Page 475 - Design and Operation of Heat Exchangers and their Networks

458 Appendix

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
Re_Pr_d_L = Re ∗ Pr ∗ d_i / L; % RePrd/L
fprintf('L = %fm\n', L);

Example 2.2 Sizing an electrically heated tube (continued)
(MatLab code)

% Example 2.2 Sizing an electrically heated tube (continued)
% The problem is the same as Example 2.1:
% The compressed air at 1.5 bar with a normal volumetric flow rate of
% 1.2 Nm3/h shall be heated from 20°Cto 80°C by the heating wire
% uniformlywrapped around the tube as it flows through the tube. The
% tube outside diameter is 25 mm, tube wall thickness is 2 mm, and
% thermal conductivity of the tube material is 15 W/mK. The tube
% temperature shall not exceed 200°C. Determine the length of the tube
% heating section.
% Example 2.1 gives a safe design of L = 0.57 m. For some reason the tube
% should be shortened. A mixing disk with many small holes is assembled at
% the inlet of the tube so that the inlet velocity distribution could be
% uniform. Considering 5% uncertainty in the calculation of the heat
% transfer coefficient, evaluate the minimal acceptable length of the
% heating section.

d_o = 0.025; % outside diameter, m
d_i = 0.021; % inside diamter, m
lambda_w = 15; % tube thermal conductivity, W/mK
V_N = 1.2; % normal volumetric flow rate, Nm3/h
p_N = 1.01325; % normal pressure, bar
t_N = 0; % normal temperature, °C
t_in = 20; %inlet temperature, °C
p_in = 1.5; % inlet pressure, bar
t_out = 80; % outlet temperature, °C
t_max = 200; % maximum allowed temperature, °C
t_m = (t_in + t_out) / 2; % mean temperature, °C
rho_N = refpropm('D','T', t_N + 273.15, 'P', p_N ∗ 100, 'air');