Modern Engineering Thermodynamics

290 CHAPTER 9: Second Law Open System Applications
Shell Tubes m
Shell Tube
B
m B
m A
m A
(a)
(b)
FIGURE 9.6
Multiple-tube, multiple-pass heat exchanger geometries: (a) single-tube, double-pass, parallel flow; (b) double-tube, double-pass, counterflow.
by using multiple tubes and multiple passes, as shown in Figure 9.6.
Figure 9.7 illustrates a typical commercial multiple tube heat
exchanger.
The temperature profiles inside single-tube, single-pass heat exchangers
are shown in Figure 9.8. In the parallel flow arrangement, the
outlet temperature of the cold flow stream can never exceed the outlet
temperature of the hot flow stream. However, in the counterflow
arrangement, this situation can occur, and consequently the required
surface area to produce a given amount of heat transfer is less in the
counterflow than the parallel flow configuration.
In heat exchanger design, the basic formula used to determine the
internal heat transfer rate for a single-pass heat exchanger is
Internal heat transfer rate for a single-pass heat exchanger
_Q heat = UAðΔTÞ LMTD
(9.21)
exchanger
ðinternalÞ
FIGURE 9.7
A cutaway of a single-pass shell and tube heat exchanger.
where U is the overall heat transfer coefficient (see Table 9.1), A is
the total internal heat transfer area, and (ΔT) LMTD is the log mean
temperature difference, defined for a single-tube, single-pass heat
exchanger as
Log mean temperature difference
ðΔTÞ LMTD
=
ðT H − T C Þj x=L − ðT H − T C Þj
x=0
(9.22)
ln ðT H − T C Þj x=L / ðT H − T C Þj x=0
Heat exchangers are normally two-fluid aergonic devices with dual inlets and dual outlets. If the entire heat
exchanger is taken as the system, it is normally adiabatic (the main heat transfer takes place inside the heat
exchanger not across its external boundary) and the modified energy rate balance equation for negligible change
in kinetic and potential energy reduces to (see Eq. (6.28))
and the MSRB for this system yields
_m H ðh in − h out Þ H = _m C ðh out − h in Þ C (9.23)
Heat exchanger entropy production rate
_S P = _m H ðs out − s in Þ H
+ _m C ðs out − s in Þ C
(9.24)
If both fluids are incompressible liquids with constant specific heats, Eqs. (6.19) and (7.33) convert Eqs. (9.23)
and (9.24) into
_m H ½cT ð in − T out Þ+ vp ð in − p out ÞŠ H
= _m C ½cT ð out − T in Þ+ vp ð out − p in Þ
Š C