Optimal Cooling Channel Layout in a Hot Enclosure Subject to Natural Convection

We analyzed the optimal cooling channel layouts emerged from minimizing the total entropy generation $S_T$ and mean enclosure temperature $\overline{T}$ in a hot enclosure subjected to natural convection. The conservation of mass, momentum, and energy were solved numerically in 2D space using the finite element method, and an ant colony optimization algorithm was employed to determine the optimal layouts with respect to the number of cooling channels (N) and Rayleigh number (Ra). The total allocatable cooling channel area was fixed in all cases and thus each channel area decreased with increasing N. Subsequently, we examined the heat transfer and flow characteristics based on temperature field, streamlines, and local Bejan number of each optimum and deduced the following: (1) All optimal channel layouts were symmetric about the vertical enclosure centerline; however, the optima resulting in $S_{T,min}$ and $\overline{T}_{min}$ did not always coincide and depended heavily on the flow configuration dictated by N and Ra; (2) the competing nature between heat transfer and its irreversibility was pronounced at low Ra and N when convection and fluid friction were ineffective; and (3) the first and second law performance improved as N increased in most cases. Furthermore, results verified the global convergence and robustness of the ant colony optimization approach in solving a layout optimization problem with natural convection.