Constructal optimizations of the elemental and first order "+" shaped high conductivity channels (HCCs) in the square bodies are carried out based on entransy dissipation rate (EDR) minimization. The optimal shapes of the HCCs and minimum EDRs of the bodies are derived. The results show that there exist optimal geometrical parameters of the first order "+" shaped HCC which lead to triple minimum dimensionless EDR of the body. The optimal shape of the first order "+" shaped HCC derived by EDR minimization makes the global heat conduction performance (GHCP) of the square body improve, and the temperature gradient more homogeneous. The optimal design scheme of the "+" shaped HCC with minimum EDR can be adopted in the heat dissipation problem of the electronic device to improve its GHCP. (C) 2017 Elsevier Ltd. All rights reserved.