Entropy transfer efficiency-effectiveness method for heat exchangers, part 2: Temperature-conductance-entropy load diagram and temperature-heat load diagram with thermal resistance limits

In a previous paper we developed an entropy transfer efficiency-effectiveness method to resolve the open problem of the second-law efficiency evaluation for heat exchangers. In that paper the efficiency and effectiveness limits were predicted by algebraic means. In this paper we reanalyze the efficiency-effectiveness method by graphical means to illustrate the operational performance limits and interpret the physical implications of efficiency, effectiveness and entropy generation numbers. We define the overall thermal resistance between inlets or outlets, pure convection thermal resistance, overall entropy generation resistance, and entropy generation number between outlets (NS,out) so that the novel thermal circuit diagrams, temperature-conductance-entropy load (T-C-Ṡ) diagrams and temperature-heat load (T−Q˙) diagrams with rational meanings are constructed. We provide the minima of all thermal resistances, and compare NS,out with previous entropy generation numbers, indicating it to be superior in its ability to characterize energy utilization. The typical nondimensionalized entropy generation numbers are graphically represented by a T-C-Ṡ diagram, and the efficiency and effectiveness extrema, including the optimum operating points for counterflow exchangers, are pinpointed from the T−Q˙ diagram. Two counterflow optimum design criteria, one for the maximum efficiency of unity and another for the actual maximum effectiveness 1/(1+τ0.5) (τ is the ratio of cold to hot inlet temperatures) or transferable heat load cp1ṁ1T1∞(1−τ0.5) (cp1ṁ1 is the cold capacity rate, T1∞ is the cold inlet temperature), are obtained. The T-C-Ṡ and T−Q˙ diagrams are easily applied for solving sizing and rating problems and directly predicting the effectiveness and efficiency limits of heat exchangers with any flow arrangement via graphical means, and pinpointing the optimum operating performance points in a counterflow exchanger via an inlet temperature circle.