Can you solve this question? It is Euler method

The model of a nonisothermal batch reactor is given by

dC/dt= -exp(-10./(T+273)).* C;
dT/dt=1000*exp(-10./(T+273)).* C-10*(T-20);
T(0)=16 'C 
C(0)=1 kmol/m^3

Find the concentration, C, and temperature, T, as a function of time. Plot the results.

Answer 1

[madhan ravi]

Since it cannot be solved symbolically we convert it to numerical method:

syms T(t) C(t)
con1=T(0)==16 ;
con2=C(0)==1 ;
ode1=diff(C) == -exp(-10./(T+273)).* C;
ode2=diff(T) == 1000*exp(-10./(T+273)).* C-10*(T-20);
vars = [T(t) ; C(t)]
V = odeToVectorField([ode1,ode2])
M = matlabFunction(V,'vars', {'t','Y'})
interval = [0 5];  %time interval
y0 = [16 1];      %initial conditions
ySol = ode45(M,interval,y0);
tValues = linspace(interval(1),interval(2),1000);
yValues = deval(ySol,tValues,1); %number 1 denotes first solution likewise you can mention 2 solution
plot(tValues,yValues,'-o')
figure
yValues = deval(ySol,tValues,2);
plot(tValues,yValues,'-or')

[Busra Tabak]

perfect!!! thank you very much :))

[madhan ravi]

Anytime :) , if it helped you make sure to accept the answer .