Question

USE EXCEL TO SOLVE

After heat treatment, the 2-cm thick metal plates (k = 180 W/m·K, ρ = 2800 kg/m3, and cp = 880 J/kg·K) are conveyed through a cooling chamber with a length of 10 m. The plates enter the cooling chamber at an initial temperature of 500°C. The cooling chamber maintains a temperature of 10°C, and the convection heat transfer coefficient is given as a function of the air velocity blowing over the plates h = 33V0.8, where h is in W/m2·K and V is in m/s. To prevent any incident of thermal burn, it is necessary for the plates to exit the cooling chamber at a temperature below 50°C. In designing the cooling process to meet this safety criteria, use EXCEL software to investigate the effect of the air velocity on the temperature of the plates at the exit of the cooling chamber. Let the air velocity vary from 0 to 40 m/s, and plot the temperatures of the plates exiting the cooling chamber as a function of air velocity at the moving plate speed of 2, 5, and 8 cm/s

Answer 1

MATLAB script

clc
clear
close
L=2e-2; k=180; rho=2800; cp=880; d=10; Ti=500; Ta=10; Va=0:40;
V=[2 5 8]/100;
h=33*Va.^0.8;
Lc=L/2;
Bi=h*Lc/k;
T=zeros(3,length(h));
for i=1:length(i)
if Bi(i)<0.1
for j=1:3
t=d/V(j);
tau=rho*cp*Lc./h;
T=Ta+(Ti-Ta)*exp(-t./tau);
plot(Va,T)
hold on
end
else
disp('The lumped system approximation does not exist')
break
end
end
plot([0 40],[50 50],'--k')
xlabel('Air velocity [m/s]'),ylabel('Plate exit temperature [^oC]')
lgnd=legend('V_{plate}=2 cm/s','V_{plate}=5 cm/s','V_{plate}=8 cm/s');
grid on
hold off