Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

ple,mi0 if no mass enters the control volume during the process,me 0
if no mass leaves, and m 1 0 if the control volume is initially evacuated.
The energy content of a control volume changes with time during an
unsteady-flow process. The magnitude of change depends on the amount of
energy transfer across the system boundaries as heat and work as well as on
the amount of energy transported into and out of the control volume by
mass during the process. When analyzing an unsteady-flow process, we
must keep track of the energy content of the control volume as well as the
energies of the incoming and outgoing flow streams.
The general energy balance was given earlier as

Energy balance: (5–44)

Net energy transfer Change in internal, kinetic,

by heat, work, and mass potential, etc., energies

The general unsteady-flow process, in general, is difficult to analyze because
the properties of the mass at the inlets and exits may change during a
process. Most unsteady-flow processes, however, can be represented reason-
ably well by the uniform-flow process,which involves the following ideal-
ization:The fluid flow at any inlet or exit is uniform and steady, and thus
the fluid properties do not change with time or position over the cross sec-
tion of an inlet or exit. If they do, they are averaged and treated as con-
stants for the entire process.
Note that unlike the steady-flow systems, the state of an unsteady-flow
system may change with time, and that the state of the mass leaving the
control volume at any instant is the same as the state of the mass in the con-
trol volume at that instant. The initial and final properties of the control vol-
ume can be determined from the knowledge of the initial and final states,
which are completely specified by two independent intensive properties for
simple compressible systems.
Then the energy balance for a uniform-flow system can be expressed
explicitly as

(5–45)

where uhke pe is the energy of a fluid stream at any inlet or exit
per unit mass, and euke pe is the energy of the nonflowing fluid
within the control volume per unit mass. When the kinetic and potential
energy changes associated with the control volume and fluid streams are
negligible, as is usually the case, the energy balance above simplifies to

(5–46)

where QQnet,inQin
Qoutis the net heat input and WWnet,outWout

Winis the net work output. Note that if no mass enters or leaves the con-
trol volume during a process (mime0, and m 1 m 2 m), this equa-
tion reduces to the energy balance relation for closed systems (Fig. 5–45).
Also note that an unsteady-flow system may involve boundary work as well
as electrical and shaft work (Fig. 5–46).
Although both the steady-flow and uniform-flow processes are somewhat
idealized, many actual processes can be approximated reasonably well by

Q
Wa

out

mh
a

in

mh 1 m 2 u 2 
m 1 u 12 system

aQinWina

in

mub
aQoutWouta

out

mub 1 m 2 e 2 
m 1 e 12 system

Ein
Eout  ¢Esystem 1 kJ 2

Chapter 5 | 247

⎭⎪⎬⎪⎫ ⎭⎪⎬⎪⎫

Closed

system

Closed

Q

Q – W = ∆U

W

Closed

FIGURE 5–45

The energy equation of a uniform-flow

system reduces to that of a closed

system when all the inlets and exits

are closed.

Wb

Moving

boundary We

Wsh

FIGURE 5–46

A uniform-flow system may involve

electrical, shaft, and boundary work

all at once.