Page 483 - Design and Operation of Heat Exchangers and their Networks

466 Appendix

% sPa
G_h = Q ∗ 1000 / (cp_h ∗ (t_h_in - t_h_out)) / (N_tube ∗ pi ∗ d_i ^ 2 / 4);
% tubeside mass velocity, kg/m2s
delta_t_LM = ((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));
% logarithmic mean temperature difference, K
kA = Q ∗ 1000 / delta_t_LM;

theta = (t_h_in - t_c_out) / (t_h_out - t_c_in);
m1 = 0.5 + sqrt(3) / 6;
m2 = 0.5 - sqrt(3) / 6;

psi_1 = (theta ^ m1 - 1) / (theta - 1);
t_h_1 = t_h_out + psi_1 ∗ (t_h_in - t_h_out);
% reference temperature 1 of hot water
t_c_1 = t_c_in + psi_1 ∗ (t_c_out - t_c_in);
% reference temperature 1 of cold water
[cp_h_1, lambda_h_1, mu_h_1] = water_properties(t_h_1);
% isobaric heat capacity, J/kg; thermal conductivity, W/mK; K; viscosity,
% sPa
Pr_h_1 = mu_h_1 ∗ cp_h_1 / lambda_h_1; % Prandtl number
Re_h_1 = G_h ∗ d_i / mu_h_1; % tubeside Reynolds number
f8_1 = (1.82 ∗ log10(Re_h_1) - 1.64) ^ (-2) / 8;
Nu_h_0_1 = f8_1 ∗ (Re_h_1 - 1000) ∗ Pr_h_1 / (1 + 12.7 ∗ sqrt(f8_1) ...
∗ (Pr_h_1 ^ (2/3) - 1));
psi_2 = (theta ^ m2 - 1) / (theta - 1);
t_h_2 = t_h_out + psi_2 ∗ (t_h_in - t_h_out);
% reference temperature 2 of hot water
t_c_2 = t_c_in + psi_2 ∗ (t_c_out - t_c_in);
% reference temperature 1 of cold water
[cp_h_2, lambda_h_2, mu_h_2] = water_properties(t_h_2);
% isobaric heat capacity, J/kg; thermal conductivity, W/mK; K; viscosity,
% sPa
Pr_h_2 = mu_h_2 ∗ cp_h_2 / lambda_h_2; % Prandtl number
Re_h_2 = G_h ∗ d_i / mu_h_2; % tubeside Reynolds number
f8_2 = (1.82 ∗ log10(Re_h_2) - 1.64) ^ (-2) / 8;
Nu_h_0_2 = f8_2 ∗ (Re_h_2 - 1000) ∗ Pr_h_2 / (1 + 12.7 ∗ sqrt(f8_2) ...
∗ (Pr_h_2 ^ (2/3) - 1));
L = 2.701; % assumed tube length, m