Inverted fins for cooling of a non-uniformly heated domain

Abstract

This paper shows that the peak temperature of a nonuniformly heated region can be decreased by embedding highconductivity tree-shaped inserts which is in contact with a heat sink from its stem. The volume fraction of the high-conductivity material is fixed, and so is the volume of the solid region. The length scale of the solid domain is L. Inside there is a cubeshaped region with length scale of 0.1L and heat production 100 times greater than the rest of the domain. The location of this hot spot was varied to uncover how its location affects the peak temperature and the design of inverted fins, i.e. highconductivity tree-shaped inserts. The volume fraction of the high-conductivity tree was varied for number of bifurcation levels of 0, 1 and 2. This showed that increasing the number of the bifurcation levels decreases the peak temperature when the volume fraction decreases. The optimal diameter ratios and optimal bifurcation angles at the each junction level are also documented. Y-shaped trees promise smaller peak temperatures than T-shaped trees. The location of the vascular tree in the z direction also affects the peak temperature when the heat generation is non-uniform. In addition, the peak temperature is minimum when z = 0.65L even though the hot spot is located on z = 0.75L

Keywords

• Constructal
• Inverted fins
• Vascular
• Non-uniform heating
• Conductive cooling
• Tree-shaped