Improvement of volume-of-solid function approach for optimization of heat conduction paths

The present study is aimed at improvement of the existing volume-of-solid (VOS) function method for optimization of heat conduction path between isothermal objects. Validity and capability of the existing VOS function method were proved by several different cases. However, it has been found that with this method one needs to carry out the grid generation repeatedly in the step selecting the cut-off value of the VOS function and the optimal shape of the heat conduction path. Thus, the selection step is still rather time-consuming. In this study, the VOS function method is improved by introducing the simplified conjugate-gradient method (SCGM) and a cell-matrix image scheme into the selection step. With the help of the SCGM method, the selection step can be facilitated and the selection of the process can be carried out iteratively. Besides, as the cell-matrix image scheme is used to portray the shape of the heat conduction path, the overwhelming grid generation is no longer required. This improved approach, which is named VOS + SCGM method in this study, has been applied to two practical cases having different thermal boundary configurations to investigate its relative performance. It is found that the cut-off value of the VOS function can be efficiently selected automatically in iteration. Meanwhile, it is favorable that various initial guesses for the cut-off value of the VOS function eventually approach to the same optimal value robustly. In this study, effects of the cell number on the quality of the cell-matrix image and the required computation efforts have been investigated.