I am trying to solve for Q,CA,T,Ts for this CSTR. while solving for these system odes and i can't seem to get answers simply using dsolve or ode45. Plz help me.
digits(4)syms E R T Q(t) CA(t) Ts(t) T(t) tQspec=700000; % Specified heat addition
Q0=700000; % heat rate at time 0
CA0=0.25; % concentration of the reactant in the feed
T0=350; % feed temperature
Ts0=350; %
tauTs=10; % time constant for the temperature sensor
tauTH=10; % time constant for actuator dynamics
F=10; %Feed rate
rho=1; % density of the reaction mixture
k0=1.97.*10^24; % rate constant
E/R==20000; %normalized activation energy
Cp=1; % heat capacity of the reaction mixture
delHrxn=160000; %heat of reaction
Vr=100; % volume
ode1=diff(Q(t),t)==(1./tauTH).*(Qspec-Q(t));ode2=Vr.*(diff(CA(t),t))==(F.*(CA0-CA(t))./rho)-Vr.*k0.*CA(t).*exp((-20000).*1./T(t));ode3=Vr.*rho.*Cp.*(diff(T(t),t))==F.*Cp.*(T0-T(t))-Vr.*delHrxn.*CA(t).*k0.*exp((-20000).*1./T(t))+Q(t);ode4=diff(Ts(t),t)==(1/tauTs).*(T(t)-Ts(t));eqns=[ode1,ode2,ode3,ode4];cond1=Q(0)==700000;cond2=CA(0)==0.25;cond3=T(0)==350;cond4=Ts(0)==350;conds=[cond1 cond2 cond3 cond4];
Using dsolve:
dsolve(eqns,conds)Warning: Unable to find explicit solution. In dsolve (line 201) ans = [ empty sym ]
Using ode45:
[V] = odeToVectorField(eqns,conds);M = matlabFunction(V,'vars', {'t','Y'});ol = ode45(M);Error using odearguments (line 18)When the first argument to ode45 is a function handle, the tspan and y0 arguments must be supplied.Error in ode45 (line 115) odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);
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