Modern Engineering Thermodynamics

184 CHAPTER 6: First Law Open System Applications
6.8 HEAT EXCHANGERS
Heat exchanger is the generic name of any device whose primary function is to promote a heat transport of
energy from one fluid to another fluid. Most heat exchangers have two separate fluid flow paths, which do not
mix the fluids but instead promote the transfer of heat from one fluid to another across a thermally conducting
but otherwise impermeable barrier. These heat exchangers have four flow streams, two inlets and two outlets.
Since the primary function of a heat exchanger is a heat transfer process, they are characteristically aergonic
devices. Also, all of the heat transfer should take place inside the heat exchanger; therefore, most heat exchangers
are normally adiabatic devices when the entire heat exchanger is insulated and taken to be the system. It is
normal for an uninsulated heat exchanger to have a net heat transfer to or from its surroundings, but when
environmental heat transfer values are not supplied in a problem statement and are not an unknown or otherwise
determinable, you are to assume that the entire heat exchanger is an adiabatic system. Figure 6.8 illustrates
a typical heat exchanger schematic and operating characteristics.
A heat exchanger can be considered to be a pair of steady state, steady flow, single-inlet, single-outlet systems
that have equal but opposite heat transfer rates. It can also be analyzed as a steady state, steady flow, doubleinlet,
double-outlet system that has no (assuming it is insulated) external heat transfer. In both cases it is common
to neglect any changes in flow stream specific kinetic or potential energy across the system. The general
ERB (Eq. (6.4)) for the latter case reduces to
_Q + _m 1 h 1 + _m 3 h 3 − _m 2 h 2 − _m 4 h 4 = 0
The conservation of mass law requires that _m 1 = _m 2 = _m a and that _m 3 = _m 4 = _m b , where the subscripts a and b
refer to the two different fluids. Therefore, the ERB becomes
_Q + _m a ðh 1 − h 2 Þ + _m b ðh 3 − h 4 Þ = 0 (6.27)
and if the heat exchanger is insulated, then _Q = 0 and this equation further reduces to
_m a ðh 1 − h 2 Þ = _m b ðh 4 − h 3 Þ (6.28)
If both fluids a and b are incompressible (e.g., liquids), then Eq. (6.19) can be used to give
_m a ½c a ðT 1 − T 2 Þ + v a ðp 1 − p 2 ÞŠ = _m b ½c b ðT 4 − T 3 Þ + v b ðp 4 − p 3 ÞŠ
where c a and c b are the specific heats of fluids a and b, respectively. For liquids, not only are v a and v b small numbers,
but the pressure drops p 1 − p 2 and p 3 − p 4 across the heat exchanger are also small. Therefore, it is common to ignore
the pressure terms in the previous equation, giving the final incompressible fluid heat exchanger ERB as
ERB when both fluids are incompressible liquids
_m a c a ðT 1 − T 2 Þ = _m b c b ðT 4 − T 3 Þ
If both fluids are ideal gases with constant specific heats, then the use of Eq. (6.22) gives
ERB when both fluids are ideal gases
_m a ðc p Þ a
ðT 1 − T 2 Þ = _m b ðc p Þ b
ðT 4 − T 3 Þ
where (c p ) a and (c p ) b are the constant pressure specific heats of gases a and b, respectively.
System
boundary
Fluid a
Fluid b
1
3
Q i
2
4
m a
m b
Assumptions:
1. Steady state, steady flow,
2. W = 0,
3. Q = 0 (unless otherwise stated),
4. Negligible changes in ke and pe
on all flow steams.
(Q i is the internal heat transfer rate)
FIGURE 6.8
Typical heat exchanger operating characteristics.