12 CHAPTER 2 LITERATURE REVIEW 2.1 METAL – MOLD INTERFACIAL HEAT TRANSFER During the solidification of metal castings, an interfacial heat transfer resistance exits at the boundary between the metal and the mould. This heat transfer resistance usually varies with time even if the cast metal remains in contact with the mold, due to the time dependence of plasticity of the freezing metal and oxide growth on the surface. This resistance to heat flow at the metal – mold interface has a marked influence on the solidification rate of metal castings, especially in permanent mould or die castings and in sand castings involving chills. The rate of heat transfer from the molten metal to the substrate is often limited by the thermal contact resistance. Ruhl (1967) and Wang et al (1991) have confirmed that the interfacial heat transfer coefficient between the casting and the mould was among the most important variables that controlled the melt cooling and solidification. In addition, it is possible to promote the accuracy of numerical solutions for different solidification models done by Wang et al (1992), Trapiga et al (1992), Bennett and Poulikakos (1994), Tong and Holt (1996) and Rangel and Bian (1998), if information regarding interfacial heat transfer coefficient is known with sufficient accuracy. It is therefore essential to
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12
CHAPTER 2
LITERATURE REVIEW
2.1 METAL – MOLD INTERFACIAL HEAT TRANSFER
During the solidification of metal castings, an interfacial heat transfer
resistance exits at the boundary between the metal and the mould. This heat
transfer resistance usually varies with time even if the cast metal remains in
contact with the mold, due to the time dependence of plasticity of the freezing
metal and oxide growth on the surface. This resistance to heat flow at the metal –
mold interface has a marked influence on the solidification rate of metal castings,
especially in permanent mould or die castings and in sand castings involving
chills.
The rate of heat transfer from the molten metal to the substrate is often
limited by the thermal contact resistance. Ruhl (1967) and Wang et al (1991)
have confirmed that the interfacial heat transfer coefficient between the casting
and the mould was among the most important variables that controlled the melt
cooling and solidification. In addition, it is possible to promote the accuracy of
numerical solutions for different solidification models done by Wang et al
(1992), Trapiga et al (1992), Bennett and Poulikakos (1994), Tong and Holt
(1996) and Rangel and Bian (1998), if information regarding interfacial heat
transfer coefficient is known with sufficient accuracy. It is therefore essential to
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investigate interfacial thermal conductance during rapid contact solidification
process.
In order to determine this thermal resistance, it is necessary to develop
a mathematical method which enables the calculation of thermal resistances at
the interface from measurable quantities such as thermal histories at various
thermocouple locations.
Among the mathematical methods described in the literature, three
main groups may be identified including
i. Purely analytical.
ii. Serial – analytical and empirical
iii. Numerical techniques based on FDM and FEM.
In purely analytical techniques for analyzing temperature data,
Roberstone and Fascetta (1977), Garcia et.al. (1979) and Clyne and Garcia
(1980) have assumed a constant interfacial heat transfer coefficient, in order to
obtain an analytical solution for the Fourier equation of heat conduction.
In contrast, the use of semi – analytical or empirical techniques does
not attempt to solve rigorously the Fourier heat equation, but involves analyzing
the experimental data by means of semi-analytical formulae, done by Prates and
Biloni (1972) and Levy et.al. (1969), and on curve fitting done by Tillman and
Berry (1972).
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In numerical technique, Ho and Pehlke (1983 and 1984) characterized
the heat transfer at the metal – mold interface in terms of physical mechanisms.
2.2 METHODS TO DETERMINE ‘h’ (HEAT TRANSFER
COEFFICIENT)
Attempts are done to calculate the heat transfer coefficient based upon
matching experimental solidification rates with analytical solutions. Flemings et
al (1961) and Prates et al (1972) conducted linear fluidity tests and Robertson et
al (1977) conducted experiments with metal at its melting point poured into a
semi-infinity mould. In the case of castings solidifying in permanent moulds it is
rather difficult to obtain exact analytical solutions for solidification rates in view
of the finite size of the mould and it has been recognized that numerical method
are better suited in these cases despite the approximate nature of the solutions
obtained as referred in Ruddle (1957).
