Improvement of constructal tree-like network for “volume-point” heat conduction with variable cross-section conducting path and without the premise of optimal last-order construct

The constructal “tree-like” network has been proved an effective way for “volume-point” heat conduction. This paper aims to further improve the constructal “tree-like” network with the optimization objectives of minimizations of maximum thermal resistance and entransy dissipation rate respectively. By removing the constraint that the last-order construct must be optimal, and using variable cross-section conducting path, the maximum thermal resistance and entransy dissipation rate can be greatly reduced. It is also found that the optimal construct for minimum peak temperature is similar to the optimal one for minimum entransy dissipation rate. They hold the same shape and configuration, and the main difference of them is the shape of high-conductivity path.