Page 400 - Design and Operation of Heat Exchangers and their Networks

Dynamic analysis of heat exchangers and their networks 383

Table 7.3 Nonzero elements of Q, Q, C, and C in Eqs. (7.304), (7.305) for different
e
e
block arrangements.
Block arrangement Nonzero elements
∗
q ijðÞ, ijðÞ ¼ sC + ψ + ψ + ϕ + ϕ ,
1<i n j p, ij ij i 1, j ij i 1, j
Þ ¼ ϕ
ij
q ijðÞ, i 1, jð i 1, j , q ijðÞ, i +1, jð Þ ¼ ϕ ,
Þ ¼ ψ ,
ij i 1, j
c ijðÞ, ijðÞ ¼ ψ , c ijðÞ, i 1, jð
q ¼ e ψ + e ψ + ϕ + ϕ ,
e
e
e ij ij i 1, j ij i 1, j
ðÞ, ijðÞ
q ¼ ϕ q ¼ ϕ ,
e
e
e ij i 1, j , e ij ij
ð
ð
ðÞ, i 1, jÞ ðÞ, i +1, jÞ
c Þ ¼ e ψ
ij
e ijðÞ, ijðÞ ¼ e ψ , ec ijðÞ, i 1, jð i 1, j
i¼1 Sequential q 1, jð Þ,1, jÞ ¼ sC ∗ p,1, j + ψ 1, j + ψ n j , j + ϕ 1, j + ϕ n j , j ,
ð
q ¼ ϕ n j , j , q 1, jð Þ,2, jÞ ¼ ϕ ,
1, j
ð
ð 1, jÞ, n j, jÞ ð
Þ,1, jÞ ¼ ψ , c ¼ ψ ,
c 1, jð ð 1, j ð 1, jÞ, n j, jÞ n j , j
ð
q ¼ e ψ + e ψ + ϕ + ϕ ,
e
e
e 1, j n j , j 1, j n j , j
ð 1, jÞ,1, jÞ
ð
q ¼ ϕ q ¼ ϕ ,
e
e
e n j , j , e 1, j
ð
ð
ð 1, jÞ, n j, jÞ ð 1, jÞ,2, jÞ
c Þ,1, jÞ ¼ e ψ , ec ¼ e ψ
e 1, jð ð 1, j ð 1, jÞ, n j, jÞ n j , j
ð
1
Symmetry I and II q 1, jð Þ,1, jÞ ¼ sC ∗ p,1, j + ψ 1, j + ϕ ,
1, j
ð
2
Þ,2, jÞ ¼ ϕ , c 1, jÞ,1, jÞ ¼ ψ ,
q 1, jð ð 1, j ð ð 1, j
q ¼ e ψ e q ¼ ϕ ,
e
1, j
e 1, j + ϕ , e 1, j
ð 1, jÞ,1, jÞ ð 1, jÞ,2, jÞ
ð
ð
c Þ,1, jÞ ¼ e ψ
e 1, jð ð 1, j
Symmetry III q (1,j), (1,j) ¼1, q (1,j), (2,j) ¼ 1
Sequential q (n j +1,j), (nj+1,j) ¼1, q (n j +1,j), (1,j) ¼ 1
1
i¼n j +1 Symmetry I q ¼ sC ∗ p, n j , j + ψ n j , j + ϕ n j , j ,
ð
ð n j +1, jÞ, n j +1, jÞ 2
q ¼ ϕ , c ¼ ψ ,
ð
ð
ð n j +1, jÞ, n j, jÞ n j , j ð n j +1, jÞ, n j, jÞ n j , j
q ¼ e ψ + ϕ ,
e
e n j , j n j , j
ð
ð n j +1, jÞ, n j +1, jÞ
q ¼ ϕ c ¼ e ψ
e
e , e n j , j
ð
ð
ð n j +1, jÞ, n j, jÞ n j , j ð n j +1, jÞ, n j, jÞ
Symmetry II and III q (n j +1,j), (nj+1,j) ¼1, q (n j +1,j), (nj,j) ¼ 1
1
n j ¼1 q 1, jð Þ,1, jÞ ¼ sC ∗ p,1, j + ψ , c 1, jð Þ,1, jÞ ¼ ψ 1, j
1, j
ð
ð
2
q c Þ,1, jÞ ¼ e ψ
e ¼e 1, jð 1, j
ð 1, jÞ,1, jÞ ð
ð