I investigated the heat-transfer behaviour of annular castings produced by sand mould casting under natural cooling and forced air-cooling conditions. The work focused on the interfacial heat-transfer coefficient (IHTC) between the casting and the sand mould or sand core, because this coefficient controls the cooling rate, solidification path, defect formation, stress state, grain size, and final mechanical properties of the casting. I combined measured temperature fields, an optimised inverse Beck algorithm, and a one-dimensional numerical heat-conduction model to obtain the IHTC for cast aluminium and cast steel in annular sand mould casting. The main variables were casting material, casting size, sand binder type, and forced air cooling through a pipe embedded in the sand core. The results provide a data basis for simulation of sand mould casting with forced cooling and for process design in foundries.
1. Research Context and Objective
Sand mould casting remains one of the most important manufacturing routes for complex metal components. In modern sand mould casting, alloy composition, moulding material, coating, gating, feeding, and external fields such as air cooling, water cooling, negative pressure, centrifugal force, and vibration are increasingly combined. These combinations make the solidification and cooling process more difficult to predict. Numerical simulation can reduce trial-and-error cost, but its accuracy depends strongly on physical parameters. Among these parameters, the IHTC is the most important thermal boundary condition at the casting–mould interface.
The IHTC is defined as the ratio of interfacial heat flux density to the temperature difference between the casting surface and the mould surface:
$$
h_i=\frac{q_i}{T_C^i-T_1^i}
$$
Here, \(h_i\) is the interfacial heat-transfer coefficient, \(q_i\) is the interfacial heat flux density, \(T_C^i\) is the measured casting temperature, and \(T_1^i\) is the back-calculated sand surface temperature. The IHTC is not a true constant. It changes with time, temperature, gap formation, surface roughness, mould material, coating, metallostatic pressure, casting geometry, and external cooling. In sand mould casting, the formation of an air gap between the casting and the sand mould is a dominant factor. The gap reduces heat transfer because air has low thermal conductivity. Therefore, understanding IHTC evolution in sand mould casting is essential for reliable simulation and process control.
My objective was to determine how the IHTC in annular sand mould casting changes with casting material, annular size, sand type, and forced air cooling. I also aimed to explain the physical mechanisms, especially the roles of air-gap formation, solid fraction, quartz phase transformation, pearlite transformation, and sand-core heat saturation.
2. Experimental Programme
I selected ZL101 aluminium alloy and 40 steel as casting materials. I used furan resin no-bake sand and water glass no-bake sand as mould and core materials. The annular castings had inner radii of 60 mm, 100 mm, and 140 mm. Forced air cooling was applied by passing compressed air through a steel pipe placed inside the sand core. The air-pipe diameters were 40 mm, 60 mm, and 80 mm. The air velocities were adjusted to 6 m/s, 8 m/s, and 10 m/s for the three pipe sizes. The pouring temperatures were approximately 730 °C for ZL101 and 1560 °C for 40 steel.
2.1 Casting Materials
| Alloy | Si | Mg | Ti | Other elements | Al |
|---|---|---|---|---|---|
| ZL101 | 6.5–7.5 | 0.25–0.45 | 0.08–0.20 | Cu ≤ 0.10, Mn ≤ 0.10, Zn ≤ 0.10, Zr ≤ 0.10 | Balance |
| Alloy | C | Si | Mn | Other elements | Fe |
|---|---|---|---|---|---|
| 40 steel | 0.37–0.44 | 0.17–0.37 | 0.50–0.80 | Cr ≤ 0.25, Ni ≤ 0.30, Cu ≤ 0.25 | Balance |
2.2 Mould and Core Materials
I prepared furan resin no-bake sand by mixing silica sand with a curing agent and a resin binder. I prepared water glass no-bake sand by mixing silica sand with an organic ester hardener and water glass. The thermophysical parameters used in the inverse calculation are listed in the following tables. Linear interpolation was used between measured points.
