Page 92 - Design and Operation of Heat Exchangers and their Networks

80 Design and operation of heat exchangers and their networks

_
_

ln Δt 1 =Δt 2 Þ ¼ 1=C h 1=C c kA (3.53)
ð

_
_
0
0
Because C h ¼ Q= t t 00 and C c ¼ Q= t t , Eq. (3.53) is finally
00
h h c c
written as

00
0
t t h 00 t t 0 c Δt 1 Δt 2
c
h
Q ¼ kA ¼ kA (3.54)
ð
ln Δt 1 =Δt 2 Þ ln Δt 1 =Δt 2 Þ
ð
The term (Δt 1 Δt 2 )/ln(Δt 1 /Δt 2 ) is called the logarithmic mean temper-
ature difference, which is equal to the real mean temperature difference in
the parallel flow and counterflow heat exchangers.
3.2.2 Effectiveness ε and number of transfer units
The ε-NTU method for the heat exchanger analysis was introduced in 1942
by London and Seban in an unpublished paper. The effectiveness ε is defined
as the ratio of the real heat load of a heat exchanger to the maximal possible
heat load:

max t t , t t 0 c
00
00
0
h
c
h
ε ¼ (3.55)
t t 0
0
h c
and NTU denotes the number of transfer units, which is a measure of the
exchanger size:
kA
NTU ¼ _ (3.56)
C min
The thermal capacity rate ratio R is defined as
_
C min
R ¼ _ (3.57)
C max
The effectiveness ε of a two-fluid heat exchanger is a dimensionless
measure of the quantity of heat actually being transferred between two
streams. It is a normalized (from zero to unity) actual quantity of heat to
be transferred in the exchanger. Effectiveness ε tells us how closely the tem-
perature of the fluid with smaller thermal capacity rate approaches the max-
imum possible temperature rise. For the counterflow arrangement and to
some extent for the crossflow arrangement, this corresponds to seeking
the closest temperature approach between the fluids. When care is taken
to keep the temperature approach as small as possible, high effectiveness
is expected. While for parallel-flow arrangements, things are different,
because parallel-flow applications are usually more concerned with limiting