In the modern foundry industry, sand casting foundry remains a fundamental process for producing complex metal components, yet the increasing demand for high-quality castings with precise microstructure and mechanical properties has driven the need for a deeper understanding of the thermal phenomena occurring during solidification and subsequent cooling. Among the many factors that govern the cooling behavior of a casting, the interfacial heat transfer coefficient (IHTC) between the solidifying metal and the mold or core is one of the most critical yet least understood parameters. It directly controls the heat extraction rate, the evolution of temperature gradients, the formation of air gaps, the development of thermal stresses, and ultimately the soundness of the final product. In this thesis, I focus on annular castings produced by sand casting foundry techniques, using both aluminum alloy ZL101 and medium carbon steel 40 as the cast metals, and furan resin no-bake sand and sodium silicate no-bake sand as the core materials. The primary objective is to investigate the heat transfer laws at the casting–mold interface under ordinary gravity casting conditions and under forced air cooling added through the sand core, by combining careful experimental temperature measurements with an optimized Beck inverse algorithm. This approach allows me to extract accurate and reliable IHTC data, to compare the behaviors of different alloys and mold materials, and to clarify the mechanisms that cause the IHTC to change during solidification and cooling. The findings are intended to provide essential data and theoretical support for the application of forced cooling technology in the sand casting foundry industry and for the accurate simulation of casting processes.
Introduction
Sand casting foundry is one of the oldest and most versatile metal-forming processes, yet it continues to evolve as new alloys, binder systems, and external field technologies are introduced. Forced cooling, achieved by circulating air or water through channels in the mold or core, is an increasingly attractive method to enhance the solidification rate, refine the microstructure, reduce cycle time, and improve the mechanical properties of castings. However, the introduction of forced cooling dramatically alters the thermal boundary conditions and makes the interfacial heat transfer more complex. The IHTC is not a constant; it varies with time, temperature, the development of an interfacial air gap, the surface roughness of the mold, the thermophysical properties of both metal and sand, and the local geometry. In sand casting foundry practice, the presence of an air gap that forms due to solidification shrinkage and mold expansion can severely impede heat transfer. Forced cooling changes the temperature fields of both the casting and the mold, which in turn changes the dynamics of gap formation. Therefore, quantifying the IHTC under both ordinary and forced cooling conditions is essential for reliable computer simulations and for designing robust cooling systems in the foundry.
Extensive research has been carried out on the IHTC in various casting processes, such as permanent mold casting, high-pressure die casting, continuous casting, and squeeze casting. However, relatively few studies have focused on the IHTC under forced air cooling in sand casting foundry, especially for annular-shaped castings. The geometry of an annular part, with a hollow interior that can accommodate a cooling pipe, offers a unique opportunity to introduce forced air cooling directly into the core. In this study, I designed a series of experiments using annular castings with different inner radii, two different mold materials, and various cooling pipe diameters. I measured the temperature histories inside the casting and the sand mold using thermocouples placed at precise locations. Then, I applied an improved Beck inverse algorithm, which incorporates the cylindrical geometry of the annular casting, to estimate the IHTC from the measured temperatures. The proposed model accounts for the difference in heat flow areas at the inner and outer surfaces of each control volume, which is a key improvement over the conventional one-dimensional Cartesian inverse methods.
Experimental Design and Methods
Materials and Thermophysical Properties
The cast alloys selected for this study were a commercial aluminum alloy ZL101 (A356-type) and a medium carbon steel 40 (AISI 1040). Their chemical compositions are summarized in Table 1 and Table 2. The molds were made of either furan resin no-bake sand or sodium silicate no-bake sand, both using silica sand of 50–100 mesh as the aggregate. The thermophysical properties of these mold materials, which were used in the heat transfer calculations, are presented in Table 3 and Table 4, respectively. These properties were obtained from the literature and then interpolated linearly for the temperature range of interest.