| Temperature (°C) | Density (kg/m³) | Heat capacity (kJ/(kg·K)) | Thermal conductivity (W/(m·K)) |
|---|---|---|---|
| 20 | 1590 | — | 0.71 |
| 50 | 1590 | 0.73 | — |
| 100 | 1590 | 0.80 | — |
| 150 | 1590 | 0.85 | — |
| 200 | 1590 | 0.92 | — |
| 232 | 1590 | — | 0.62 |
| 250 | 1590 | 0.90 | — |
| 350 | 1590 | 0.94 | — |
| 400 | 1590 | 1.00 | — |
| 414 | 1590 | — | 0.55 |
| 500 | 1590 | 1.00 | — |
| 600 | 1590 | — | 0.50 |
| 708 | 1590 | — | 0.61 |
| 980 | 1590 | — | 0.78 |
| Temperature (°C) | Density (kg/m³) | Heat capacity (kJ/(kg·K)) | Thermal conductivity (W/(m·K)) |
|---|---|---|---|
| 50 | 1590 | 0.77 | 0.77 |
| 200 | 1590 | 0.72 | 0.84 |
| 500 | 1590 | 0.62 | 0.88 |
| 700 | 1590 | 0.58 | 0.92 |
| 900 | 1590 | 0.53 | 0.99 |
| 1100 | 1590 | 0.55 | 1.03 |
| 1350 | 1590 | 0.62 | 1.06 |
| 1450 | 1590 | 0.68 | 1.08 |
| 1500 | 1590 | 0.76 | 1.09 |
| 1550 | 1590 | 0.80 | 1.10 |
2.3 Temperature Measurement and Forced Air Cooling
I placed one thermocouple in the casting cavity about 2 mm from the mould surface to record the casting temperature \(T_C\). I placed three thermocouples in the sand mould at distances of 6 mm, 14 mm, and 22 mm from the casting outer surface; these are denoted \(T_{m1}\), \(T_{m2}\), and \(T_{m3}\). I used K-type thermocouples for aluminium and B-type thermocouples for steel. The temperature recorder collected data at a frequency of 1 Hz. I embedded the forced-air pipe in the sand core. The air compressor supplied high-pressure air after pouring. The air valve remained closed during pouring and was opened immediately after filling to begin forced air cooling.
| No. | Casting material | Sand type | Inner radius (mm) | Air pipe diameter (mm) |
|---|---|---|---|---|
| 1 | Aluminium | Furan resin no-bake sand | 60 | None |
| 2 | Aluminium | Furan resin no-bake sand | 100 | None |
| 3 | Aluminium | Furan resin no-bake sand | 140 | None |
| 4 | Aluminium | Furan resin no-bake sand | 100 | 60 |
| 5 | Aluminium | Water glass no-bake sand | 60 | None |
| 6 | Aluminium | Water glass no-bake sand | 100 | None |
| 7 | Aluminium | Water glass no-bake sand | 140 | None |
| 8 | 40 steel | Furan resin no-bake sand | 100 | None |
| 9 | 40 steel | Furan resin no-bake sand | 100 | 40 |
| 10 | 40 steel | Furan resin no-bake sand | 100 | 60 |
| 11 | 40 steel | Furan resin no-bake sand | 100 | 80 |
3. Inverse Heat-Transfer Model
I simplified the annular sand mould casting problem into a one-dimensional transient heat-conduction problem in the sand mould near the casting. The governing Fourier equation is:
$$
\frac{\partial}{\partial x}\left(k\frac{\partial T}{\partial x}\right)=\rho C_P\frac{\partial T}{\partial t}
$$
Here, \(k\) is thermal conductivity, \(\rho\) is density, \(C_P\) is effective specific heat, \(T\) is temperature, and \(t\) is time. The initial condition is:
$$
T(x,0)=T_{\mathrm{in}}(x)
$$
The boundary conditions are a heat-flux condition at the casting–mould interface and a measured temperature condition at the far sand node:
$$
-k(T)\left.\frac{\partial T}{\partial x}\right|_{x=0}=q(0,t)
$$
$$
T(x_6,t)=T_{m3}(t)
$$
I used an implicit finite-volume method. For each control volume, the energy balance is:
$$
\Delta u=A_{\mathrm{in},j}q_{\mathrm{in},i}+A_{\mathrm{out},j}q_{\mathrm{out},i}
$$
For the first node adjacent to the interface, the discretised equation becomes:
