Find Optimum Temperature where Concentration of product vs Time is high.

I know how to solve ODE with const Temperature, but with temperature range I find it difficult to solve.

    function dYdt = odereal2(t,Yf);

    CA = Yf(1);
    CB = Yf(2);

    T = 335.32; %just assumed the constant temperature.

    k1 = 4000*exp(-2500/T); 
    k2 = 620000*exp(-5000/T);  

    dCAdt = -k1*CA^2;
    dCBdt = k1*CA^2-k2*CB; 

    dYdt = [dCAdt; dCBdt;];

This is my function that includes Derivative equation.

    tspan = [0 3];

    C0 = [1.; 0];

    [t,C]=ode45(@odereal2,tspan,C0);

      for i=1:size(C,2)

      plot(t,C,'pr') %from that plot we can infer the maximum yield of product B 

      axis([0 3 0 1])

      title(' Plot of concentration(C) profiles at optimal residence time' );

      xlabel(' Time (hr)');

      ylabel(' Concentration (C)');  

      pause

      end

And here is my ODE solver code. I just want to find the optimum temperature when concentration of product B reaches the maximum.

Kindly help me in this problem. Thanks in advance

Answer 1

[Alan Stevens]

Does this help:

    tspan = 0:0.1:3;
    C0 = [1.; 0];
    T = 330:5:360;
    
    for i = 1:numel(T)
        [t,C]=ode45(@odereal2,tspan,C0,[],T(i));
        CA(:,i) = C(:,1);
        CB(:,i) = C(:,2);
        
    end

     plot(t,CA,'pr-',t,CB,'bo-') %from that plot we can infer the maximum yield of product B 
     axis([0 3 0 1])
     title(' Plot of concentration(C) profiles at optimal residence time' );
     xlabel(' Time (hr)');
     ylabel(' Concentration (C)');  


function dYdt = odereal2(~,Yf,T)

    CA = Yf(1);
    CB = Yf(2);

    % T = 335.32; %just assumed the constant temperature.

    k1 = 4000*exp(-2500/T); 
    k2 = 620000*exp(-5000/T);  

    dCAdt = -k1*CA^2;
    dCBdt = k1*CA^2-k2*CB; 

    dYdt = [dCAdt; dCBdt;];
end

[Niyaz Khan]

Thank you, so much. That did work.