# Lattice Structure for Improving Cooling Uniformity in HPDC Mould Corners
## 5 Results and Discussions
### Baseline Analysis and Understanding the Problem  
To understand the heat transfer process from the cast part (assumed to be the heat generation source) to the cooling pipes, a schematic diagram and heat flux streamlines are presented in Figure 3. Figure 4a illustrates that the volume of the cast at the corner, \(V1\), is in contact with a limited area on the pipe, \(A1\), when heat is transferred perpendicularly to the interface. On the corner's sides, the same area, \(A2=A1\), is available to transfer only a fraction of the heat generated by \(V2\). This constrained area for heat transfer to the pipe results in high thermal resistance along the perpendicular path. Because of the high resistance normal for the cast/mould interface, the heat transfer from the corner thus involves two components: one perpendicular to the interface and one parallel. The parallel heat transfer component alters the direction of the heat flux along the sides of the corner, as shown in Figure 3b. The figure also indicates that the heat path along the sides is longer, with the heat flux decreasing as the distance from the corner increases, eventually becoming perpendicular to the interface further away from the corner. Whilethe interface thermal resistance impedes heat transfer, it assists in adjusting the direction of the heat flux and leads to the temperature gradient along the sides within the mould. To analyse the temperature variation near the corners of the mould and the molten cast and to evaluate the impact of lattice structures on temperature distribution, temperatures at 19 points along the cast interface were measured and plotted in Figure 3. This figure represents the baseline case without any lattice structure. It shows how the temperature increases as the located points approach the corner, where the temperature reaches its maximum. It also shows that the rate of temperature increase becomes more pronounced as the points get closer to the corner. This temperature variation along the two sides of the corner is attributed to the parallel heat flux generated at the corner and the low cast volume to cooling surface area compared to that at the corner. The standard deviation of the temperature measured at the interface was found to be 29 \({}^{\circ}\)C, while the difference between the maximum and minimum temperatures at the interface reached approximately 90 \({}^{\circ}\)C, which is 32% of the mean temperature value of 282 \({}^{\circ}\)C. By examining the temperature distribution along the sides, the data can be segmented into three distinct regions. The first region, starting 10 mm from the corner, exhibits a temperature gradient of 40 \({}^{\circ}\)C/cm. The second region shows a gradient of 17 \({}^{\circ}\)C/cm, and the third region, 20 mm from the corner, has a gradient of only 5 \({}^{\circ}\)C/cm. Figure 4: Baseline temperature distribution: (**a**) contours of temperature at the cast/mould interface, pipe surface, and a central section. (**b**) temperature at different probe points starting from the part corner. Figure 3: Sketch of the available area for cooling the mould corner and heat flux distribution in the cast and mould. (**a**) available cooling area; (**b**) heat flux distribution. The location where cracking is observed is usually at the highest temperature gradient region, after the end of the corner curvature. This cracking can be attributed to thermal stress resulting from solidification and contraction of the material on both sides before the corner has fully solidified. Based on the analysis above, achieving uniform cooling can be accomplished by adjusting the thermal conductivity along the sides of the corner to increase thermal resistance with distance from the corner. However, modifying the thermal conductivity near the cast may impact tool rigidity and cause significant changes in the overall temperature distribution within the tool. The region closer to the cooling channel, which has lower temperatures, can be effectively utilised by surrounding the cooling channel with lattice structures.