Constructal design of tree shaped cavities inserted into a cylindrical body with heat generation

The present work is guided by the Constructal theory to identify the best shapes for the cavity inserted in a cylindrical solid body with a constant heat generation rate. From the assertion that a system must evolve to persist in time, an evolution of the elemental (I-shaped) cavity to a tree-shaped cavity with two branches added to a single branch is proposed. With these modifications, two restrictions (area occupied by the trunk and area occupied by the branches of the cavity) and seven degrees of freedom are used to represent the geometry. The study focused on investigating the effect of the degrees of freedom associated with the cavity branches and the number of cavities. Results show that the optimization of each new degree reduces the maximum excess of temperature. However, the results obtained with a more complex cavity were similar to those obtained by the elemental cavity in reducing the maximum excess temperature. In practical terms, the results are similar. Despite the similarity between the present results and those achieved with a most simple shape. The increase of performance with the increase of degrees of freedom studied here indicates that for complete optimization, the performance of complex shapes can surpass that of the simplest cavity.