Based on constructal theory,a construct of a volume that generates heat at every point and is cooled by the coolant in the constant or tapered channel is optimized by minimizing entransy dissipation rate and flow resistance.The optimal constructs of the rectangular elements with dimensionless mean thermal resistance minimization as well as the first-,secondand thirdorder assemblies with dimensionless global flow resistance minimizations are obtained respectively.The results show that both the mean temperature difference and the limiting temperature difference of rectangular elements based on EDR (entransy dissipation rate) and MTD (maximum temperature difference) minimizations respectively are almost equal.Comparing heat transfer performances from the two optimization procedures,the dimensionless global flow resistance is decreased more for the former procedure when the assembly’s order is high.It may create great superiority for constructal optimization to combine the entransy dissipation extreme principle with heat convection. Based on constructal theory, a construct of a volume that generates heat at every point and is cooled by the coolant in the constant or tapered channel is optimized by minimizing entransy dissipation rate and flow resistance. The optimal constructs of the rectangular elements with dimensionless mean thermal resistance minimization as well as the first-, second and thirdorder assemblies with dimensionless global flow resistance minimizations are obtained respectively. The results show that both both mean temperature difference and the limiting temperature difference of rectangular elements based on EDR (entransy dissipation rate) and MTD ( maximum temperature difference) minimized respectively are almost equal. Comparing heat transfer performances from the two optimization procedures, the dimensionless global flow resistance is decreased more for the former procedure when the assembly's order is high. It may create great superiority for constructal optimization to combine the entransy dissi pation extreme principle with heat convection