# Homework Help: ODE 45 with coupled ODE's in a matrix, reactor temp.

1. Sep 9, 2015

### Maylis

1. The problem statement, all variables and given/known data
My question is regarding part (e), I just gave all the questions for reference.

2. Relevant equations

3. The attempt at a solution
These are the coupled equations I should solve (from part d)

My issue is using ode45 to get $C_{A}(t)$, $C_{P}(t)$, and $T(t)$. Here is my m-file

Code (Text):

function G = parte(t,x,u)

V = 150; % L
k = 0.02; % L/mol*min
beta = 0.15; % kJ L^.5 / mol^.5 min
DeltaH = -15; % kJ/mol A
rho = 4.2; % kg/L
cp = 1.2; % kJ/kg K

u = zeros(3,1);
u(1) = 1.4; % L/min
u(2) = 300; % K
u(3) = 40; % mol/L

A = [-u(1)/V, u(1)*DeltaH/(rho*V*cp), beta/(2*rho*V*cp)*x(3)^(-0.5);
0, -(u(1)/V) -2*k*x(2), 0;
0, 2*k*x(2), -u(1)/V];

B = [(u(2)-x(1))/V + (x(2)-u(3))*DeltaH/(rho*V*cp), u(1)/V, -u(1)*DeltaH/(rho*V*cp);
(u(3)-x(2))/V, 0, u(1)/V;
-x(3)/V, 0, 0];

G = A*x + B*u;

end
Then I run it on my script
Code (Text):

Ti = 300; % K
CAi = 40; % mol/L
CPi = 0; % mol/L
[T4,Y4] = ode45(@parte,[0 10],[Ti CAi CPi]);
subplot(1,2,1)
plot(T4,[Y4(:,2),Y4(:,3)])
xlabel('time (minutes)')
ylabel('Concentration (lb mol/ft^{3})')
legend('A','P','location','best')
title('Concentration vs. time')
And here is my output
Code (Text):

[T4,Y4]

ans =

0  300.0000  40.0000  0
0.2500  NaN  NaN  NaN
0.5000  NaN  NaN  NaN
0.7500  NaN  NaN  NaN
1.0000  NaN  NaN  NaN
1.2500  NaN  NaN  NaN
1.5000  NaN  NaN  NaN
1.7500  NaN  NaN  NaN
2.0000  NaN  NaN  NaN
2.2500  NaN  NaN  NaN
2.5000  NaN  NaN  NaN
2.7500  NaN  NaN  NaN
3.0000  NaN  NaN  NaN
3.2500  NaN  NaN  NaN
3.5000  NaN  NaN  NaN
3.7500  NaN  NaN  NaN
4.0000  NaN  NaN  NaN
4.2500  NaN  NaN  NaN
4.5000  NaN  NaN  NaN
4.7500  NaN  NaN  NaN
5.0000  NaN  NaN  NaN
5.2500  NaN  NaN  NaN
5.5000  NaN  NaN  NaN
5.7500  NaN  NaN  NaN
6.0000  NaN  NaN  NaN
6.2500  NaN  NaN  NaN
6.5000  NaN  NaN  NaN
6.7500  NaN  NaN  NaN
7.0000  NaN  NaN  NaN
7.2500  NaN  NaN  NaN
7.5000  NaN  NaN  NaN
7.7500  NaN  NaN  NaN
8.0000  NaN  NaN  NaN
8.2500  NaN  NaN  NaN
8.5000  NaN  NaN  NaN
8.7500  NaN  NaN  NaN
9.0000  NaN  NaN  NaN
9.2500  NaN  NaN  NaN
9.5000  NaN  NaN  NaN
9.7500  NaN  NaN  NaN
10.0000  NaN  NaN  NaN

I am not sure how to do this thing with the matrix format. I thought I set up my equations correctly, but can't figure out why it won't output correctly. I should note that the $\sqrt {C_{P}}$ is the concentration of P, whereas $c_{p}$ is a constant, in case that is confusing to anyone.

Last edited: Sep 9, 2015
2. Sep 10, 2015

### Staff: Mentor

There is a problem with your definition of the ODE function:
Code (Matlab M):

function G = parte(t,x,u)

It has to be of the form
Code (Matlab M):

function G = parte(t,x)

3. Sep 10, 2015

### Maylis

I decided to solve these explicitly rather than try the matrix formulation, so now I got it