Page 147 - Design and Operation of Heat Exchangers and their Networks

Steady-state characteristics of heat exchangers 135

3.6.2.1 Sequential block arrangement
For sequential block arrangement,
1
P ¼ Q C (3.343)
where P, Q, and C are mn mn matrices. The nonzero elements of Q and C
are given as follows:

Þm + j ¼ μ (3.344)
i ¼ 1;j ¼ 1,2,…,m : q j, n 1ð f, nj U f, nj

q jj ¼ U p,1, j + η + μ U f,1, j + U p, nj + η + μ (3.345)
f,1, j f,1, j f , nj f, nj U f, nj
q j,m + j ¼ μ f,1, j U f,1, j (3.346)
Þm + j ¼ U p, nj + η (3.347)
c j, n 1ð f , nj U f, nj
c jj ¼ U p,1, j + η f,1, j U f,1, j (3.348)

Þm + j, n 2Þm + j ¼ μ (3.349)
i ¼ n;j ¼ 1,2,…,m : q n 1ð ð f,n 1, j U f ,n 1, j

Þm + j, n 1Þm + j ¼ U p, nj + η + μ
q n 1ð ð f , nj f, nj U f, nj + U p,n 1, j
(3.350)

+ η f,n 1, j + μ f,n 1, j U f ,n 1, j
Þm + j, j ¼ μ (3.351)
q n 1ð f, nj U f, nj
Þm + j, n 2Þm + j ¼ U p,n 1, j + η (3.352)
c n 1ð ð f,n 1, j U f,n 1, j
Þm + j, n 1Þm + j ¼ U p, nj + η (3.353)
c n 1ð ð f, nj U f , nj
Þm + j, i 2Þm + j ¼ μ
i ¼ 2,3,…,n 1;j ¼ 1,2,…,m : q i 1ð ð f,i 1, j U f,i 1, j
(3.354)

Þm + j, i 1Þm + j ¼U p, ij + η + μ
q i 1ð ð f, ij f , ij U f, ij + U p,i 1, j
(3.355)

+ η f,i 1, j + μ f,i 1, j U f,i 1, j
Þm + j,im + j ¼ μ (3.356)
q i 1ð f , ij U f, ij
Þm + j, i 2Þm + j ¼ U p,i 1, j + η (3.357)
c i 1ð ð f,i 1, j U f ,i 1, j
Þm + j, i 1Þm + j ¼ U p, ij + η (3.358)
c i 1ð ð f, ij U f, ij

3.6.2.2 Symmetrical block arrangement
For symmetrical block arrangement, P is an m (n+1) mn matrix:
( ∗
p , i ¼ 1,⋯,n 1
l, i 1ð Þm + j
p l, i 1ð Þm + j ¼ ∗ ∗
p + p , i ¼ n (3.359)
l, n 1ð Þm + j l,nm + j
ð l ¼ 1, 2, …, mn +1Þ; j ¼ 1, 2, …, mÞ
ð