$$
(1+S_{\mathrm{out}}(1))T_1^{i+1}-S_{\mathrm{out}}(1)T_2^{i+1}=T_1^i+S_{\mathrm{in}}(j)\Delta X q^{i+1}
$$
For internal nodes, the discretised equation is:
$$
-S_{\mathrm{in}}(j)T_{j-1}^{i+1}+\left[1+S_{\mathrm{in}}(j)+S_{\mathrm{out}}(j)\right]T_j^{i+1}-S_{\mathrm{out}}(j)T_{j+1}^{i+1}=T_j^i
$$
The coefficients \(S_{\mathrm{in}}\) and \(S_{\mathrm{out}}\) account for annular geometry and are defined as:
$$
S_{\mathrm{in}}(j)=\frac{A_{\mathrm{in},j}}{V_j}\frac{\Delta t\,k_i}{\rho C_P^i\Delta X}
$$
$$
S_{\mathrm{out}}(j)=\frac{A_{\mathrm{out},j}}{V_j}\frac{\Delta t\,k_i}{\rho C_P^i\Delta X}
$$
Because the annular geometry has different areas for heat inflow and outflow, I introduced geometric factors:
$$
\frac{A_{\mathrm{in},j}}{V_j}=\frac{r_{\mathrm{use}}-j\Delta r+\Delta r}{\Delta r\left(r_{\mathrm{use}}-j\Delta r+0.5\Delta r\right)}
$$
$$
\frac{A_{\mathrm{out},j}}{V_j}=\frac{r_{\mathrm{use}}-j\Delta r}{\Delta r\left(r_{\mathrm{use}}-j\Delta r+0.5\Delta r\right)}
$$
These equations form a tridiagonal matrix system that I solved with the Thomas algorithm. The unknown interfacial heat flux \(q\) was obtained by the Beck inverse method. The objective function is:
$$
F(q_{\mathrm{set}})=\sum_{f=M+1}^{M+r}\sum_{j=1}^{J}\left[T_j^f-T_{mj}^f(q_{\mathrm{set}})\right]^2
$$
Minimising this function gives the iterative update:
$$
q^{(k+1)}=q^{(k)}+\frac{\sum_{f=M+1}^{M+r}\sum_{j=1}^{J}\left[T_j^f-T_{mj}^f(q_{\mathrm{set}})\right]\varphi_j^f}{\sum_{f=M+1}^{M+r}\sum_{j=1}^{J}\left(\varphi_j^f\right)^2}
$$
The sensitivity coefficient \(\varphi_j^f\) is computed by a small perturbation of the heat flux:
$$
\varphi_j^f=\frac{\partial T_j^f}{\partial q}\bigg|_{q=q_{\mathrm{set}}}
=\frac{T_j^f(q_{\mathrm{set}}+\varepsilon q_{\mathrm{set}})-T_j^f(q_{\mathrm{set}})}{\varepsilon q_{\mathrm{set}}}
$$
Iteration stops when:
$$
\frac{\left|q^{(k+1)}-q^{(k)}\right|}{\left|q^{(k+1)}\right|}<\varepsilon
$$
I verified the inverse model by comparing back-calculated temperatures of nodes 2 and 4 with measured \(T_{m1}\) and \(T_{m2}\). The relative deviation was calculated as:
$$
\delta=\frac{\left|T_2-T_{m1}\right|}{T_2}\times100\%
$$
For aluminium sand mould casting, the maximum relative deviation was about 5%, and the average deviation was about 1.02%. For steel sand mould casting, the maximum relative deviation was about 3%, and the average deviation was about 0.13%. These small deviations indicate that the optimised inverse method is reliable for annular sand mould casting.
4. Interfacial Heat Transfer Without Forced Air Cooling
4.1 ZL101 Aluminium in Sand Mould Casting
In natural cooling, the ZL101 casting temperature decreased rapidly after pouring, then showed a plateau caused by latent heat release during eutectic solidification, and finally decreased slowly with the sand mould. The sand temperature first increased rapidly, then decreased together with the casting. The IHTC followed an S-shaped curve when plotted against casting temperature. The IHTC increased as the casting temperature decreased until about 614 °C, where a small temporary decrease appeared. It then increased again until the critical solid fraction temperature near 575 °C. At 575 °C, the IHTC dropped sharply. Below 575 °C, the IHTC remained nearly constant or decreased slowly.