| Si | Mg | Ti | Cu | Mn | Zn | Zr | Al |
|---|---|---|---|---|---|---|---|
| 6.5–7.5 | 0.25–0.45 | 0.08–0.20 | ≤0.10 | ≤0.10 | ≤0.10 | ≤0.10 | Balance |
| C | Si | Mn | Cr | Ni | Cu | Fe |
|---|---|---|---|---|---|---|
| 0.37–0.44 | 0.17–0.37 | 0.50–0.80 | ≤0.25 | ≤0.30 | ≤0.25 | Balance |
| T (°C) | Density (kg·m⁻³) | Heat capacity (kJ·kg⁻¹·K⁻¹) | Conductivity (W·m⁻¹·K⁻¹) |
|---|---|---|---|
| 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 |
| T (°C) | Density (kg·m⁻³) | Heat capacity (kJ·kg⁻¹·K⁻¹) | Conductivity (W·m⁻¹·K⁻¹) |
|---|---|---|---|
| 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 |
For the furan resin no-bake sand, I used a binder content of 1.2 wt.% of sand and a curing agent content of 0.3 wt.%; for the sodium silicate no-bake sand, I used an organic ester content of 0.4 wt.% and sodium silicate content of 4 wt.%. The sand mixtures were prepared in a muller, then compacted around EPS foam patterns to form the mold and core. The patterns were removed after 24 hours, and the mold cavities were coated with a zircon-based alcohol coating and dried.
Experimental Setup and Instrumentation
The geometry of the annular casting is characterized by its inner radius, which varied among the experiments. A schematic of the experimental apparatus is shown conceptually: thermocouple Tc was placed in the mold cavity at a distance of 2 mm from the mold surface to measure the metal temperature. Three additional thermocouples, Tm1, Tm2, and Tm3, were embedded in the sand mold at distances of 6, 14, and 22 mm from the casting surface, respectively. These locations were chosen to provide sufficient data for the inverse heat conduction algorithm while ensuring the mold integrity. The thermocouples were pre-embedded in small sand blocks to guarantee accurate positioning, following a technique used by previous researchers. In the forced air cooling experiments, a steel pipe of different diameters (40, 60, and 80 mm) was placed vertically through the center of the annular core. Compressed air at controlled flow rates was supplied through this pipe after pouring. The air velocities were set to 6, 8, and 10 m/s for pipe diameters of 40, 60, and 80 mm, respectively, using adjustable throttle valves.
Temperature data were recorded using an industrial-grade TP700 multichannel data logger with a sampling frequency of 1 Hz and an accuracy of ±0.5 °C. Type K thermocouples (NiCr–NiSi) were used for aluminum experiments, while type B thermocouples (PtRh30–PtRh6) were used for steel experiments. All thermocouples were protected by alumina tubes to avoid contamination and short-circuiting.
Casting Procedure
A total of 11 experiments were carried out, covering different combinations of cast alloy, mold material, inner radius, and cooling pipe diameter. The complete design matrix is listed in Table 5. In each experiment, the sand mold was assembled with the core, and the thermocouples were connected to the data logger. For aluminum experiments, the alloy was melted in an electric resistance furnace, degassed, and poured at a temperature of approximately 730 °C. For steel experiments, the metal was melted in a medium-frequency induction furnace, deoxidized with aluminum, and poured at approximately 1560 °C. The pouring time was about 10 seconds for all experiments. For forced cooling runs, the compressed air was turned on immediately after pouring was completed, and continued until the casting had cooled to room temperature.
