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This paper applies Constructal design to study the geometry of a X-shaped cavity that penetrates into a solid conductive wall. The objective is minimizing the dimensionless maximal excess of temperature between the solid body and the cavity. There is uniform heat generation on the solid body. The cavity surfaces are cooled by convection heat transfer while the solid body is subjected to adiabatic conditions on its outer surfaces. The total volume and the cavity volume are fixed, but the lengths and thickness of the X-shaped cavity can vary. The emerged optimal configurations and performance are reported. The effect of the area fraction φ which denotes the ratio between the cavity area and the total area of the geometry, and the ratio between the length and thickness of the branch cavity, H1/L 1, on the dimensionless maximal excess of temperature is numerically investigated. The results show that the dimensionless maximal excess of temperature θ max,min decreases approximately 60% when the cavity fraction increases from φ = 0.05 to 0.25. The results also show that the X-shaped cavity performs approximately 45% better when compared to a C-shaped cavity under the same thermal conditions. The optimal X-shaped cavity is also in accordance with the optimal distribution of imperfections principle.

CONSTRUCTAL DESIGN OF A X-SHAPED CAVITY COOLED BY CONVECTION