The physical reason is air-gap formation. When the first solid shell forms, small gaps appear between the shell and the sand surface. These gaps reduce heat transfer and cause a small IHTC decrease. However, before the critical solid fraction, the shell is thin and cannot resist the metallostatic pressure, so the gap cannot grow freely. Latent heat release also keeps the local temperature high and increases the temperature difference influence. As solid fraction approaches the critical value, the remaining liquid can no longer feed shrinkage, and gap formation becomes extensive. The solid shell also becomes thick enough to support the liquid, so the gap can grow. Therefore, the IHTC drops abruptly near 575 °C.
I fitted the aluminium IHTC versus casting surface temperature with a sigmoid-type relation:
$$
y=h_{\min}+\frac{h_{\max}-h_{\min}}{1+\exp\left((x-a)/b\right)}
$$
Here, \(x\) is casting surface temperature, \(y\) is IHTC, \(h_{\min}\) and \(h_{\max}\) are limiting values, \(a\) is the critical temperature related to solidification, and \(b\) is a size-related coefficient. The fitted parameters are summarised below.
| Inner radius (mm) | \(h_{\min}\) (W/(m²·°C)) | \(h_{\max}\) (W/(m²·°C)) | \(a\) (°C) | \(b\) |
|---|---|---|---|---|
| 60 | 60 | 109 | 575 | 1.5 |
| 100 | 83 | 127 | 575 | 0.36 |
| 140 | 45 | 91 | 575 | 0.44 |
4.2 40 Steel in Sand Mould Casting
For 40 steel in sand mould casting, the IHTC showed a bimodal shape with time. After pouring, the IHTC first increased rapidly to a maximum, then dropped in a step-like manner to a minimum, then increased slowly to a second maximum, and finally decreased slowly. The initial IHTC was about 449 W/(m²·°C). The first maximum reached about 493 W/(m²·°C), and the first minimum was about 186 W/(m²·°C). The second maximum reached about 372 W/(m²·°C).
| Stage | Approximate time | IHTC trend | Mechanism |
|---|---|---|---|
| 1 | 0–200 s | Slight decrease | Rapid solidification forms a thin shell and small air gaps. |
| 2 | 200–1425 s | Rapid increase to first maximum | Sand expansion and quartz transformation reduce gap thickness. |
| 3 | 1425–2710 s | Rapid decrease to minimum | Casting and sand both cool and contract, increasing gap thickness. |
| 4 | 2710–4100 s | Increase to second maximum | Pearlite transformation in steel causes local volume expansion and reduces gap thickness. |
| 5 | 4100–5260 s and later | Rapid then slow decrease | Quartz transformation in sand and reduced thermal driving force increase gap resistance and lower heat flow. |
The bimodal behaviour is therefore not caused by a single event. It is the result of competition between casting contraction, sand expansion, casting phase transformation, sand phase transformation, and air-gap evolution. In sand mould casting of steel, these volume changes are large because the pouring temperature is high and the cooling interval is long.
4.3 Effect of Casting Material
The casting material strongly affects the IHTC curve shape. Aluminium solidifies at a lower temperature and has a longer solidification interval with a clear latent-heat plateau. Steel solidifies at a much higher temperature and cools over a longer time. The interfacial temperature difference and heat flux both decrease rapidly at the beginning and then stabilise. However, the IHTC curves differ: aluminium follows an S-shaped curve, while steel follows a bimodal curve.
| Feature | ZL101 aluminium | 40 steel |
|---|---|---|
| Pouring temperature | About 730 °C | About 1560 °C |
| IHTC shape | S-shaped with a sharp drop near 575 °C | Bimodal with two maxima and two minima |
| Main gap-control mechanism | Solid shell formation, critical solid fraction, shrinkage feeding stop | Thermal contraction, sand expansion, quartz transformation, pearlite transformation |
| Cooling duration | Shorter | Longer |
| Typical IHTC range | About 60–127 W/(m²·°C) | About 186–493 W/(m²·°C) |
4.4 Effect of Annular Size
For annular sand mould casting, the IHTC changed with inner radius. The maximum, average, and final stable values first increased and then decreased as the inner radius increased from 60 mm to 100 mm and then to 140 mm. This differs from simple plate or cylinder castings, where IHTC often increases monotonically with size. The annular geometry introduces two curvature-related effects: a larger radius increases the total shrinkage displacement, but it also changes the local sand constraint and gap distribution.