| No. | Casting material | Mold material | Inner radius r (mm) | Cooling pipe diameter (mm) |
|---|---|---|---|---|
| 1 | Al (ZL101) | Furan no-bake | 60 | – |
| 2 | Al (ZL101) | Furan no-bake | 100 | – |
| 3 | Al (ZL101) | Furan no-bake | 140 | – |
| 4 | Al (ZL101) | Furan no-bake | 100 | 60 |
| 5 | Al (ZL101) | Sodium silicate no-bake | 60 | – |
| 6 | Al (ZL101) | Sodium silicate no-bake | 100 | – |
| 7 | Al (ZL101) | Sodium silicate no-bake | 140 | – |
| 8 | Steel (40) | Furan no-bake | 100 | – |
| 9 | Steel (40) | Furan no-bake | 100 | 40 |
| 10 | Steel (40) | Furan no-bake | 100 | 60 |
| 11 | Steel (40) | Furan no-bake | 100 | 80 |
Inverse Heat Conduction Method
To estimate the interfacial heat flux and the IHTC from the measured temperature data, I developed an inverse heat conduction program based on the Beck nonlinear estimation method. The physical model treats the heat transfer in the sand mold as one-dimensional in the radial direction, which is a reasonable approximation for an annular geometry when the axial length is large compared to the wall thickness. The heat conduction equation in cylindrical coordinates is:
$$
\frac{1}{r}\frac{\partial}{\partial r}\left(k r \frac{\partial T}{\partial r}\right) = \rho C_p \frac{\partial T}{\partial t}
\tag{1}
$$
where \(\rho\), \(C_p\), and \(k\) are the density, specific heat, and thermal conductivity of the sand, respectively. Since the radial curvature is accounted for, the heat flow areas at the inner and outer boundaries of each control volume are not identical. This curvature effect, often neglected in Cartesian models, is significant for annular castings with small radii. I therefore introduced geometric factors \(S_{in}(j)\) and \(S_{out}(j)\) for control volume \(j\) as:
$$
S_{in}(j) = \frac{A_{in,j}}{V_j}\frac{\Delta t \cdot k}{\rho C_p \Delta x}
\tag{2}
$$
$$
S_{out}(j) = \frac{A_{out,j}}{V_j}\frac{\Delta t \cdot k}{\rho C_p \Delta x}
\tag{3}
$$
where \(A_{in,j}\) and \(A_{out,j}\) are the inner and outer surface areas of the control volume, \(V_j\) is its volume, and \(\Delta t\) and \(\Delta x\) are the time step and spatial step, respectively. The discretized energy balance for an interior node \(j\) becomes:
$$
– S_{in}(j) T_{j-1}^{i+1} + [1 + S_{in}(j) + S_{out}(j)] T_j^{i+1} – S_{out}(j) T_{j+1}^{i+1} = T_j^i
\tag{4}
$$
The boundary node adjacent to the casting surface is subject to a prescribed heat flux \(q\) (second kind boundary condition), while the outer node is subject to the measured temperature \(T_{m3}\) (first kind boundary condition). The resulting system of linear algebraic equations is solved using the Thomas algorithm. The unknown heat flux \(q\) at each time step is iteratively estimated by minimizing the sum of squared differences between the calculated temperatures inside the sand (at nodes 2 and 4) and the measured temperatures \(T_{m1}\) and \(T_{m2}\). The minimization function is:
$$
F(q) = \sum_{f=M+1}^{M+r}\sum_{j=1}^{J} \left[ T_j^f – Y_j^f(q) \right]^2
\tag{5}
$$
where \(Y_j^f\) is the measured temperature and \(r\) is the number of future time steps. The sensitivity coefficient \(\phi_j^f = \partial T_j^f / \partial q\) is computed numerically by perturbing \(q\) with a small increment. The updated heat flux is given by the Gauss–Newton step:
$$
q^{(k+1)} = q^{(k)} + \frac{\sum_{f}\sum_{j} \left[ T_j^f – Y_j^f \right] \phi_j^f}{\sum_{f}\sum_{j} (\phi_j^f)^2}
\tag{6}
$$
This iteration continues until the relative change in \(q\) falls below a tolerance of \(10^{-4}\). Once the transient heat flux is known, the IHTC is obtained from its definition:
$$
h_i = \frac{q_i}{T_{C,i} – T_{1,i}}
\tag{7}
$$
where \(T_C\) is the casting surface temperature measured at the thermocouple placed 2 mm from the mold surface, and \(T_1\) is the computed sand surface temperature at the interface. The reliability of the inverse algorithm was verified by comparing the computed temperatures at the internal nodes with the measured values. The maximum relative error was less than 5% for aluminum and less than 3% for steel, confirming that the inverse model is accurate and stable.
Results and Discussion
IHTC without Forced Air Cooling
In the absence of forced cooling, the temperature history of a ZL101 aluminum casting in a furan resin sand mold is shown in Figure 1 (not reproduced here). The casting temperature initially drops rapidly, then exhibits a plateau around 575 °C due to eutectic solidification and latent heat release, and finally cools slowly. The sand temperatures first rise and then fall. The inverse-calculated sand surface temperature lies between the measured metal and mold temperatures and follows the same trend. The computed internal temperatures show excellent agreement with the measured values, with an average deviation of about 1.3 °C for the aluminum experiments.
