Design optimization of an air‐filled cavity: control of the constrained maximum temperature at the directly heated vertical wall

A detailed review of the archival literature on: fluid dynamics, heat transfer and shape optimization reveals that the optimal shape of natural convective cavities has not been investigated so far, and of course, its physical features are not understood. A prominent application of cavities cooled by natural convection arises in the miniaturization of electronic packaging where some type of temperature constraint must be applied at the directly heated wall. This contemporary issue has been addressed in the present work in an elegant manner by linking a code on computational fluid dynamics with a shape optimization code. Once the velocity and temperature fields were accurately computed for an initial cavity with a certain heat load, a two‐step optimization procedure was implemented in a methodical fashion. A first optimization sub‐problem transformed a square cavity into a rectangular cavity, while the second optimization sub‐problem sculpted the shape of the upper horizontal insulated wall in order to bring down the maximum wall temperature of the directly heated vertical wall, i.e. the so‐called “hot spot”. A bird's eye inspection of the numerical results revealed that the first optimization sub‐problem produced a significant reduction in area (volume), while raising the maximum wall temperature of the heated vertical wall by a small amount. The second optimization sub‐problem supplied a remarkable decrease in the maximum wall temperature of the heated vertical wall, carrying with it a moderate increase in area (volume). At the end, the optimal shape of the cavity turns out to be a disfigured vertical rectangular cavity in which the upper insulated wall forming a parabolic‐skewed cap.