Trying to code from Polymath

Im supposed to turn this Polymath code into a Matlab code but Im not sure how. Please help. Its supposed to use an ode solver and a graph

Answer 1

[Rishabh Singh]

Hi Sagarika,

Below is the code for MATLAB Version.

% Initial conditions
X0 = 0;
T0 = 450;
Ta0 = 323;

IC = [X0 T0 Ta0];
% W range
Wspan = [0 50];
% Call ode solver
[W, CT] = ode45(@fn, Wspan, IC);
% Extract parameters
 X = CT(:,1);
 T = CT(:,2);
 Ta = CT(:,3);

 % Plot graphs
 figure
 plot(W,X,W,T,W,Ta),grid
 xlabel('W'),ylabel('X.T.Ta')
 legend('X','T','Ta')
 
 figure
 plot(W,T),grid
 xlabel('W'),ylabel('T')
% ODE function
function dCTdW = fn(~,CT)
        % Data
        V0 = 20;
        T0 = 450;
        Uabyrho = 0.08;
        CPc = 5000;
        mc=0.2;
        P0 = 1013250;
        % Extract parameters
         X = CT(1);
         T = CT(2);
         Ta = CT(3);

        %supporting functions
        k = 0.133*exp(31400/8.314*(1/T0 - 1/T));
        CA0 = P0/(8.314*T0);
        CA = CA0*(1-X)*(T0/T)/(1+X);
        rA = -k*CA;
         % odes
         dCTdW = [(k*(1-X)*T0)/(V0*(1+X)*T);
                   (Uabyrho*(Ta-T)+rA*20000)/(V0*CA*40);
                   (Uabyrho*(T-Ta)/(mc*CPc))];
 
end