Topology optimization for the conduction cooling of a heat-generating volume with orthotropic material

For the optimal distribution of an orthotropic conduit material within an isotropic heat-generating material is was found that an optimal conduit material angle exists giving the best thermal performance (lowest τmax). It was found that the optimal conduit material angle remains the same for different conductivity ratios and different heat-generating material angles. It was also found that the optimal conduit material angle directly corresponds to the domain aspect ratio, θ1,opt=tan-1(2H/L), with a minimum improvement of 3% and a maximum improvement of 50% of the thermal performance when using an orthotropic conduit material over that of an isotropic conduit material. A 50% improvement of the thermal performance effectively translates to either double the allowable heat generation or half the peak operating temperature of the isotropic heat-generating material.