Page 476 - Design and Operation of Heat Exchangers and their Networks

Appendix 459

% density at normal condition, kg/m3
[mu, lambda, cp] = refpropm('VLC','T', t_m + 273.15, ...
'P', p_in ∗ 100, 'air');
% viscosity, sPa; thermal conductivity, W/mK; isobaric heat capacity, J/kgK
Pr = mu ∗ cp / lambda; % Prandtl number
m = rho_N ∗ V_N / 3600; % mass flow rate, kg/s
G=m ∗ 4/pi / d_i ^ 2; % mass velocity, kg/m2s
Re = G ∗ d_i / mu; % Reynolds number
Q=m ∗ cp ∗ (t_out - t_in); % heat load, W
Nu_H = 4.36; % Nusselt number for constant wall heat flux
alpha_H = Nu_H ∗ lambda / d_i; % heat transfer coefficient, W/m2K
k=1/(1 / alpha_H + d_i ∗ log(d_o / d_i) / 2 / lambda_w);
% overall heat transfer coefficient, W/m2K
delta_t = t_max - t_out; % temperature difference at the tube outlet, K
A=Q/k / delta_t; % heat transfer area, m2
%L=A/ pi / d_i; % tube length, m
L = 0.57; % initial value of tube length, m
c = 0.05; % uncertainty in the calculation of the heat transfer coefficient
Re_Pr_d_L = Re ∗ Pr ∗ d_i / L; % initial value of RePrd/L
for iter = 1 : 1000
Nu_x_H =(4.354 ^ 3 + (1.302 ∗ Re_Pr_d_L ^ (1 / 3) - 1) ^ 3 ...
+ (0.462 ∗ Re_Pr_d_L ^ 0.5 / Pr ^ (1 / 6)) ^ 3) ^ (1 / 3);
% local Nusselt number at tube outlet for constant wall heat flux
alpha_x_H = Nu_x_H ∗ lambda / d_i;
% local heat transfer coefficient at tube outlet, W/m2K
k=1/(1/ (1 -c)/ alpha_x_H ...
+ d_i ∗ log(d_o / d_i) / 2 / lambda_w);
% local overall heat transfer coefficient at tube outlet, W/m2K
A=Q/k/ delta_t; % heat transfer area, m2
L=A/pi/ d_i; % tube length, m
s=Re ∗ Pr ∗ d_i / L - Re_Pr_d_L; % deviation in RePrd/L
Re_Pr_d_L = Re_Pr_d_L + s;
if (abs(s) < 1E-6)
break;
end
end
fprintf('L = %fm\n', L);