The slope of the IHTC drop near the critical solid fraction became steeper as the inner radius increased. A larger annular casting contracts more in absolute terms, producing a larger gap and a faster IHTC decrease. I therefore included both a critical temperature parameter and a size-related coefficient in the fitting equation.
4.5 Effect of Sand Type
I compared furan resin no-bake sand and water glass no-bake sand in sand mould casting. Both sand types produced an S-shaped IHTC curve for aluminium. The main difference appeared near 614 °C. In water glass sand, the IHTC showed a clear temporary decrease, while in furan resin sand, the decrease was only a slight oscillation. The reason is that water glass sand has a rougher surface and releases more gas and moisture, so the initial gap is larger. Furan resin sand has a smoother surface and a more stable heat capacity below 575 °C, so its IHTC remains more stable after the critical drop.
| Sand type | IHTC shape | Behaviour near 614 °C | Behaviour below 575 °C | Overall IHTC level |
|---|---|---|---|---|
| Furan resin no-bake sand | S-shaped | Slight oscillation | Nearly stable | Higher |
| Water glass no-bake sand | S-shaped | Clear temporary decrease | Gradual decrease | Lower |
5. Forced Air Cooling in Sand Mould Casting
5.1 Effect on Aluminium Castings
Forced air cooling did not change the overall temperature-field sequence in sand mould casting, but it accelerated cooling. The latent-heat plateau remained visible, and the sand still first heated and then cooled. However, the casting temperature dropped much faster after latent-heat release. In natural cooling, the cooling rate after solidification was about 0.05 °C/s; with forced air cooling, it increased to about 0.2 °C/s. The solidification time, estimated as the time to reach the solidus temperature, decreased from about 1655 s without air cooling to about 1224 s with air cooling, a reduction of about 25%.
Forced air cooling also eliminated heat saturation in the sand core. Without air cooling, the sand core temperature could approach or exceed the casting temperature, reducing the driving force for heat extraction. With air cooling, the flowing air removed heat from the core, so the core remained cooler than the casting. This increased the effective heat extraction and shortened the cooling time.
The IHTC under forced air cooling still followed an S-shaped trend with casting temperature, but the values were much higher. The average IHTC increased from about 94 W/(m²·°C) without air cooling to about 143 W/(m²·°C) with air cooling, an increase of about 52%. The period of IHTC increase was shortened, and the period of IHTC decrease was extended. Before reaching 575 °C, the air-cooled casting showed a slow decrease in IHTC, whereas the naturally cooled casting showed a slow increase. This difference is caused by early gap formation under rapid cooling. The rapidly solidified shell becomes thick enough to maintain small gaps, so the IHTC decreases gradually before the critical solid fraction is reached.
| Condition | Cooling rate after solidification | Time to solidus | Average IHTC | IHTC shape |
|---|---|---|---|---|
| No air cooling | About 0.05 °C/s | About 1655 s | About 94 W/(m²·°C) | S-shaped |
| Forced air cooling | About 0.2 °C/s | About 1224 s | About 143 W/(m²·°C) | S-shaped with early slow decrease |
5.2 Effect on Steel Castings
Forced air cooling also accelerated steel sand mould casting. The temperature-field sequence remained similar, but the cooling rate increased. The IHTC still showed a bimodal shape, but the values increased significantly. The average IHTC under forced air cooling reached more than twice the value obtained without air cooling. As the air-pipe diameter increased from 40 mm to 60 mm and then to 80 mm, the peak values increased, and the peaks appeared earlier.
| Condition | Air velocity | Time to 400 °C | IHTC shape | Average IHTC relative to no air cooling |
|---|---|---|---|---|
| No air cooling | — | About 1119 s | Bimodal | Baseline |
| Air pipe 40 mm | About 6 m/s | About 864 s | Bimodal, stronger peaks | More than 2 times |
| Air pipe 60 mm | About 8 m/s | About 744 s | Bimodal, stronger peaks | More than 2 times |
| Air pipe 80 mm | About 10 m/s | About 493 s | Bimodal, strongest peaks | More than 2 times |
The air-pipe size also affected the sand temperature field. As the pipe diameter increased, the sand heating rate increased, and the maximum sand temperature increased. With an 80 mm pipe, the maximum sand temperature reached about 1050 °C. However, a small air pipe such as 40 mm did not always produce a higher sand temperature than natural cooling. This is because forced air cooling increases the casting cooling rate and therefore increases the driving force, but it also removes heat through the core and reduces the total heat that enters the sand mould. The two effects compete. A larger pipe shifts the balance toward faster sand heating and a higher sand peak temperature.
