Need Help Solving Two Coupled ODEs

Hi I am trying to solve two coupled ODEs simultaneously.

My equations are:

dT1/dz = -U*a1/(p1*q1*Cp1*L)*(T1 - T2) - Q*a1/(p1*Cp1)

dT2/dz = U*a2/(p2*Cp2*q2*L)*(T1 - T2)

I have tried programming Matlab in several different ways this is the code for the one I think I am the closest to solving.

function [z, T] = Term_project2
    U= 280;
    a=2*.45*3.14159;
    p1= 0.5;
    L= 8000;
    Cp1= 10;
    Q=284;
    p2= 1;
    Cp2= 15;
    q1= 0.5;
    q2= 1;
    zspan=[0:40];
    T0= [12 5];
dT(1) = -(U*a)/(L*p1*Cp1*q1)*(T1(z)-T2(z))-Q/(p1*Cp1);
dT(2) = (U*a)/(L*p2*Cp2*q2)*(T1(z)-T2(z))-Q/(p2*Cp2);


[z,T]= ode45(Term_project2(z,p1,p2,q1,q2,U,Q,Cp1,Cp2L),zspan,T0);
plot(z,T1(:,1),'-o',z,T2(:,2),'-.')
end

Errors: Unrecognized function or variable 't'.

Which doesn't make sense since I don't have t.

Answer 1

[James Tursa]

The derivative function needs to have the input arguments specified. In your current code above, you have no inputs specified.

For the ode45 call, you need to pass a function handle that has only two inputs, the independent variable and the current state.

So your derivative function should look something like this:

function dTdz = Term_project2(z,T,p1,p2,q1,q2,U,Q,Cp1,Cp2L) % pass in all needed inputs
dTdz(1,1) = -(U*a)/(L*p1*Cp1*q1)*(T(1)-T(2))-Q/(p1*Cp1); % use T(1) and T(2) for T1 and T2
dTdz(2,1) = (U*a)/(L*p2*Cp2*q2)*(T(1)-T(2))-Q/(p2*Cp2);
end

And your calling code should look something like this:

U= 280;
a=2*.45*3.14159;
p1= 0.5;
L= 8000;
Cp1= 10;
Q=284;
p2= 1;
Cp2= 15;
q1= 0.5;
q2= 1;
zspan=[0:40];
T0= [12 5];
% 1st argument to ode45 below needs to be a function handle
% that takes z and T as inputs
[z,T]= ode45(@(z,T)Term_project2(z,T,p1,p2,q1,q2,U,Q,Cp1,Cp2L),zspan,T0);
plot(z,T(:,1),'-o',z,T(:,2),'-.')

[Alyssa Garreau]

Thank you so much for your help. This is how I have it written in Matlab, but I am told that there is not enough input arguments.

function dTdz = Term_project_soln(z,T,p1,p2,q1,q2,U,Q,Cp1,Cp2,L,a) % pass in all needed inputs
U= 280;
    a=2*0.45*3.14159;
    p1= 1.2041;
    L= 1000;
    Cp1= 10;
    Q=284;
    p2= 2400;
    Cp2= 3962;
    q1= (3.5*a);
    q2= (0.1/1000);
zspan=[0:40];
T0= [12 5];
% 1st argument to ode45 below needs to be a function handle
% that takes z and T as inputs

dT(1,1) = -(U*a)/(L*p1*Cp1*q1)*(T(1)-T(2))-Q/(p1*Cp1); % use T(1) and T(2) for T1 and T2
dT(2,1) = (U*a)/(L*p2*Cp2*q2)*(T(1)-T(2))-Q/(p2*Cp2);


[z,T]= ode45(@(z,T)Term_project_soln(z,T,p1,p2,q1,q2,U,Q,Cp1,Cp2,L,a),zspan,T0);
plot(z,T(:,1),'-o',z,T(:,2),'-.')
end

[James Tursa]

You still have all your code mixed together. The function needs to be only the four lines I have written above. Nothing else. You could put that in a file called Term_project_soln.m

Then have your other code in a separate script file that sets the constants, calls ode45, and does the plotting.

[Alyssa Garreau]

Thank you.