can then be calculated by:

p p p

corrq q q (20)

The above procedure is repeated until one of the stopping criteria is satisfied.

Eventually, the IHTC is calculated by using equation (16) and the algorithm

proceeds to the next time step. Stopping criteria used in this investigation were as

follows:

2p

corrq (21)

0.0005p

p

q

q

(21)

maxn n (22)

13

A flowchart of the solution procedure used for estimation of IHTC is shown in

Fig. 3.

Fig. 3 Flowchart of the solution procedure used for estimation of IHTC

14

4 Results and discussion

Typical temperature versus time curves obtained during one of the casting trials

are shown in Fig. 4. This chart includes measurements of the casting surface

temperature and temperatures at different depths under the mold surface. The

highest recorded casting temperature was 740°C. The moment this temperature

was reached was selected as the initial time during analysis (τ=0). All subsequent

TC1 measurements show decrease of temperature with time. After approximately

50 seconds all superheat is removed. Noticeable change in the slope of the cooling

curve indicates the start of solidification. Following cooling rates varied with the

rate of latent heat release until 190th

second when eutectic composition was

reached. Subsequent crystallization continued at the near constant temperature. A

rapid increase in the cooling rate after approx. 370 seconds indicates the end of

solidification. Measurements of mold thermocouples TC3 and TC4 show

temperature arrest at around 106°C. This can be explained by vapor transportation

inside the mold. When the molten metal reaches observed mold surface, moisture

in the sand near the metal-mold interface flashes into vapor. The vapor moves

away from the metal penetrating further into the sand mold leading to the rise in

the recorded temperatures. The influence of vapor transportation can be avoided

by heating the mold assembly prior to pouring [9, 26]. Although this technique is

sometimes employed in foundries, it does not yield typical sand casting conditions

and is avoided in this investigation.

Fig. 4 Temperature versus time curves obtained during solidification of Al-9 wt.% Si in CO2

sand mold and estimated mold surface temperature curve

Transient heat flux and IHTC values estimated from the temperature readings

shown in Fig. 4 are presented in Fig. 5 and Fig. 6, respectively. During initial 50

15

seconds the IHTC increases rapidly from 85 to 900 W/m2K. This behavior is

probably a consequence of the used algorithm. Although the initial interface heat

flux density is probably very high, the numerical model underestimates the heat

flux until the heat diffuses to the thermocouples [16] and until thermocouples

respond to the change in the mold temperature. The low thermal diffusivity of

sand amplifies this effect. After discussed initial period, fairly uniform values of

approx. 930 W/m2K are reached. In the period from 110th to 500th second the

IHTC relatively steadily decreases to a near constant value of around 600 W/m2K.

Three nadirs disturb uniformity of the decreasing part of the IHTC curve. They

can be correlated to the start of eutectic reaction, end of solidification and gap

formation.

Fig. 5 Estimated transient heat flux values

Fig. 6 Estimated transient IHTC values

The error between estimates and temperatures measured at the thermocouple

locations TC2 and TC3 is given in Fig. 7. The figure clearly indicates that the

error is higher at the early stages and reduces as time passes. The highest absolute

error was 11°C and 39°C for thermocouple locations TC2 and TC3, respectively.

16

This confirms earlier assumption that the algorithm is unreliable in the first 50

seconds. After this time, highest absolute errors were 0.7°C for thermocouple

location TC2 and 2.7°C for TC3.

Fig. 7 Temperature difference between calculated and measured values for thermocouple

locations TC2 and TC3

Fig. 8 IHTC as a function of casting surface temperature

The IHTC plotted against the casting surface temperature is shown in Fig. 8. It has

a near constant value at temperatures up to about 560°C. Thereafter, with a rise in

temperature to its liquidus value, the IHTC increases following “S” shape curve to

a value of 920 W/m2K. Disturbances near Tsol (573°C) which results in deviation

of the curve from smooth “S” shape are associated with the occurrences of first

two nadirs visible at the transient IHTC curve (Fig. 6). Between 588°C and 598°C

the IHTC is again nearly constant before sudden drop with further rise in the

casting surface temperature. This drop is a consequence of the underestimation of

heat flux values during the first 50 seconds and therefore does not represent the

physics at the metal-mold interface.

The arithmetic average of the profile height deviations from the mean line (Ra) of

the mold surface was measured to be Ra=20.3 μm. It should be noted that during

measurements the profilometer stylus slides against mold surface and exerts some

17

force on it. This force can be large enough to displace certain sand grains and thus

introduce error in roughness measurements. Therefore, the obtained Ra value

should be treated as approximate.

A comparison of the presented results to our previous findings [19] is given in

Table 2. Surface roughness of the mold from reference [19] exceeded profilometer

maximum range of Ra = 38 μm. Considering the average grain size of the sand

used in that experiment, real roughness value is not expected to be substantially

higher. Approximate IHTC values in present and previous work, estimated for the

period prior to start of solidification are 930 and 600 W/m2K, respectively. The

only parameters that differ between two experiments are casting thickness and

grain fineness number. Kim et al. [8] postulated that liquid IHTC most likely

depends only on roughness and surface wetting. Wetting conditions should be

constant since the casting alloy, mold material and temperature at the end of

pouring are identical for two cases considered. Therefore, different surface

roughness due to coarser grain sand used in reference [19] is probably the only

reason for 30% drop in maximum IHTC values. This trend is consistent with the

findings of Kim et al [8] and Coates and Argyropoulos [14] who reported a

decrease in liquid aluminum – metal mold IHTC values for the rougher permanent

molds or coatings.

