Cascade of heated tanks

In this case, Assumption 6.2 translates to Qi/Hq = 0(1), Q2/H0 = 0(1). Let us now assume that the rate at which material is recycled is very high, i.e., Fs/Rs = e C 1. Observing that the energy flows Hi are, in effect, a product of a material flow rate and a specific enthalpy, i.e., Hi = Fihi, (6.23) becomes 

Proceeding with the analysis as outlined in Section 6.3, we derive a fast component of the energy dynamics in the form 

Clearly, this very simple process belongs to the class considered in Section 6.2. From the defining assumptions, we can expect that the enthalpy in the second tank will not differ significantly from the enthalpy of the feed stream. Thus, the energy recovery number of the process, 

A similar result was reported earlier (Georgakis 1986), when an eigenvalue analysis was used to prove that a time-scale separation is present in the transient evolution of the states 91 and 92. It is noteworthy, however, that, in contrast to the approach presented in this chapter, an eigenvalue analysis does not provide a means by which to derive physically meaningful reduced-order models for the dynamics in each time scale. 

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