Page 218 - Modelling in Transport Phenomena A Conceptual Approach

198 CHAPTER 7'. UNSTEADY-STATE MACROSCOPIC BALANCES

7.5 CONSERVATION OF ENERGY

The conservation statement for total energy under unsteady-state conditions is
given by

Rate of energy ) (7.5-1)
accumulation

For a system shown in Figure 7.2, following the discussion explained in Section 6.3,
Eq. (7.5-1) is written as

Figure 7.2 Unsteady-state flow system exchanging energy in the form of heat
and work with the surroundings.

Note that, contrary to the steady-state flow system, the boundaries of this sys
tem are not ked in space. Therefore, besides shaft and flow works, work associated
with the expansion or compression of the system boundaries must be included in
Vk so that it takes the form

dKys + ws + (PPm)in - (pcm)
w = - Psvs- (7.53)
dt v , out
- B
A C
where terms A, B, and C represent, respectively, work associated with the expan-
sion or compression of the system boundaries, shaft work, and flow work.
Substitution of Eq. (7.5-3) into Eq. (7.5-2) and the use of the definition of
enthalpy, i.e., a = U + PP, gives