In this paper, heat pump systems are analyzed with entransy increase and entropy generation. The extremum entransy increase principle is developed. When the equivalent temperatures of the high and low temperature heat sources are fixed, the theoretical analyses and numerical results both show that the maximum COP leads to the maximum entransy increase rate for fixed input power, while it leads to the minimum entransy increase rate for fixed heat flow absorbed from the low temperature heat source.The minimum entropy generation principle shows that the minimum entropy generation rate always leads to the maximum COP for fixed input power or fixed heat flow absorbed from the low temperature heat source when the equivalent thermodynamic forces of the high and low temperature heat sources are given. Further discussions show that only the entransy increase rate always increases with increasing heat flow rate into the high temperature heat source for the discussed cases.
entransy loss, entransy increase,entropy generation, heat pump, optimizationHeat pump systems are common industrial equipments and have many applications [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. For instance, in the heating and air conditioning system, the heat pump is applied to driving the heat from the environment into the room [15]. The optimization design of heat pump systems has received more and more attention because it can improve the system performance and increase the energy utilization efficiency [6][7][8][9][10][11][12].There are different optimization objectives for heat pump systems, such as the thermo-economic performance [6] and the thermodynamic performance optimization [4,5,[7][8][9][10][11][12]. For instance, Quoilin et al. [6] analyzed the thermo-economic performance of heat pump systems. Chen et al. [4] optimized the piston speed ratios to get the maximum COP for the irreversible Carnot refrigerator and heat pump using the finite time thermodynamics. In this paper, we focus on the thermodynamic performance optimization. As the thermodynamic processes in heat pump systems are mainly composed of heat transfer processes and thermodynamic cycles, the analyses of the heat transfer processes and thermodynamic cycles are very important for the optimization designs. In the past decades, some optimization theories have already been developed and applied to heat transfer and thermodynamic cycles [15][16][17][18].Practical heat transfer processes are irreversible from the thermodynamic viewpoint, and entropy generation will be produced. Many researchers applied the entropy generation minimization method to analyzing and optimizing heat transfer processes [18][19][20]. However, the entropy generation paradox tells us that the effectiveness of heat exchangers ε does not always decrease when the entropy generation number increases [18]. When Bejan [18] analyzed a balanced counter flow heat exchanger, he explained the entropy generation paradox as following: when ε→0, the heat exchanger would disappear as an engineering component, a...