Question

Air, initially at atmospheric conditions, flows through an atmospheric-pressure heat exchanger. Assume that the process in the heat exchanger can be discretized into 100 steps, where 5 kJ/kg of heat is added to the air at each step.

a) Derive an equation that can be used to calculate the temperature of the air at each step.
b) Derive an equation that can be used to calculate the exergy of air at each step.

c) Implement the equations in MATLAB and generate a plot of exergy of air as a function of temperature at each step. Show your code (with clear comments) and clearly label the figure.
d) Is the trend obtained in part (c) expected? Briefly comment.

Answer 1

c. The code is given below

Ti=input('enter initial temperature in K ')
q=5 %heat added in Kj/kg
Cp=1.005 %Cp of air in Kj/Kg-k
n=0:100;
Tfn=(n.*q./1.005)+Ti;
c=1;
for itr=1:100
En(c)=Ti*Cp*log(Tfn(c+1)/Tfn(c));
c=c+1;
end
Tfn(end)=[]; %deleting the last final temperature so that the plot can be created
plot(Tfn,En)
xlabel('Initial temperature for nth heat exhange in k')
ylabel('Exergy in Kj/Kg')

Let us take an example for initial conditions for 300k