The air-gap resulting from physical separation of the solidifying skin
results in a significant lowering of heat flux at the interface, and it is the most
important phenomena controlling the solidification of the casting in the metallic
mould. Many research workers like Ho and Pehlke (1984 and 1985), Sully
(1976), Issac et al (1984), Nishida et al (1986) Veinic (1968), Durham and Berry
(1974), Morgan et al (1981), Gozalan et al (1987) and Bamberger et al (1987)
have contributed to the understanding of heat flow across interface, the formation
air-gap, its spread over the entire casting surface, etc. The interfacial heat transfer
coefficient, h for various casting conditions have been reported by them.
The interfacial heat transfer coefficient, ‘h’ is measured by two methods viz.
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(i) Inverse method and
(ii) Measurement of air-gap width.
2.2.1 Inverse Method
The basic idea of the inverse method is as follows:
Here an appropriate set of equations is required to describe the heat
transfer behavior in a thermal analysis. With the boundary condition, initial
condition and the thermo physical property of the material known, the
temperature at any point within the system can be obtained. Although, one of the
thermo physical properties of the material being unknown, the temperature
distribution can be obtained by the reverse method.
One of the first efforts to solve the inverse heat conduction problem
was reported by Stolz (1960). Sparrow et al (1964) adopted the use of operational
mathematics to solve the inverse heat conduction problem in one-dimensional
geometries.
Burggraf (1964) solved the inverse heat conduction problem by
assuming a solution of the surface temperature in the form of an infinite series,
whose terms involve higher order derivatives of the temperature and heat flux
histories at an interior point multiplied by some unknown spatial functions.
Beck (1965, 1969, 1967, 1968, 1979, 1970 & 1980) has studied the
inverse heat conduction problem from the stand point of effective treatment of
experimental data.
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Analytical and numerical methods are available for solving the heat
flow equations by Jones (1969), Carslaw and Jaeger (1959), Croft and Lilley
(1977) and Segerlind (1976). For solving the inverse heat conduction problems
(IHCP), exact solutions are available. These are analytical procedures which
develop expressions for the boundary condition for a given temperature history
in the casting. A few analytical solutions to the IHCP in which a temperature
sensor is placed at an arbitrary location in the conducting body are available in
literature Burggraf (1964), Grysa (1980), Stolz (1960), Tikhonov and Arsebub
(1977) and Imber and Khan (1972).
A combined method of function specification and regularization was
reported by Tu (1988). The method of dynamic programming and its use for the
formulation and solution of the IHCP are presented in matrix form Nicholas et al
(1988 & 1989) investigated the two dimensional linear IHCP. The non linear
estimation procedure was used by Beck (1985) for numerical solution of the
IHCP. This procedure has the advantage over the other numerical procedures
that it takes into account inaccuracies in measuring the location of the
thermocouples, statistical errors in temperature measurement and uncertainty in
material properties Beck (1970).
Woodbury et al (1998) used the inverse method to measure the IHTC
between a resin-bonded mould and cast aluminum plates. Shivkumar (1993)
made some preliminary work on the heat transfer in Lost Foam Casting (LFC).
Venkataramani and Ravindran (1996) have analyzed the effects of coating
thickness and pouring temperature on thermal response in LFC.
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In this method, the temperature at some locations near the cast – mould
interface is measured and using that data, the interfacial heat transfer coefficient
is determined. Ho and Pehlke (1985) and Beck (1991) have used this technique to
find ‘h’, Hwang et al (1994) have employed both the techniques to measure ‘h’.
Mahallawy (1984) Assar (1992) and Taha et al (1992) have determined ‘h’ of the
chills. Nishida et al (1986) have estimated it for Al and Al alloy for plate and
cylindrical geometries. Zavarise et al (1992) used a thermo mechanical approach
while Zu Zanak (1991) gave criterion for the neglect of ‘h’ in metallic and sand
moulds.
