The variable density method has been mostly adopted in designing cooling channels.However,it still has some major drawbacks.The thermal conductivity of the material,in physical truth,should be a certain value.However,based on the variable density method,this value can vary between the upper and lower bounds (high and low thermal conductivity),hence needs to be manually adjusted.A bi-directional evolutionary structural optimization (BESO) method based on the principle of extremum entranspy dissipation was proposed to enhance the heat transfer efficiency.Three numerical examples were studied and the simulation results reveal that by the extremum entranspy dissipation method,it shows the overall entranspy dissipation is 14%,24%,and 9% less then that by the conventional variable density method.