This study investigates the interfacial heat transfer coefficient (IHTC) between aluminum alloy castings and resin-bonded sand molds/cores during solidification. By combining temperature field measurements with inverse heat transfer modeling, the relationship between IHTC and casting geometry is systematically analyzed. The findings provide critical insights for improving numerical simulation accuracy in sand casting processes.
Experimental Methodology
Three geometric configurations were tested:
| Specimen Type | Dimensions (mm) | Measurement Points |
|---|---|---|
| Flat Plate | 150×150×50 | 8 symmetric positions |
| Annular Casting | Rin/Rout = 30/80, 50/100, 70/120 | Radial thermal couples |
The thermal physical properties of ZL101 aluminum alloy and resin-bonded sand were characterized through temperature-dependent measurements:
$$ k_{sand}(T) = 0.65 – 2.5 \times 10^{-4}T \quad [W/(m \cdot {}^\circ C)] $$
$$ C_{p,sand}(T) = 900 + 0.25T \quad [J/(kg \cdot {}^\circ C)] $$
Mathematical Modeling
The inverse heat transfer problem was solved using Beck’s nonlinear estimation method with finite volume discretization. For annular castings, the governing equation in cylindrical coordinates:
$$ \frac{1}{r}\frac{\partial}{\partial r}\left(rk\frac{\partial T}{\partial r}\right) = \rho C_p\frac{\partial T}{\partial t} $$
Key algorithm parameters:
| Parameter | Value | Description |
|---|---|---|
| Δx | 4 mm | Spatial discretization |
| Δt | 0.5 s | Temporal step |
| f | 6 | Future time steps |
Results and Discussion
The IHTC evolution shows distinct characteristics for different sand casting geometries:
$$ h_{\text{max}} = 263\ \text{W}/(\text{m}^2 \cdot {}^\circ \text{C})\ (30\ \text{mm core}) $$
$$ h_{\text{min}} = 61\ \text{W}/(\text{m}^2 \cdot {}^\circ \text{C})\ (flat\ plate) $$
Key findings from inverse analysis:
| Geometry | IHTC Range (W/m²°C) | Phase Transition Behavior |
|---|---|---|
| Flat Plate | 61-108 | Classic S-curve transition |
| Annular (80mm) | 83-131 | Enhanced high-T phase |
| Core (30mm) | 144-263 | Delayed solidus transition |
The thermal resistance model explains geometry-dependent behavior:
$$ \frac{1}{h_{total}} = \frac{1}{h_{contact}} + \frac{\delta_{gap}}{k_{gas}} $$
Numerical Validation
ProCAST simulations using derived IHTC values showed excellent agreement with experimental measurements:
$$ \Delta T_{\text{max}} = 17^\circ \text{C}\ (600\ \text{s simulation}) $$
$$ R^2 = 0.983\ (solidification\ stage) $$
This research demonstrates that proper IHTC characterization significantly improves sand casting simulation accuracy. The developed inverse calculation method provides a practical framework for optimizing mold design and process parameters in industrial sand casting applications.