Setting up ODE in Matlab for ODE 45 solver

Hi, I am having difficulty setting this problem up for the ODE45 solver. It is a kinetics equation, relating R (rate constants as a function of concentrations C), T (Temperature) and h (heat of formation) all of which vary with distance x. There are 3 species that take part in the reaction.

How do I formulate the function that calculates all these parameters to call in the ODE45 solver ( something like dTdx = .... ) How to plot x,T and x,C (what would be the correct syntax to plot these). Any help with a pseudo code will be greatly appreciated.

[Torsten]

The molar balances run fine now ?

https://de.mathworks.com/matlabcentral/answers/327213-trouble-with-ode45-for-an-array-of-values

Best wishes

Torsten.

[DIP]

Yes Torsten. I am a noob. There were discrepancies in the units which I somehow missed. I will update the answers in a bit.

[Torsten]

Just add the equation for T to the three molar balances and solve the four ODEs simultaneously.

Best wishes

Torsten.

[DIP]

function dTdx=hw2_5(x,C,T)

% Constants
A  = 2.2e10;
Ea = 130000;
Ru = 8.3145;
rho=1.3;
cp=1200;
u=1.5;

% Rate Constants and heat of formation
h(1)=-110530;
h(2)=0;
h(3)=-393520;
R(1)     = -A * (exp(-Ea /(Ru*T))) * C(1) * sqrt(C(2)); 
R(2)     = 0.5 * R(1);  
R(3)     = -R(1);
dTdx=-(sum(R(1)*h(1)+R(2)*h(2)-R(3)*h(3)))/(cp*rho*u);

[DIP]

% Solution 4: Chemical Species as a Function of Axial Distance

clc
clear

% Constants
L  = 0.12;
N  = 39;

delx     = L/(N-1);
xspan    = 0:delx:0.12;
C0       = [0.52 0.99 0.0 750];

% ODE 45 Code
[x,C]=ode45('hw2_5',xspan,C0);

% Plots
% subplot(2,1,1);
plot(x,C(:,1),'b--o',x,C(:,2),'g--+',x,C(:,3),'r--s')
legend('C_{CO}','C_{O2}','C_{CO2}')
xlabel('Axial (x) Direction [m]')
ylabel('Concentrations [mol/m^3]')
title('Molar Concentration vs Distance')

[DIP]

Hi Torsten, I am getting matrix dimension errors.

[DIP]

hi Torsten, there are only 2 ODEs
dC/dx=R
dT/dx=RH
R and H are functions of T and C. R and C are arrays.

Answer 1

[Torsten]

function dydx = hw2_5(x,y)

C(1) = y(1);
C(2) = y(2);
C(3) = y(3);
T    = y(4);

% Constants
A  = 2.2e10;
Ea = 130000;
Ru = 8.3145;
rho=1.3;
cp=1200;
u=1.5;

% Rate Constants and heat of formation
h(1)=-110530;
h(2)=0;
h(3)=-393520;
R(1)     = -A * (exp(-Ea /(Ru*T))) * C(1) * sqrt(C(2)); 
R(2)     = 0.5 * R(1);  
R(3)     = -R(1);
dTdx=-(R(1)*h(1)+R(2)*h(2)+R(3)*h(3))/(cp*rho*u);

dydx = [R(1);R(2);R(3);dTdx]

Best wishes

Torsten.

[DIP]

That worked awesome. Thank You Torsten. Could you recommend any ODE book that has examples solved in matlab ???? Thank you again