2.2.2 Measurement of air-gap width
The air-gap, forms during casting solidification between the cast and
mould, has always been a matter of importance to researchers for simulating the
casting solidification. It is a cumulative movement of cast, which shrinks, and the
mould, which expands. This air-gap among several other factors resists heat
transfer between the cast and mould. It influences the solidification rate and
solidification time substantially. Interfacial heat transfer coefficient (IHTC)
decreases when the air-gap increases and there by increases the solidification
time of any casting. Hence to estimate the change in IHTC, the transient variation
of the size of air-gap is very much required.
Many researchers have used various techniques either to measure the
air-gap or to measure the IHTC directly. Henzel and Keverian (1960) have
reviewed in detail the literature on air gap formation. Veinik (1968), Mackenzie
and Donald (1950) have suggested that the total air gap formed is the sum of the
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contraction of the casting and expansion of the mould. Based on their
experimental investigation, Mackenzie and Donald (1950) have found that the
time of start of formation of air gap is different from bottom to the top.
Lewis et al (1956) and Fredrickson et al (1979) have reported that the
air gap causes a substantial reduction in the rate of heat transfer from casting to
mould, which in turn may affect the size of the air-gap.
The rate of heat transfer may also be affected by the type of the contact
between mould surface and the liquid /thin shell of the casting as has been
discussed by Prates and Biloni (1972) and Davies (1980).
However, in most of the cases as suggested by other investigators,
Pehlke (1971) and Durham (1974) also mentioned that the heat transfer through
the air gap may be due to the combined conduction and radiation.
Nelson et al (1970), Roth (1933), Bishop et al (1951), Srinivasan et al
(1970), Nehru (1974) and Thamban (1978) have reported the influence of
volume ratio on solidification time. All the investigators have assumed certain
value for the thermal resistance offered by the air-gap, since no information was
available on the size, distribution and formation of air-gap.
Isotani et al (1969) and Nehru (1974) have studied the influence of
coating thickness on the solidification time.
Determination of the air-gap during solidification requires
simultaneous measurements of both the mould wall and casting movements.
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Gittus (1954) observed both motions by measuring the movements of silica
probes in sand and metal by means of dial gauges. Engler et al (1973) improved
measurement accuracy by employing inductive movement sensors.
Malur N.Srinivasan (1982) has done experiments with plate and
cylindrical castings by pouring the metal at different temperatures into the
moulds of different wall thickness and pre heated to different temperatures.
Solidification time of these castings was matched with the experimental
solidification times and the heat transfer coefficients at the cast-mould interface
in the experimental castings were computed.
Pehlke et al (1982) have conducted experiments to find gap formation
of vertically cast cylinders of iron, copper and aluminum based alloys in dry and
green sand. The advantage of a vertical configuration is that the gap should be
radially symmetric about the perimeter of the cylinder.
Chiesa (1990) measured the temperature variation of molten metal
during the casting. By comparing the theoretical model, he obtained the ‘h’ under
various coating conditions. His results also demonstrated that interfacial heat
transfer resistance existed even in the filling period when the metal was still in
liquid state. Kumar and Prabhu (1991) found that the heat flux was actually an
exponential function of time.
Ho and Pehlke (1983) have used two methods to measure the
interfacial heat transfer coefficient, viz.
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(i) computer simulation of the inverse heat conduction problem
using thermocouple measurements at selected locations in the
casting and the mould and
(ii) measurement of the variation of the interfacial gap size with
time using a differential displacement between two transducers
which continuously record the mould and metal movements
respectively in the vicinity of the interface.
They explained three different mechanisms which may affect the
transition of a metal and mould in solid contact to an interfacial gap viz.
(i) surface interaction of the metal and mould,
(ii) transformation of metal and mould materials and
(iii) effects of geometry.
They studied the interfacial heat transfer on two related types of
castings. The influence of air-gap on solidification time with three mould
materials is compared by a numerical example, and criteria for utilizing
chvorinov’s rule are discussed.