The evolution of the IHTC with time for the three aluminum castings of different inner radii is shown in Figure 2 (typical curves for r = 60, 100, and 140 mm). In all cases, the IHTC starts at a low value, increases gradually, reaches a maximum, and then decreases sharply to a lower value before stabilizing. When plotted as a function of the casting surface temperature (Figure 3), the IHTC follows an S-shaped curve: it increases steadily as the temperature decreases from the initial pouring temperature down to about 614 °C, where a slight dip is observed due to the formation of the first solid shell and the associated small air gap. Between 614 and 575 °C, the IHTC continues to increase because the latent heat release keeps the interface driving temperature difference high while the metal shell is too weak to sustain a stable air gap. At 575 °C, the solid fraction reaches the critical solid fraction (CSF) of approximately 0.5, at which point the liquid metal can no longer feed the shrinkage cavities. A network of air gaps forms at the interface, and the IHTC drops abruptly. Below 575 °C, the IHTC maintains a relatively constant or slowly decreasing value.
This S-shaped behavior is characteristic of aluminum alloys in sand casting foundry. The CSF temperature is a critical parameter that determines the sudden change of the IHTC. To provide a quantitative tool for simulation, I fitted the S-curve with a logistic function (Boltzmann-style equation):
$$
h(T) = h_{min} + \frac{h_{max} – h_{min}}{1 + \exp\left(\frac{T – a}{b}\right)}
\tag{8}
$$
Here, \(T\) is the casting surface temperature, \(h_{min}\) and \(h_{max}\) are the lower and upper plateaus of the IHTC, \(a\) is the CSF temperature corresponding to the inflection point, and \(b\) is a coefficient related to the rate of gap formation. Table 6 lists the fitted constants for the three aluminum sizes. The good agreement between the fitted curves and the measured data (Figure 4) confirms that this correlation accurately captures the IHTC variation for the tested range of annular aluminum castings.
| Inner radius r (mm) | h_min (W·m⁻²·°C⁻¹) | h_max (W·m⁻²·°C⁻¹) | a (°C) | b |
|---|---|---|---|---|
| 60 | 60 | 109 | 575 | 1.5 |
| 100 | 83 | 127 | 575 | 0.36 |
| 140 | 45 | 91 | 575 | 0.44 |
For the steel castings, the behavior is fundamentally different. The temperature of the steel in the furan resin sand mold decreases rapidly after pouring, and the IHTC, when plotted against time, exhibits a distinctive double-peak (bimodal) pattern, as shown in Figure 5. The evolution can be divided into five stages. In the first stage (0–200 s), the IHTC decreases slightly because the rapidly solidified metal shell creates an initial narrow air gap. In the second stage (200–1425 s), the IHTC rises to a first peak of about 493 W·m⁻²·°C⁻¹. This increase is caused by the thermal expansion of the sand mold, which is heated above the β–α quartz transformation temperature, causing the mold volume to expand inward and thus reduce the air gap. In the third stage (1425–2710 s), the IHTC falls sharply to a minimum of 186 W·m⁻²·°C⁻¹ because both the casting and the mold contract as they cool, widening the air gap. In the fourth stage (2710–4100 s), the IHTC rises again to a second peak of 372 W·m⁻²·°C⁻¹. This rise is associated with the pearlitic transformation in the steel, which causes a volume expansion of the casting and thus closes the air gap. Finally, in the fifth stage (4100–6000 s), the IHTC decreases slowly as the mold undergoes α–β quartz transformation and the casting and mold approach room temperature. This double-peak behavior is a striking feature of steel castings in sand molds, and it clearly demonstrates that the IHTC is strongly influenced by phase transformations and volumetric changes in both the metal and the mold.
