Page 486 - Design and Operation of Heat Exchangers and their Networks

Appendix 469

% logarithmic mean temperature difference, K
G_h = Q ∗ 1000 / (cp_h ∗ (t_h_in - t_h_out)) / (N_tube ∗ pi ∗ d_i ^ 2 / 4);
% tubeside mass velocity, kg/m2s
Re_h = G_h ∗ d_i / mu_h; % tubeside Reynolds number
f8 = (1.82 ∗ log10(Re_h) - 1.64) ^ (-2) / 8;
t_c_m = (t_c_in + t_c_out) / 2;

L = 2.701; % assumed tube length, m
Pr_w = Pr_h; % assumed Prandtl number at the tubeside wall
for iter = 1 : 1000
n = ceil(L / delta_L); % number of axially mixed zones
Pe_c = 2 ∗ n; % shellside dispersive Peclet number
delta_t_m_d = ((t_h_in - t_c_out) - (t_h_out - t_c_in)) ...
/ log((t_h_in - t_c_out) / (t_h_out - t_c_in)) ...
- (t_h_in - t_h_out) / Pe_h - (t_c_out - t_c_in) / Pe_c;
% mean temperature difference for dispersive flow, K
kA = Q ∗ 1000 / delta_t_m_d;
% overall heat transfer coefficient based on tubeside area, W/m2K
Nu_h = f8 ∗ (Re_h - 1000) ∗ Pr_h / (1 + 12.7 ∗ sqrt(f8) ∗ (Pr_h ...
^ ^ ^
(2/3) - 1)) ∗ (1 + (d_i / L) (2 / 3)) ∗ (Pr_h / Pr_w) 0.11;
alpha_h = Nu_h ∗ lambda_h / d_i;
% tubeside heat transfer coefficient, W/m2K
s = kA / (N_tube ∗ pi ∗ d_i) ∗ (1 / alpha_h + R_w_i + d_i ...
/ (alpha_c ∗ d_o)) - L;
L=L+s;% calculated tube length, m
k_i = kA / (N_tube ∗ pi ∗ d_i ∗ L);
% overall heat transfer coefficient based on tubeside area, W/m2K
C = 1 - ((t_h_in - t_h_out) / Pe_h + (t_c_out - t_c_in) / Pe_c) / delta_t_LM;
t_h_w_m = t_h_m - C ∗ k_i ∗ (t_h_m - t_c_m) / alpha_h;
% mean wall temperature at hot water side (tubeside), °C
[cp_w, lambda_w, mu_w] = water_properties(t_h_w_m);
% viscosity at the tubeside wall, sPa
Pr_w = mu_w ∗ cp_w / lambda_w; % Prandtl number at the tubeside wall
if (abs(s) < 1E-6)
break;
end
end
fprintf('L = %fm\n', L);