Geometry optimization of T-shaped cavities according to constructal theory

In this paper, constructal theory is applied to optimize the configuration of a body that a T-shaped cavity intruded into a trapezoidal solid conducting wall. The volumes of the solid and the cavity are fixed but their aspect ratios are variables. The solid generates heat uniformly and has adiabatic boundary conditions, the cavity temperature is fixed. In the most fundamental sense, the maximum dimensionless excess temperature between the full system (the solid conducting wall and the cavity) and the surrounding is minimized with respect to four degrees of freedom. Numerical examples show that there is an optimal T-shaped cavity for a given trapezoidal solid conducting wall. The optimal stem length of the cavity, L"1, decreases with the increase of the height of the trapezoidal solid body, He, and the all optimal cavity branches, 2L"0, almost penetrate the bodies. The results can provide some guidelines for conceptual configuration optimization in the thermal design for nucleate boiling and condensation, and cooling packages for micro-electronics.

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