Designing biologically inspired heat conduction paths for ‘volume-to-point’ problems

In this article, an evolutionary algorithm is presented for constructal optimization of high conductivity paths by mimicking the morphogenesis of leaf veins in nature. To get a physically meaningful continuous path solution, the optimization is conducted as a sequence of growth steps which begins with the heat sink and proceeds toward the whole conduction domain. The growth simulation is explored by making use of the interpolation scheme called “conductivity spreading approach” (CSA). Unlike other evolutionary algorithms, the CSA method separates growing channels from the underlying ground structure so that the growth dependency on node locations and element connections is eliminated and cooling channels are provided with more flexibility to grow toward an arbitrary direction in the conduction domain. Notably, this approach incorporates more geometry and thermal information into constructal optimization and improves the definiteness of frontiers between high and low conductivity materials. The feasibility and effectiveness of the proposed method are demonstrated in examples of ‘volume-to-point’ heat conduction, which forms at convergence a dendritic configuration. In addition, the influence of different design objectives, like the thermal compliance, average temperature and temperature variance, on the resulting dendritic configurations is discussed through both numerical analyses and experimental tests.