Isaac et al (1985) have done experimental investigations and found
that the time of start of air-gap formation, its growth, total size and solidification
time depend on the different combinations of volume ratio and coating thickness.
Hao et al (1987) have indicated, based on experiments with ductile iron and
calculations that there is no air-gap between the ductile iron casting and the
mould due to the expansion of graphite precipitated during the solidification
period. Hou and Pehlke (1988) have done experiments with Al 13% Si casting
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and measured the air-gap size and from that they determined the interfacial heat
transfer coefficients at the interface. Lukens, Hou and Pehlke (1990) have
measured the air-gap formation in cylindrical castings of Al alloy 356
horizontally in dry and green sand. They found that more heat transfer occurred
in the drag and the final solidification occurred in the top of the mould cavity.
Chiesa (1990) has measured the thermal conductance at the interface in
permanent moulds and studied the influence of insulation coating thickness on
the thermal conductance. Prasanna Kumar and Narayan Prabhu (1991) have done
experiments with Al13.2%Si and Al3%Cu 4.5%Si alloys of casting square bars
for different metal / chill combinations with and without coatings. Hwang et al
(1994) have found, by the measurement of air-gap size, the value of h varies with
time/temperature during casting. ‘h’ is very high as the air-gap starts forming and
keeps dropping by as the air-gap size increases. It approaches constant when the
air-gap fully developed. By inverse method, they found that the value of ‘h’
increases in the beginning and reaches a peak value. Then it drops rapidly at the
eutectic temperature and rises again until the end of solidification. After that ‘h’
keeps dropping until the end of casting.
Gerber et al (1995) has done numerical investigation on the influence
of air-gaps upon the solidification in a rotary caster. Mythily Krishnan and
Sharma (1996) have determined ‘h’ in steady state unidirectional heat flow using
Beck’s non-linear estimation procedure. Lau et al (1998) has used inverse
heat-conduction analysis to find ‘h’. They suggested a three stage segmented
linear equation for ‘h’. Khan et al (2000) have used inverse heat conduction
method on LFC and found that the value of the IHTC initially as 120-150
W/m2Kand gradually decreased to approximately 100W/m2K. IHTC was not
significantly affected by the amount of super heat over the range studied.
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Shenefelt et al (2000) have used a new method for solving linear inverse heat
conduction problems using temperature data. The method employs a pulse
sensitivity matrix and singular value decomposition to convert the heat transfer
problem into the frequency domain. This method reduced material size, robust
treatment of noisy temperature data and lack of ad hoc parameters.
Parker and Piwonka (2000) have used eddy-current proximity sensor
for non-contact measurement of the gap formation between a solidifying
aluminum casting and a resin bonded sand mould. Woodburry et al (2000) have
investigated the interfacial heat transfer coefficients for resin bonded sand
casting of plate aluminum castings. Lewis and Ransing (2000) have done a
thermo-mechanical analysis of solidification process to predict the air-gap. They
used Lewis-Ransing correlation to link the stress model with an optimization
model for the optimal feeding design. Krishna et al (2001) have done the
evaluation of ‘h’ in LPPM (Low Pressure Permanent Mould) on Aluminum
casting process. They observed that the air-gap does not influence ‘h’ after a
lapse of about 300sec. and it approaches a constant value of about 400W/m2K for
any size of the air-gap. Santos et al (2001) have determined the transient ‘h’
values in chill mould castings. Using FDM technique, air-gap determined in
Al-Cu and Sn-Pb alloys were used for their study. Robinson and Palaninathan
(2001) have done 3D FE modeling of solidification of piston castings.
Wang and Qiu (2002) have studied the interfacial thermal conductance
in rapid contact solidification process. They used a temperature sensor of 1µm
thick to measure the rapid temperature changes. Wang and Mathys (2002) have
done experiments to determine ‘h’ during cooling and solidification of molten
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metal droplets on a metallic substrate. The effect of melt super heat and surface
roughness were studied.
