Entropy Generation Paradox In Parallel And Counterflow Heat Transfer Optimization And Its Thermodynamic Analysis

In the development and utilization of energy, more than eighty percent of the energy is used in the form of heat, and the optimal design and manufacturing of high efficient heat exchangers is the foundation of the efficient utilization of thermal energy in many industrial areas. Since the minimum entropy generation principle was introduced to the optimal design theory, it has achieved good results in designing high efficient heat exchangers. However, if the effectiveness of the counter-flow heat exchanger ranges from 0 to 0.5, the occurrence of entropy generation paradox has been becoming a key issue in the heat exchangers optimization.In this work, two typical theories in the optimal design of heat exchangers are analyzed,namely, the minimum entropy generation theory that entropy generation number represents the heat transfer performance, and entransy dissipation optimization theory that minimum thermal resistance represents the heat transfer performance. The latter has better solved the entropy generation paradox, but it is on the premise that ignoring the dissipation in the flow process.The thorough solution to the problem of entropy generation paradox must rely on the further understanding of the mechanism of heat transfer enhancement caused by the interaction between the heat transfer and mass transfer processes from the point of view of thermodynamics.In fact,according to the field synergy theory, the smaller intersection angle between the velocity vector and temperature gradient, the more the heat transfer process enhanced. However, for the two cases that the intersection angle between the two vectors is 0 and π, no theoretical explanation has been given at present.If the entropy flow of the system is equal to zero, for the quasi isolated system composed of steady flow, it is possible for the nonspontaneous process which entropy generation is less than zero to happen simultaneously driven by the spontaneous process which entropy generation is greater than zero. Based on the divergence equation of heat flow, two kinds of thermodynamic mechanism behind convection heat transfer are revealed, namely, the field synergy mechanism that mass transfer and heat transfer are the spontaneous processes, and thermodynamic coupling mechanism that the mass transfer is a spontaneous process, while the heat transfer is a nonspontaneous process.In a heat exchanger with a dividing wall between the two fluids, when hot fluidreleases heat governed by the field synergy mechanism, the smaller the intersection angle between mass flow and heat flow, the better the heat transfer effect is.Moreover, for cold fluid absorbing heat governed by the thermodynamic coupling mechanism, the larger the intersection angle between mass flow and heat flow,the better the heat transfer effect is. In the parallel-flow configuration, the enhanced effect of the heat transfer process of hot fluid is nearly offset by the weakened effect of the heat transfer process of cold fluid, therefore the total effect is neither enhanced nor weakened. Nevertheless, in the counterflow configuration, both heat transfer processes of the hot fluid and cold fluid are enhanced. Hence it is the essential reason that the heat transfer effect of counterflow is better than that of parallel-flow configuration.In the counterflow configuration, since cold fluid absorbing heat is governed by the thermodynamic coupling mechanism, if the entropy generation rate of the mass transfer process increases, and owing to the heat pump effect,the negative entropy generation rate of the heat transfer process becomes larger, which means that the larger the degree of the fluid temperature increment, the larger effectiveness of the heat exchanger. In other words, when the flow entropy generation rate of the cold fluid increases, the greater the entropy generation rate of the flow process is offset by the negative entropy generation rate of the heat transfer process, the smaller the total entropy generation rate. Therefore the final effect for the counterflow heat transfer is that the smaller the total entropy generation rate, the higher the effectiveness of the heat exchanger.That is to say, there is no entropy generation paradox occurring in the process of counterflow heat transfer.