Table 2 Comparison of current results to results from reference [19]

Current result Reference [19]

Casting thickness (m) 0.02 0.01

Grain fineness number of the sand 80 47

Average roughness of mold surface -

Ra (μm) 20.3 above 38

Maximum measured casting surface

temperature (°C) 740 740.1

Maximum IHTC plateau (W/m2K) 930 600

Minimum IHTC plateau (W/m2K) 600 360

Application of experimental IHTC curves, as the one shown in Fig. 8, has some

limitations [27]. Lewis and Ransing [27] pointed out the need for an empirical

equation that could lead to a proper choice of design variables required for feeder

optimization analysis.

18

Therefore, for vertical casting surfaces with horizontally solidifying melts the

following equation can be proposed to correlate the casting surface temperature

with the respective IHTC:

1 2

max minmin

1a T a

h hh h

e

(23)

min max

1

1 1ln 1 ln 1

sol liq

r ra

T T T

(24)

min

2

1

1ln 1

sol

ra T T

a

(25)

where hmin is the minimum value of IHTC; hmax is the maximum value of IHTC;

rmin is coefficient in the range of 0.00001 to 0.1 which controls lower radius of the

“S” curve; rmax is coefficient in the range of 0.9 to 0.99999 which controls upper

radius of the “S” curve; ΔT is temperature drop between Tsol and temperature

which corresponds to the IHTC minimum; a1 and a2 are intermediate variables.

For correlated IHTC curve shown in Fig. 8 optimal coefficients for the correlation

are: hmin = 598, hmax = 942, rmin =0.0457, rmax = 0.9892 and ΔT=10. The proposed

correlation provides satisfactory fit since the coefficient of multiple determination

for values up to the Tliq was computed to be R2=0.918. Broader applicability of the

Kovacevic correlation has been explained elsewhere [19].

It should be noted that IHTC–casting surface temperature correlation has some

advantages over the more usually applied IHTC–time or IHTC–air gap

correlations. As already explained, time dependence of IHTC is limited to the

mold configuration and the gating system design. Any change in the shape of the

casting can alter solidification dynamics and introduce errors in the applied IHTC

values. Air gap correlations overcome mentioned drawbacks and offer

substantially improved robustness. However, they only address the time period

after the air gap has formed. During the initial solidification period IHTC values

are considered constant. This can be source of significant errors. As an example

one can use results from Coates and Argyropoulos [14] investigation of heat

transfer between solidifying commercial purity aluminum and 1020 steel chill.

19

For chill surface roughness of Ra=1,41 µm and pouring temperature of 760°C

they found that air gap started to form after 1551s. During that time, initial peak

value of the IHTC was calculated to be 6817 W/m2K. Average IHTC value up to

the time of air gap formation was estimated to a 4467 W/m2K. On the other hand,

implementation of the IHTC–air gap correlation would result in the use of

constant IHTC value of 3022W/m2K during the same period. Such large

underestimation of the IHTC during the first 1550s of the process can lead to

erroneous results during computer simulation of the casting process. The probable

explanation of the underestimation is following. Immediately after pouring heat

transfer coefficients are high due to high fluidity of molten metal which conforms

more easily to rough mold surface. As superheat is lost and solidification starts

contact area diminishes, gas pockets in the roughness profile valleys get bigger

and IHTC values gradually decrease. When casting skin develops enough rigidity

to offset the effects of hydrostatic pressure the macroscopic gap starts to form.

Therefore, by the time of air gap formation the IHTC values are already decreased

(in given example from 6817 to 3022 W/m2K ). Proposed IHTC–casting surface

temperature correlation has potential to overcome mentioned problems. The rate

of IHTC decrease due to initial solid skin formation can be easily controlled by

one independent parameter, rmin.

5 Conclusions

The interfacial heat transfer coefficient (IHTC) between Al-9 wt.% Si alloy plate

casting and CO2 sand mold was evaluated by solving inverse heat conduction

problem (IHCP). Obtained transient IHTC values are then plotted against casting

surface temperature. The IHTC has nearly constant values at temperatures up to

about 560°C. With a rise in temperature to its liquidus value, the IHTC increases

following “S” shape curve to the value of 920 W/m2K.

Kovacevic correlation has been applied to describe experimentally determined

IHTC values. Correlated and experimentally obtained IHTC curves show

satisfactory agreement. Coefficient of multiple determination for the IHTC values

calculated for temperatures up to the liquidus temperature was computed to be

R2=0.918.

20

Acknowledgements

The authors gratefully acknowledge financial support provided by the Serbian Ministry of

Education , Science and Technological Development.

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Figure captions

Fig. 1 Model of experimental plate casting with thermocouple positioning

Fig. 2 Computational grid with thermocouple positions

Fig. 3 Flowchart of the solution procedure used for estimation of IHTC

Fig. 4 Temperature versus time curves obtained during solidification of Al-9 wt.% Si in CO2 sand

mold and estimated mold surface temperature curve

Fig. 5 Estimated transient heat flux values

Fig. 6 Estimated transient IHTC values

Fig. 7 Temperature difference between calculated and measured values for thermocouple locations

TC2 and TC3

Fig. 8 IHTC as a function of casting surface temperature