Page 488 - Design and Operation of Heat Exchangers and their Networks

Appendix 471

x_in = [0, x1, x1, x2, x1, x2, L];
x_out = [x1, x2, x2, L, 0, x1, x2];
A_H1C1 = 2.3; % m2
A_H1C2 = 2.2; % m2
G = zeros(7, 7);
G1 = zeros(7, 3);
G2 = zeros(3, 7);
G(2, 1) = 1;
G(4, 3) = 1;
G(5, 6) = 1;
G(6, 7) = 1;
G1(1, 3) = 1;
G1(3, 2) = 1;
G1(7, 1) = 1;
G2(1, 5) = 1;
G2(2, 4) = 1;
G2(3, 2) = 1;
A = zeros(7, 7);
A(1, 5) = k ∗ A_H1C2 / C_C2 / L; % 1/m
A(1, 1) = - A(1, 5);
A(2, 6) = A(1, 5);
A(2, 2) = - A(2, 6);
A(3, 6) = k ∗ A_H1C1 / C_C1 / L; % 1/m
A(3, 3) = - A(3, 6);
A(4, 7) = A(3, 6);
A(4, 4) = - A(4, 7);
A(5, 1) = k ∗ A_H1C2 / C_H1 / L;
A(5, 5) = - A(5, 1);
A(6, 2) = A(5, 1);
A(6, 3) = k ∗ A_H1C1 / C_H1 / L;
A(6, 6) = - A(6, 2) - A(6, 3);
A(7, 4) = A(6, 3);
A(7, 7) = - A(7, 4);
V_in = zeros(7, 7);
V_out = zeros(7, 7);
[A_V, A_D] = eig(A);
for i=1:7
for j =1:7
V_in(i, j) = A_V(i, j) ∗ exp(A_D(j, j) ∗ x_in(i));
V_out(i, j) = A_V(i, j) ∗ exp(A_D(j, j) ∗ x_out(i));