Calculation of the efectiveness of a regenerator

[ochodoce]

Hi all.
I am a student of a university degree on Chemical Engineering in Madrid, and I have one question that I would like to have your feedback about.
It is related to Thermodynamics and, more specifically, to the formula to calculate the efectiveness of a regenerator in a Rankine or in a refrigeration cycle.

Until now, the formula that I had always used is the following one:

Efectiveness _{reg, version 1} = ( h _{cold, out} - h _{cold, in} ) / ( h _{hot, in} - h _{cold, in} )

In other words, the difference of enthalpies in the cold stream, (out - in), divided by the difference of entalphies between the hot and the cold streams, when entering in the regenerator.

However, in a problem of an exam, the professor has used this variation of the formula;

Efectiveness _{reg, version 2} = ( h _{cold, out} - h _{cold, in} ) / ( h ^* _{hot, in} - h _{cold, in} )
where:
h ^* = h ( P_{cold stream}, T_hot,in )

Thus, he is replacing the entalphy of the hot stream (in) by the value of the entalphy of the fluid at the pressure of the cold stream and the temperature of the hot stream (in)

The comparison of the results of both formulas are very different. As a consequence, the rest of the calculations of the whole problem vary a lot.

Can anyone of you give me some light on this matter? When should I use each of them? They are clearly not interchangeable, since their results are very different

Thanks very much

 

[shvet]

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