Gafur (2003) has investigated the effect of chill thickness and super
heat on ‘h’ during solidification of commercially pure aluminum. They have
done inverse analysis of the non-linear one-dimensional Fourier heat conduction
equation. Narayan Prabhu and Ravishankar (2003) have investigated the effect of
modification melt treatment on ‘h’ and electrical conductivity of Al 13%Si alloy.
Kayikci (2003) has used ultrasonic flaw detection techniques for the
determination of casting-chill contact during solidification. They used Al alloy
on to a Cu chill and observed a peak in ultrasound transmission, in the first two
seconds correlating to a maximum in the area of casting-chill contact. This was
followed by a decrease in the ultrasound transmission that corresponded to actual
contact areas between the casting and the chill in the region of 5 to 10%. Heinrich
and Poirier (2004) examined the effect of volume change during directional
solidification of binary alloys through numerical simulations of hypoeutectic Pb
– Sn alloys.
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2.3 TECHNIQUES TO MEASURE THE AIR-GAP WIDTH
The interfacial heat transfer coefficient (IHTC), ‘h’ can be calculated
either by measuring the width of air-gap and using the formula,
h = k/a (2.1)
where
k – Thermal conductivity of air or gases in the air-gap and
a – width of the air-gap,
or by measuring the temperature at certain locations of the metal and mould using
the inverse method. Many researchers measured the air-gap width using various
techniques. Ho and Pehlke (1984) have explained the mechanisms of heat
transfer at the metal-mould interface. They explained three different mechanisms
which may affect the transition of a metal and mould in solid contact to an
interfacial gap viz.
(i) surface interaction of the metal and mould,
(ii) transformation of metal and mould materials and
(iii) effects of geometry.
Their work has drawn the importance of knowing what is in the air-gap
and the size of the gap width. Although the gap is universally called as the
‘air-gap’, this term may be somewhat misleading. In fact in many instances there
won’t be any air in it. For example, iron and steel castings in sand moulds, the
main gas present is H2. Campbell (1991) has estimated the size of the air-gap as
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a = R [ αc (Tf – T) + αm ( Ti – To )] (2.2)
where
a – width of air-gap,
R – Radius of the casting,
αc & αm – thermal coefficients of the casting and mould,
Tf & T – freezing and final temperature of casting,
Ti – To – instantaneous and original temperature of the mould interface.
Kesavan and Seethramu (1994) have presented an entirely numerically
simulated program, which needs only the properties of the cast metal and mould
material as input. Ho and Pehlke (1983) have measured the magnitude of the
dynamic gap using the differential displacement between two transducers, which
continuously record the mould and metal movements respectively in the vicinity
of the interface. They used an experimental setup with a casting geometry of a
bottom gater vertical cylinder of 12.7cm diameter and 15.0cm height as shown in
Figure 2.1.
Using an insulating riser sleeve whose outer wall is covered by a layer
of fibrous kaowool minimizes heat flow in the radial direction. A Cu chill placed
on the top opening of the riser sleeve is forced cooled by a water cooled cap
which also supports linear transducers for measuring chill and metal movements.
As a result an approximately vertical heat flow pattern develops in the cast metal
as solidification progresses.
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Figure 2.1 Schematic diagram of the apparatus (Ho and Pehlke, 1983)
.
The measurement of metal-chill interfacial gap width is carried out using two
linear transducers, which continuously record the movements of the metal and
chill independently in the vicinity of the interface. These linear transducers
thereby show the interfacial gap width. As solidification commences, a dual-pen
recorder continuously records outputs from these two linear transducers.
Isaac et al (1985) revealed their investigations that the gap starts
forming at different times on the surface of the casting and that the gap sizes on
the surface vary from point to point during solidification. The influence of
coating thickness and mould volume ratio on behavior of the air-gap has also
been studied. They conducted experiments and found that the air-gap formation
starting time, its growth, total size and solidification time were depend on the
different combinations of volume ratio and coating thickness. In their
experiment, aluminum was poured into a cast iron mould with a cavity size of
7x7x28cm as shown in Figure 2.2 (a). The casting was fed from the sides (two
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risers) and only the central section was investigated. Their mechanical air-gap