Thermal performance of C-shaped cavities on the basis of Constructal Theory

The objective of this paper is to optimize, by means of the numerical investigation, the geometry of a C-shaped cavity intruding into a solid conducting wall. The cavity is rectangular, with fixed volume and variable aspect ratio. The optimal cavity shape is predicted for two sets of boundary conditions: isothermal cavity and cavity cooled by convection heat transfer. The results demonstrated that the optimal cavity is the one that penetrates almost completely the conducting wall and it is practically independent of the boundary thermal conditions, for the external ratio of the solid wall smaller than 2. As for the convective cavity, it is worthy to know that for values of H/L greater than 2 the best shape is no longer the one that penetrates completely into the solid wall, but the one that presents the largest cavity aspect ratio H0/L0. Finally, in the range 0.3 ≤ ϕ0 ≤ 0.7, the performance of the cavities cooled by convection proved to be greater than the one presented by isothermal cavities. This difference is approximately 17% when λ = 0.1 and ϕ0 = 0.7, and 20% for λ = 1 and ϕ0 = 0.5.