Analogizing with the definition of thermal efficiency of a heat exchanger,the entransy dissipation efficiency of a heat exchanger is defined as the ratio of dimensionless entransy dissipation rate to dimensionless pumping power of the heat exchanger.For the constraints of the total tube volume and total tube surface area of the heat exchanger,the constructal optimization of an H-shaped multi-scale heat exchanger is carried out by taking entransy dissipation efficiency maximization as optimization objective,and the optimal construct of the H-shaped multi-scale heat exchanger with maximum entransy dissipation efficiency is obtained.The results show that for the specified total tube volume of the heat exchanger,the optimal constructs of the first order T-shaped heat exchanger based on the maximizations of the thermal efficiency and entransy dissipation efficiency are obviously different with the lower mass flow rates of the cold and hot fluids.For the H-shaped multi-scale heat exchanger,the entransy dissipation efficiency decreases with the increase in mass flow rate when the heat exchanger order is fixed;for the specified dimensionless mass flow rate M(M<32.9),the entransy dissipation efficiency decreases with the increase in the heat exchanger order.The performance of the multi-scale heat exchanger is obviously improved compared with that of the single-scale heat exchanger.Moreover,the heat exchanger subjected to the total tube surface area constraint is also discussed in the paper.The optimization results obtained in this paper can provide a great compromise between the heat transfer and flow performances of the heat exchanger,provide some guidelines for the optimal designs of heat exchangers,and also enrich the connotation of entransy theory. Analogizing with the definition of thermal efficiency of a heat exchanger, the entransy dissipation efficiency of a heat exchanger is defined as the ratio of dimensionless entransy dissipation rate to dimensionless pumping power of the heat exchanger. For the constraints of the total tube volume and total tube surface area of ​​the heat exchanger, the constructal optimization of an H-shaped multi-scale heat exchanger is carried out by taking entransy dissipation efficiency maximization as optimization objective, and the optimal construct of the H-shaped multi-scale heat exchanger with maximum entransy dissipation efficiency is obtained. results show that for the specified total tube volume of the heat exchanger, the optimal constructs of the first order T-shaped heat exchanger based on the maximizations of the thermal efficiency and entransy dissipation efficiency are obviously with the lower mass flow rates of the cold and hot fluids. For the H-shaped multi-scale heat exchanger, t he entransy dissipation efficiency decreases with the increase in mass flow rate when the heat exchanger order is fixed; for the specified dimensionless mass flow rate M (M <32.9), the entransy dissipation efficiency decreases with the increase in the heat exchanger order.The performance of the multi-scale heat exchanger is significantly improved compared with that of the single-scale heat exchanger. Moreover, the heat exchanger subjected to the total tube surface area constraint is also discussed in the paper. a great compromise between the heat transfer and flow performances of the heat exchanger, provide some guidelines for the optimal designs of heat exchangers, and also enrich the connotation of entransy theory.