Page 144 - Design and Operation of Heat Exchangers and their Networks

132 Design and operation of heat exchangers and their networks

M
X
r j x 00
t i x 00 ¼ h ij e i d j i ¼ 1, 2, …, MÞ (3.324)
ð
i
j¼1
0 00
ð
t i xðÞ ¼ t i xðÞ ¼ d i i ¼ M +1, M +2, …, M + M M Þ (3.325)
or in the matrix form as
0
0
Θ x ðÞ ¼ V D (3.326)
00
00
Θ x ðÞ ¼ V D (3.327)
0
where V and V are (M+M M ) (M+M M ) matrices, whose nonzero ele-
00
ments are
0
r j x
0
00
v ¼ h ij e , v ¼ h ij e r j x 00 i ð i ¼ 1, 2, …, M; j ¼ 1, 2, …, MÞ (3.328)
i
ij ij
0 00
ð
v ¼ v ¼ 1 i ¼ M +1, M +2, …, M + M M Þ (3.329)
ii ii
Substitution of Eqs. (3.326), (3.327) into Eq. (3.320) yields
0 00 1 0
D ¼ V GVð Þ G T in (3.330)
0 00 1 0
T xðÞ ¼ V xðÞ V GVð Þ G T in (3.331)
The fluid temperatures at the channel outlets and those at the outlets of
the exchangers can then be expressed explicitly as
00 00 0 00 1 0
Tx ðÞ ¼ V V GVð Þ G T in (3.332)
00 00 0 00 1 0
T out ¼ G V V GVð Þ G T in (3.333)
3.6.2 Multistream parallel channel plate-fin heat exchangers

A plate-fin heat exchanger consists of fins separated by flat plates, clamped
and brazed together. The plates separating two fluids function as the primary
heat transfer surface. The fin sheets between the adjacent plates hold the
plates together and form a secondary surface for heat transfer. The space
of fin sheets between two plates forms a flow channel and is known as a layer.
A multistream plate-fin heat exchanger contains more than two streams
flowing through different layers and sections of the exchanger. The
exchanger usually consists of many passage blocks, which are repetitively
arranged. Each block consists of n layers. Since there is a very large number
of layers in an exchanger, we usually assume that the behavior of a block can
adequately describe that of the entire exchanger; therefore, only n layers
need to be analyzed.