Schematic representation of an ideal countercurrent heat exchanger

The number of governing expressions as listed in table 8.2 equals 8. Out of the five remaining variables to be specified, three are considered fixed inputs and given by the vector I, 

The entropy of the system is assumed to be exclusively generated by the heat conduction from the hot to the cold fluids. The entropy production rate, at microscopic level, can be estimated as the product of thermal driving force and heat flux. From a macroscopic stand-point the measurable heat flow is used for this computation. A better approximation can be obtained by introducing phenomenological coefficients (Hasse, 1969 Koeijer, 2002 Meeuse, 2003). For our analysis, however, we adopt an alternative approach. The overall steady state entropy equation of change is applied and the production term is related to the net change of entropy. 

Therefore, for this ideal system the entropy production rate is given by the overall contributions of both streams. 

Summing up all the contributions leads to the overall entropy production rate of the system, 

Exergy is similarly estimated by summing up the exergy individual contributions of both liquids, 

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Figure 8.3. Schematic representation of an ideal countercurrent heat exchanger to assess the responsiveness index.

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