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n=5+1;m=100;
dr=0.01; dz=0.0585;

Ramda=0.45; G=2500;Cp=2.18;
dH=140e3;rh0=1440;a=0.05;
u0c0=0.069/(pi*a^2);
Cp1=1.0e3; F=130/3600;

a1=Ramda/(G*Cp*1000)*3600;
b1=dH*rh0/G/Cp;
a2=0.000427; b2=rh0/u0c0;
C1=2*pi*a*Ramda/(F*Cp1); C2=4*dr/(dz*C1);
M=a1*dz/dr^2; M1=a2*dz/dr^2;
C3=M*C2/2*(1+0.5/(n-1))-(1+M);
C4=M*C2/2*(1+0.5/(n-1))-(1-M);

T(1:n-1)=873; T(n)=893; x(1:n)=0; X0=[T;x];
Tresult(1,=X0(1,; xresult(1,=X0(2,;
FGrc(T,x);
for j=2:m
X=fsolve(@TxEquations,X0);
T=X(1,; x=X(2,; Tresult(j,=T, xresult(j,=x
xa(j,=sum(2*xresult(j,2)+4*xresult(j,3)+6*xresult(i,4)+8*xresult(j,5)+5*xresult(j,6))/25
if xa(j)>0.45, break, end
FGrc(T,x)
end
z=dz*[0:j-1];r=dr*[0:n-1];
z=z',L=spline(xa,z,0.45)

plot(z,xa), xlabel('z(m)'), ylabel('x_a_v')
figure, surf(r,z,Tresult), xlabel('r(m)'), ylabel('z(m)'), zlabel('T(K)')
figure, surf(r,z,xresutt), xlabel('r(m)'), ylabel('z(m)'), zlabel('x')

function f=ReactionRate(T,x)
k=0.027*exp(0.021*(T-773));
f=15100*exp(-11000/T)*((1-x)/(11+x)-1.2*x^2/k/(11+x)^2);
function f=FGrc(T,x);
global F G rc n dz M M1 b1 b2 C2 C3 C4
rc=ReactionRate(T,x);
F(1)=((1-2*M)*T(1)+2*M*T(2)-b1*dz/2*rc(1))/(1+2*M);
G(1)=(1-2*M1)*x(1)+2*M1*x(2)+b2*dz/2*rc(1))/(1+2*M1);
i=(2:5);
var1=1-0.5/(i-1); var2=1+0.5/(i-1);
F(i)=(M/2*(varl*T(i-1)+var2*T(i+1))+(1-M)*T(i)-b1*dz/2*rc(i))/(M+1);
G(i)=(M1/2*(var1*x(i-1)+var2*x(i+1))+(1-M1)*x(i)+b2*dz/2*rc(i))/(M1+1)
F(n)=(-M*T(n-1)+C4*T(n)+b1*dz/2*rc(n)/C3;
G(n)=(M1*x(n-1)+(1-M1)*x(n)+b2*dz/2*rc(n))/(1+M1);

function f=TxEquations(X)
global n F G rc dz M M1 b1 b2 C2 C3
T=X(l,, x=X(2,
fT(1)=F(1)+(2*M*T(2)-b1/2*dz*rc(1))/(l+2*M)-T(1);
fx(1)=G(1)+(2*M1*x(2)+b2/2*dz*rc(1))/(1+2*M1)-x(1);
for i=2:n-1
var1(i)=(1-0.5/(i-1)); var2(i)=(1+0.5/(i-1));
fT(i)=F(i)+(M/2*(var1(i)*T(i-1)+var2(i)*T(i+1))-b1/2*dz*rc(i))/(M+1)-T(i);
fx(i)=G(i)+(M1/2*(var1(i)*x(i-1)+var2(i)*x(i+1))+b2/2*dz*rc(i))/(M1+1)-x(i);% (21)
end
fT(n)=F(n)+(-M*T(n-1)+b1/2*dz*rc(n))/C3-T(n);
fx(n)=G(n)+(M1*x(n-1)+b2/2*dz*rc(n))/(1+M1)-x(n);
f=[fT;fx];


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