Topology optimization of heat conduction paths by a non-constrained volume-of-solid function method

A novel computational approach based on a non-constrained formulation with a volume-of-solid (VOS) function equation is firstly presented for topology design of heat conductive solid paths between constant-temperature objects. In the first step of the approach, the distributions of the VOS function and the temperature in the original design domain are carried out by simultaneously solving the VOS function equation and the heat conduction equation. Secondly, the shape outline of the heat conduction path leading to a maximum heat transfer rate per unit solid mass is determined by selecting a cut-off value of the VOS function. Performance of this approach is tested for three two-dimensional test cases. Various thermal boundary configurations are taken into consideration to demonstrate the validity of the present method. Results show that the present computational method is capable of predicting the optimal shapes of the heat conduction paths for the test cases efficiently.