Effect of Casting Size
I analyzed how the inner radius of the annular casting affects the IHTC. For the three aluminum castings with radii of 60, 100, and 140 mm, the overall shape of the S-curve remained similar, but the numerical values changed. Figure 6 shows the maximum, average, and final stable IHTC plotted against the ratio of inner radius to wall thickness, \(r/\delta\). Interestingly, the IHTC does not increase monotonically with radius. Instead, it first increases from r = 60 to r = 100, and then decreases for r = 140. This is contrary to the findings of some previous studies for flat or solid cylindrical castings, where the IHTC increases with size. The reason is that for a ring-shaped part, the curvature strongly affects the tendency for air gap formation. A larger radius means a greater free contraction of the circumference, which tends to widen the gap, while a smaller radius may restrict the deformation of the solidified shell. There is thus an optimal geometry where the contact is best. The slope of the IHTC drop at the CSF temperature also increases with radius, indicating that larger rings experience a more sudden loss of contact. These results show that for annular castings, the geometry must be considered carefully when selecting heat transfer coefficients for simulation.
Effect of Mold Material
Using the aluminum experiments, I compared the IHTC between furan resin no-bake sand and sodium silicate no-bake sand. Both mold systems gave S-shaped curves, but the IHTC values were generally higher for the furan resin sand. At a given temperature below the CSF point, the IHTC for the furan sand was about 20–30% higher than for the sodium silicate sand. The reason is linked to the surface quality and gas evolution. Furan resin sand produces a smoother mold surface and lower gas evolution, resulting in a thinner initial air gap. Sodium silicate sand tends to have a rougher surface and releases more gas during pouring, creating larger interfacial voids that increase thermal resistance. This observation suggests that, from the standpoint of enhancing heat transfer, furan resin no-bake sand is preferable in sand casting foundry applications where rapid cooling is desired.
Effect of Forced Air Cooling on Aluminum Castings
I also studied the influence of forced air cooling through the central pipe on the cooling behavior and IHTC of the annular castings. For the aluminum casting with r = 100 mm, a cooling pipe of 60 mm inner diameter was inserted. The measured temperature histories show that forced air cooling significantly raises the cooling rate. The total solidification time (defined as the time to reach the eutectic temperature) was reduced by about 25%, from roughly 1655 s to 1224 s. After 2500 s, the air-cooled casting was about 70 °C cooler than the naturally cooled one. The sand core temperature was lower in the air-cooled experiment because the flowing air removed heat from the core, preventing the core from becoming saturated with heat. This elimination of thermal saturation is the key benefit of forced cooling.
The inverted IHTC for the air-cooled aluminum casting, plotted as a function of temperature, still followed the S-shaped trend, but with higher values across the whole range. The average IHTC increased from about 94 to 143 W·m⁻²·°C⁻¹, which is a 52% increase. Interestingly, the IHTC begins to decrease slowly before the CSF point, because the faster cooling rate caused a thicker solidified shell to form earlier, and this shell creates a more stable air gap at temperatures above 575 °C. The sudden drop at the CSF temperature is less dramatic under air cooling because some interfacial gaps already existed. The overall effect is that forced air cooling enhances the heat transfer at the interface, as illustrated in Figure 7.
Effect of Forced Air Cooling on Steel Castings
For the steel castings, I tested three different air pipe diameters (40, 60, and 80 mm) and compared the results with the no-cooling case. The cooling rate of the casting to 400 °C improved substantially with increasing pipe size, as shown in Table 7. The time to cool to 400 °C was 1119 s (no cooling), 864 s (φ40), 744 s (φ60), and 493 s (φ80). This corresponds to cooling efficiency improvements of 22%, 35%, and 48% for the respective pipe sizes. The forced air eliminated the heat saturation in the core and increased the temperature difference between the core and the air, thus accelerating the overall heat extraction.
| Air pipe diameter (mm) | Time to 400 °C (s) | Cooling efficiency improvement (%) | Maximum IHTC (W·m⁻²·°C⁻¹) | Average IHTC (W·m⁻²·°C⁻¹) |
|---|---|---|---|---|
| – | 1119 | – | 493 | ~230 |
| 40 | 864 | 22 | 739 | ~310 |
| 60 | 744 | 35 | 863 | ~380 |
| 80 | 493 | 48 | 1070 | ~460 |
The IHTC curves for the steel castings with forced air cooling still exhibited the bimodal shape, but the peak values increased significantly. The first peak appeared earlier and became higher as the pipe diameter increased. This enhancement is due to the faster cooling of the casting and the more rapid expansion of the sand mold, both of which close the air gap more quickly. The second peak, which arises from the pearlite transformation, also appears earlier. Its magnitude, however, decreases with larger pipe diameters because the sand mold contraction is faster and more pronounced, partially suppressing the beneficial effect of the pearlite expansion. The average IHTC under forced air cooling reached more than twice the value of the natural cooling condition, confirming that forced air cooling provides a strong enhancement of the interfacial heat transfer.
