Trouble with ODE45 for an array of values

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DIP
DIP on 27 Feb 2017
Edited: DIP on 8 Apr 2017
Hi,
I have an equation udC/dx=R, where C and R are arrays. I've written a code but its giving a linear plot. Need help
% Solve ODE for Multi-Species Isothermally
% Constants
u = 1.5;
A = 2.2e10;
Ea = 130;
Ru = 8.3145;
T = 750;
L = 0.12;
N = 39;
% Initial Conditions
Cco(1) = 0.52;
Co2(1) = 0.99;
Ch2o(1) = 0;
delx = L/(N-1);
x = 0:delx:0.12;
C0 = [Cco(1) Co2(1) Ch2o(1)];
C = zeros(3,1);
Rco = -A * (exp(-Ea / (Ru*T))) * Cco * sqrt(Co2);
Ro2 = 0.5 * Rco;
Rh2o = -Rco;
dC = [Rco Ro2 Rh2o] / u;
R = [Rco Ro2 Rh2o];
R = zeros(3,1);
% ODE45 solver
[x,C] = ode45(@(x,C) R/u, x, C0);
plot(x,C,'-+')
title('Molar Concentration vs. Distance');
legend('CO','O2','CO2');
xlabel('Axial(x) Direction [m]');
ylabel('Concentrations [mol/m3]');
Thank you.

Accepted Answer

DIP
DIP on 6 Mar 2017
% Solution 4: Chemical Species Concentration as a Function of Axial Distance
clc
clear
% Constants
L = 0.12;
N = 39;
T(1:N) = 750;
delx = L/(N-1);
xspan = 0:delx:0.12;
C0 = [0.52 0.99 0.0];
% ODE 45 Code
[x,C]=ode45('hw2_4',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')
Function File:
function dcdx=hw2_4(x,C)
% Constants
u = 1.5;
A = 2.2e10;
Ea = 130000;
Ru = 8.3145;
T = 750;
% Rate Constants
R(1) = -A * (exp(-Ea / (Ru*T))) * C(1) * sqrt(C(2));
R(2) = 0.5 * R(1);
R(3) = -R(1);
dcdx = [R(1);R(2);R(3)]/u;

More Answers (1)

Walter Roberson
Walter Roberson on 28 Feb 2017
You have
[x,C] = ode45(@(x,C) R/u, x, C0);
and R and u are constants, 3 x 1 and 1 x 1. The integral of a constant is the straight line a*x + b so all of your lines are linear, not curved.
Note that you have
R = [Rco Ro2 Rh2o];
R = zeros(3,1);
which constructs R and then overwrites it with 0. You might have wanted
R = [Rco Ro2 Rh2o] .';
which would give you lines with different slopes, not curves.
You cannot get a curve unless your function depends upon the time or the input derivatives.
  11 Comments
DIP
DIP on 28 Feb 2017
are you able to run the code and get any answers with the modifications ?
Torsten
Torsten on 1 Mar 2017
Use a stiff solver, e.g. ODE15S, instead of ODE45.
Best wishes
Torsten.

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