Constructal design of internal cooling geometries in heat conduction system using the optimality of natural branching structures

This paper proposes a growth simulation approach to optimize the internal cooling geometries in heat conduction system. The idea is inspired by the well-known constructal theory which generates the heat conducting paths by a sequence of optimization and organization steps. Firstly, numerical experiments are implemented to confirm the potential of leaf veins as concept generators for conducting path design. Then, a computational framework is built to simulate the adaptive growth of conductive cooling channels. To make the channels being able to grow freely in the domain, a new method called ‘conductivity spreading approach (CSA)’ is developed to transform nodal temperatures of growing channels into those of the underlying ground structure. With such transformation, growth dependences on the initial ground structure, like the nodes connections and locations, are eliminated and cooling channels can therefore grow towards an arbitrary direction to form an optimum layout solution. To illustrate the growth simulation in a directive and descriptive manner, a fundamental ‘volume-to-point’ problem is considered, in which the high conductivity material grows starting from the heat sink, extends spreading the whole region, and forms at convergence a configuration of tree-like network. The proposed constructal optimization method promises to be an “intelligent” CAD approach for various conductive cooling design applications.