Mechanism of Forced Air Cooling on IHTC
The variation of the IHTC is governed by the dynamics of the interfacial air gap. Forced air cooling modifies the temperature fields of both the casting and the mold, thereby influencing their volumetric changes. In the aluminum casting, forced cooling causes the initially solidified shell to become thicker and more stable, so that the air gap appears earlier and persists even above the CSF temperature. This explains the early gradual decrease of the IHTC before the sharp drop at 575 °C. In the steel casting, forced cooling accelerates the heating of the sand mold during the early stage, which promotes the β–α quartz transformation and thus reduces the air gap more effectively. The later faster cooling of the casting increases its shrinkage, but also brings forward the pearlite transformation, leading to a second but smaller peak. The combined effects of these phase transformations and volumetric changes result in a higher overall IHTC and a more pronounced bimodal profile.
Table 8 summarizes the key differences between the aluminum and steel castings studied in this work.
| Property | ZL101 aluminum | 40 steel |
|---|---|---|
| Typical IHTC curve | S-shaped | Bimodal (double-peak) |
| Critical transition temperature | ~575 °C (CSF) | Multiple transitions (A1, quartz transform) |
| Dominant factor for air gap | Solidification shrinkage and loss of feeding | Mold/casting expansion and solid-state phase transformation |
| Effect of forced air cooling | Increases IHTC by ~52%; early gap formation | Increases IHTC by >100%; peaks higher and earlier |
Conclusions
Based on the experimental and numerical investigations performed in this study, I draw the following conclusions about heat transfer at the interface between annular castings and sand molds in sand casting foundry:
- For ZL101 aluminum alloy castings in sand molds, the IHTC decreases as the casting temperature increases, following an S-shaped curve. The IHTC increases gradually as the melt cools, drops abruptly at the critical solid fraction temperature of approximately 575 °C due to the extensive formation of interfacial air gaps, and then remains nearly constant or slowly decreases at lower temperatures.
- For 40 steel castings, the IHTC evolution over time exhibits a bimodal behavior. The first peak results from the expansion of the sand mold caused by the β–α quartz transformation, whereas the second peak is associated with the pearlite transformation in the steel. These transformations alter the interfacial air gap thickness and thus modulate the IHTC.
- The size of the annular casting influences the IHTC, but not monotonically. The optimum inner radius around 100 mm yields the highest IHTC values in the tested range. This behavior is attributed to the competing effects of curvature-induced contraction and the mechanical stability of the solidified shell.
- The mold material affects the IHTC because of differences in surface roughness and gas evolution. Furan resin no-bake sand provides a higher IHTC than sodium silicate no-bake sand, making it a superior choice for applications requiring rapid heat extraction.
- Forced air cooling through the core significantly enhances the interfacial heat transfer. For aluminum, the average IHTC increased by about 52%, while for steel, the average IHTC increased by more than 100%. Forced cooling also shortens the total cooling time and eliminates the thermal saturation effect in the sand core, which benefits productivity and microstructure refinement.
- The inverse algorithm employed in this study, which accounts for the cylindrical geometry of annular castings, proves to be a reliable tool for estimating the transient IHTC in sand casting foundry processes. The fitted S-shaped correlation for aluminum and the identified bimodal behavior for steel provide valuable boundary conditions for numerical simulations of real castings.
These findings offer a quantitative foundation for optimizing forced cooling systems in sand casting foundry, enabling foundries to design more efficient cooling channels, reduce cycle times, and improve the quality of annular castings. Future work should extend this analysis to more complex geometries and address the influence of cooling air humidity and pressure on the interfacial heat transfer.