Need Help Solving Two Coupled ODEs

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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.

Accepted Answer

James Tursa
James Tursa on 29 Apr 2021
Edited: James Tursa on 29 Apr 2021
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),'-.')
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