Abstract
This paper relies on the Constructal Design to optimize the geometry of a cavity that penetrates into a solid conducting wall. The objective is to minimize the global thermal resistance between the solid and the cavity. There is uniform heat generation on the solid wall. We studied three shapes of the cavity: rectangular, triangular, and elliptical. The total volume and the cavity volume are fixed with variable aspect ratios. The cavity shape is optimal when it penetrates the conducting wall completely. The rectangular cavity performs better than the elliptical and triangular ones. On the other side, the elliptical cavity has better performance than the triangular one. We also optimized a first construct, i.e., a cavity shaped as T. The performance of the T-shaped cavity is superior to that of the rectangular cavity optimized in the first part of the paper.
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