There were some errors in your code:
- For ode45 you give numerical functions, not symbolic ones
- There were some variables that were used in the function but initialized after the loop
- If you have time dependent variables, you ideally should define them inside the function
- Your variable order in the function was inverted
- You didn't declared v0 anywhere
I choosed a random value for v0 and fix the other issues of your code, you just have to make sure that the considerations you made for your function and variables are right to fully trust the results.
R=8.314/32;
T0=2930;
a=(12)/((2.027*10^6)^0.45);
rhoP=1920;
Astar=pi*0.25^2;
k=1.35;
n=0.45;
P0=101325;
P = P0;
%syms P(t)
%at beginning of the integration set initial values for the persistent variables
rp=0.35; %initial port radius
t1=0; %initial time step
rhoO=P/(R*T0); %gas density
rp=min(rp+((a*P^n)*10^-3)*(t1-t1),0.7);
Ab=2*pi*rp*8;%burn area
v0 = 0.1;
dP=@(t,P)Fun(t,P,R,T0,rp,a,n,t1,Ab,rhoP,Astar,k,v0);%@(t,P)(Ab.*a.*P.^n.*(rhoP-rhoO)-P.*Astar.*sqrt(k/(R.*T0)).*(2/(k+1)).^((k+1)/(2.*(k-1)))).*R.*T0./v0;
[t,P]=ode45(dP, [0,0.1], P);
y = P;
figure(2)
plot(t,y)
xlabel("Time (s)")
ylabel("Chamber Pressure (Pa)")
title("Chamber Pressure vs Time (Start-Up)")
function dP = Fun(t,P,R,T0,rp,a,n,t1,Ab,rhoP,Astar,k,v0)
rhoO=P/(R*T0); %gas density
rp=min(rp+((a*P^n)*10^-3)*(t-t1),0.7);
Ab=2*pi*rp*8;%burn area
dP = (Ab.*a.*P.^n.*(rhoP-rhoO)-P.*Astar.*sqrt(k/(R.*T0)).*(2/(k+1)).^((k+1)/(2.*(k-1)))).*R.*T0./v0;
end
