Page 151 - Design and Operation of Heat Exchangers and their Networks

Steady-state characteristics of heat exchangers 139

According to the flow arrangement shown in Fig. 3.17, the nonzero
elements of the 7 7 interchannel matching matrix G can be found as

g 2,1 ¼ g 4,3 ¼ g 6,7 ¼ g 5,6 ¼ 1

0
the nonzero elements of the 7 3 entrance matching matrix G are
g 0 7,1 ¼ g 0 3,2 ¼ g 0 1,3 ¼ 1

00
the nonzero elements of the 3 7 exit matching matrix G are
g 00 ¼ g 00 ¼ g 00 ¼ 1
1,5 2,4 3,2
T
Theinletcoordinatevectorisx ¼[0, 0.28, 0.28, 0.55,0.28, 0.55, 1]
0
00
and the outlet coordinate vector is x ¼[0.28, 0.55, 0.55, 1, 0,
T
0.28, 0.55] .
With previous settings, we can easily calculate the outlet temperatures of
the fluids with the help of MatLab:
[A_V, A_D] ¼ eig(A);
for i ¼ 1:1:7
for j ¼ 1:1:7
V_in(i, j) ¼ A_V(i, j) * exp(A_D(j, j) * x_in(i));
V_out(i, j) ¼ A_V(i, j) * exp(A_D(j, j) * x_out(i));
end
end
T_out ¼ G2 * V_out / (V_in - G * V_out) * G1 * T_in;
T
00
and obtain T ¼[383.27 340.13 306.67] (K). The detailed calculation
procedure can be found in the MatLab code for Example 3.2 in the
appendix.

A plate heat exchanger consists of a number of parallel channels formed
by a stack of heat transfer plates. According to the combination of the plates
with holes or blanks located at the four corners of the plates and the addi-
tional manifold axes if necessary, various flow patterns may be created in a
multistream plate heat exchanger, which can be classified into three catego-
ries: series flow pattern, parallel flow pattern, and complex flow pattern. It is
assumed that in the plate heat exchanger, the fluid in each channel has ther-
mal contact only with the two adjacent channels. The corresponding coef-
ficient matrix of the governing equation system reads