The interfacial heat flux density under forced air cooling remained highest at the beginning and then decreased to a stable value. As the pipe diameter increased, the initial heat flux increased because the casting cooled faster and the driving force was larger. In the later stage, however, the heat flux toward the sand mould decreased because the core removed more heat. The IHTC increased with pipe diameter in both maximum and minimum values, and the bimodal shape became more pronounced.
| Parameter | No air cooling | 40 mm pipe | 60 mm pipe | 80 mm pipe |
|---|---|---|---|---|
| First peak time | Latest | Earlier | Earlier still | Earliest |
| First peak value | Lowest | Higher | Higher | Highest |
| Second peak time | Latest | Earlier | Earlier | Earlier |
| Second peak value | Highest | Lower | Lower | Lowest |
| Average IHTC | Baseline | Increased | Increased | Highest |
| Cooling time | Longest | Shorter | Shorter | Shortest |
6. Mechanism of Forced Air Cooling on IHTC
6.1 Aluminium Sand Mould Casting
In aluminium sand mould casting, forced air cooling changes the competition between latent heat release and air-gap formation. When solid fraction reaches about 10%, heterogeneous nucleation forms small solid shells. These shells create tiny gaps and cause a small IHTC decrease. Under natural cooling, the shell remains thin and cannot maintain a large gap, so the IHTC continues to rise. Under forced air cooling, the shell becomes thicker quickly. The thicker shell can support the metallostatic pressure and maintain the gaps. As solidification continues, more small gaps form, and the IHTC slowly decreases before the critical solid fraction.
At the critical solid fraction near 50%, both natural and forced cooling show a sharp IHTC drop. In natural cooling, few gaps existed before this point, so the sudden formation of many gaps causes a large drop. In forced cooling, many gaps already existed, so the additional drop is smaller. After the critical solid fraction, the gap is already large, and further contraction changes the IHTC only slowly.
6.2 Steel Sand Mould Casting
In steel sand mould casting, forced air cooling changes the rate of gap-thickness evolution. The IHTC has five stages. In stage 1, rapid solidification creates an initial gap, and air cooling makes the initial gap larger, so the IHTC decrease is greater. In stage 2, sand expansion reduces the gap and increases the IHTC. Air cooling accelerates both casting contraction and sand expansion, but sand expansion dominates, so the first IHTC peak appears earlier and becomes sharper. In stage 3, both casting and sand cool and contract, so the gap grows and the IHTC falls. Air cooling makes this contraction faster, so the IHTC decreases more. In stage 4, pearlite transformation in the steel causes volume expansion and reduces the gap. Air cooling accelerates sand contraction, which opposes the gap reduction, so the second peak becomes smaller when the air cooling is strong. In stage 5, sand phase transformation and reduced thermal driving force cause the IHTC to decrease. Air cooling has only a limited effect on this final stage.
Thus, in steel sand mould casting, forced air cooling increases the IHTC mainly by accelerating volume changes and making gap-thickness changes more rapid. The casting cools faster, the sand core no longer reaches heat saturation, and the sand temperature field changes more quickly. These effects combine to produce higher IHTC values and stronger bimodal peaks.
6.3 Comparison Between Aluminium and Steel
| Feature | Aluminium sand mould casting | Steel sand mould casting |
|---|---|---|
| IHTC shape with air cooling | S-shaped, with a slow decrease before 575 °C | Bimodal, with stronger and earlier peaks |
| Main effect of air cooling | Earlier gap formation and larger initial gaps | Faster gap-thickness changes and stronger volume-change competition |
| Average IHTC increase | About 52% for the tested condition | More than 2 times the natural-cooling value |
| Cooling-time reduction | About 25% to solidus | Substantial reduction; time to 400 °C decreases with air-pipe diameter |
| Role of sand core | Heat saturation is eliminated | Heat saturation is eliminated, sand peak temperature changes with pipe size |
For both materials, forced air cooling has an enhancing effect on the IHTC in annular sand mould casting. It increases the heat extraction rate, changes the gap formation process, and shortens the cooling time. The exact IHTC response depends on the alloy solidification characteristics, the casting geometry, and the air-cooling intensity.
