An aerospace company makes ceramic tiles for shuttle thermal protection systems. As an intermediate stage in the manufacturing process, the company produces large blocks of ceramic. These blocks are initially at a temperature of 900°C, but need to be cooled to 50°C before further processing can take place. The company has two options to achieve this: active or passive convective cooling. Although both methods will achieve the desired results, there are cost and time issues that have to be considered. With passive convective cooling, the blocks are left to cool naturally in a large warehouse. This method takes more time and requires a large storage capacity. With active convective cooling, forced air is used to lower the temperature over a shorter period of time. This method takes less time, but demands the construction of costly cooling equipment.
To make this decision, the company must determine the time required for the core of the block to cool to a temperature of 50°C, given changes in the dimensions of the block and other parameters. Laboratory tests were not practical for exploring the entire parameter space, but could be used to calibrate a theoretical software model. The company considered finite element method (FEM) modeling of the spatial temperature dynamics, but quickly discarded this approach since FEM software was expensive, required extensive operator training, and gave a level of detail that was not required. Ideally they wanted to create a spatially discretized lumped parameter model that could be optimized to match experimental data.
Using MapleSim, two models were created with very little effort, requiring half a day to assemble the models. The first model discretized the ceramic block along one spatial dimension. This approach is suitable if the heat loss from the sides of the block is negligible, and it was a reasonable assumption for the force-air cooling. Expanding on this model, a second model was created discretizing the block along three spatial dimensions. Sixteen vertical slices were used to represent the block, with each slice consisting of four segments. Parameters for the convective heat transfer coefficients for both active and passive cooling were used to fit the model to the experimental data.
With the model now complete, the company can accurately calculate the required cooling time for each block. With these results, together with the costs associated with building a cooling unit or obtaining larger storage facilities, the company now has the information it requires to make the most cost-effective decision for its manufacturing process.