7. Practical Implications for Sand Mould Casting
The results show that the IHTC in sand mould casting should not be treated as a constant. For aluminium annular sand mould casting without forced air cooling, the IHTC can be described by an S-shaped function of casting surface temperature. For steel annular sand mould casting without forced air cooling, the IHTC should be described by a time-dependent bimodal function. When forced air cooling is used, the IHTC values increase, and the curve shape changes. Simulation models that use a constant IHTC will therefore mispredict the cooling rate, solidification time, and temperature field.
I also found that sand type matters. Furan resin no-bake sand gives a higher and more stable IHTC than water glass no-bake sand in aluminium sand mould casting. For process design, furan resin sand may be preferred when faster and more stable cooling is desired. For annular castings, the inner radius affects the IHTC through curvature and shrinkage displacement, so the IHTC should be calibrated for the specific annular geometry rather than taken from a plate or cylinder database.
Forced air cooling is a practical method to shorten production cycles in sand mould casting. It is flexible, relatively safe, and easy to install. The air pipe embedded in the sand core removes heat and prevents heat saturation. Increasing the air-pipe diameter increases the IHTC and reduces the time required to reach a given temperature. However, the air-cooling intensity should be controlled because rapid cooling can increase thermal gradients and may affect defect distribution and residual stress. The IHTC data obtained here can be used as boundary conditions in simulation of sand mould casting with forced air cooling.
8. Conclusions
I studied the heat-transfer law of annular castings in sand mould casting with and without forced air cooling. The main conclusions are as follows.
First, the IHTC of ZL101 aluminium in sand mould casting follows an S-shaped curve with casting temperature. It increases as temperature decreases, shows a small disturbance near 614 °C, and then drops sharply near 575 °C, which is close to the critical solid fraction. Below 575 °C, the IHTC remains stable or decreases slowly. The sharp drop is caused by extensive air-gap formation when the remaining liquid can no longer feed shrinkage.
Second, the IHTC of 40 steel in sand mould casting shows a bimodal shape with time. It first increases to a maximum, then drops to a minimum, then rises to a second maximum, and finally decreases slowly. The first peak is related to sand expansion and quartz transformation, while the second peak is related to pearlite transformation in the steel. The minima are related to contraction of both casting and sand and to later sand phase transformation.
Third, forced air cooling enhances the IHTC in annular sand mould casting. For aluminium, the IHTC remains S-shaped but reaches higher values; the average IHTC increased from about 94 to about 143 W/(m²·°C) in the tested condition. For steel, the IHTC remains bimodal but the peaks become stronger and appear earlier, and the average IHTC can exceed twice the natural-cooling value. Forced air cooling also shortens the cooling time and eliminates heat saturation in the sand core.
Fourth, the air-pipe diameter affects the forced-air-cooling performance. Larger pipes increase the IHTC, raise the peak values, and shorten the time to reach a given casting temperature. In the tested steel sand mould casting, the time to 400 °C decreased from about 1119 s without air cooling to about 864 s, 744 s, and 493 s for pipe diameters of 40 mm, 60 mm, and 80 mm, respectively. The sand temperature field also changes with pipe size because forced air cooling both increases the cooling driving force and removes heat through the core.
Fifth, the IHTC in sand mould casting is controlled by air-gap evolution. Any factor that increases gap thickness reduces the IHTC, while any factor that reduces gap thickness increases the IHTC. In aluminium sand mould casting, gap formation is mainly controlled by solid shell growth and the critical solid fraction. In steel sand mould casting, gap formation is controlled by thermal contraction, sand expansion, quartz transformation, and pearlite transformation. Forced air cooling changes the rates of these processes and therefore changes both the value and shape of the IHTC curve.
Overall, I established an optimised inverse method for annular sand mould casting and provided IHTC data for aluminium and steel under natural and forced-air-cooling conditions. These results can improve the accuracy of numerical simulation of sand mould casting and support the design of forced cooling systems in foundry production.