# This is the code for 5 effect backward feed evaporator with vapor bleeding. But when I run this code I didn't get values for all iteration. Please help to get it.

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JAGATH M NAIR on 23 Jun 2021
Answered: Alan Moses on 1 Jul 2021
T0=120;
lat0=2225.804;
Tf=108;
F=37.8;
xf=0.13;
cpf=4.19-2.35*xf;
V0=5.7;
T=rand(5,1);
x=rand(5,1);
L=rand(5,1);
V=rand(5,1);
V1=rand(5,1);
A=rand(5,1);
cp=rand(5,1);
bpe=rand(5,1);
lat=rand(5,1);
gamma=rand(5,1);
phi=rand(5,1);
A(1)=1800;
A(2)=1400;
A(3)=600;
A(4)=300;
A(5)=300;
T(1)=108.4;
T(2)=96.8;
T(3)=85.2;
T(4)=73.6;
T(5)=62;
L(5)=32.188;
L(4)=26.598;
L(3)=21.008;
L(2)=15.418;
L(1)=9.828;
V1(1)=0.096;
V1(2)=0.19;
V1(3)=0.25;
V1(4)=0.31;
V1(5)=1.46;
ho=9000;
hd=566;
hi=rand(5,1);
U=rand(5,1);
for i=1:5
V(i)=5.6;
x(i)=37.8*0.13/L(i);
cp(i)=4.19-2.35*x(i);
bpe(i)=1.78*x(i)+6.22*(x(i)^2);
lat(i)=2823.2-4.9783*T(i);
gamma(i)=L(i)/4;
end
phi(1)=V0*lat0/A(1);
phi(2)=(V(1)*lat(1))/A(2);
phi(3)=(V(2)*lat(2))/A(3);
phi(4)=(V(3)*lat(3))/A(4);
phi(5)=(V(4)*lat(4))/A(5);
for i=1:5
hi(i)=218+24*phi(i)-37*100*x(i)+1090*gamma(i)+32*(T(i)+bpe(i));
U(i)=((1/hi(i))+(1/ho)+1/hd)^-1;
end
f=rand(15,1);
j=rand(15,15);
z=rand(15,1);
z(1:15,1)=1;
count=0;
for i=1:3
f(1)=(V0*lat0+L(2)*cp(2)*(T(2)+bpe(2))-(L(2)-L(1))*(lat(1)+cp(1)*T(1))-L(1)*cp(1)*(T(1)+bpe(1)))*1000;
f(2)=U(1)*A(1)*(T0-T(1))-V0*lat0*1000;
f(3)=((L(2)-L(1)-V1(1))*lat(1)+L(3)*cp(3)*(T(3)+bpe(3))-(L(3)-L(2))*(lat(2)+cp(2)*T(2))-L(2)*cp(2)*(T(2)+bpe(2)))*1000;
f(4)=U(2)*A(2)*(T(1)-T(2))-(L(2)-L(1)-V1(1))*lat(1)*1000;
f(5)=((L(3)-L(2)-V1(2))*lat(2)+L(4)*cp(4)*(T(4)+bpe(4))-(L(4)-L(3))*(lat(3)+cp(3)*T(3))-L(3)*cp(3)*(T(3)+bpe(3)))*1000;
f(6)=U(3)*A(3)*(T(2)-T(3))-(L(3)-L(2)-V1(2))*lat(2)*1000;
f(7)=((L(4)-L(3)-V1(3))*lat(3)+L(5)*cp(5)*(T(5)+bpe(5))-(L(5)-L(4))*(lat(4)+cp(4)*T(4))-L(4)*cp(4)*(T(4)+bpe(4)))*1000;
f(8)=U(4)*A(4)*(T(3)-T(4))-(L(4)-L(3)-V1(3))*lat(3)*1000;
f(9)=((L(5)-L(4)-V1(4))*lat(4)+F*cpf*Tf-(F-L(5))*(cp(5)*T(5)+lat(5))-L(5)*cp(5)*(T(5)+bpe(5)))*1000;
f(10)=U(5)*A(5)*(T(4)-T(5))-(L(5)-L(4)-V1(4))*lat(4)*1000;
f(11)=(V1(5)*lat(5)-3670.85)*1000;
f(12)=(V1(4)*lat(4)-L(5)*cp(5)*(T(4)-5-(T(5)+bpe(5))))*1000;
f(13)=(V1(3)*lat(3)-L(4)*cp(4)*(T(3)-5-(T(4)+bpe(4))))*1000;
f(14)=(V1(2)*lat(2)-L(3)*cp(3)*(T(2)-5-(T(3)+bpe(3))))*1000;
f(15)=(V1(1)*lat(1)-L(2)*cp(2)*(T(1)-5-(T(2)+bpe(2))))*1000;
j(1,1)=lat0*1000; j(1,2)=(-(L(2)-L(1))*cp(1)-L(1)*cp(1))*1000; j(1,3)=L(2)*cp(2)*1000; j(1,4)=0; j(1,5)=0;
j(1,6)=((lat(1)+cp(1)*T(1))-cp(1)*(T(1)+bpe(1)))*1000; j(1,7)=(cp(2)*(T(2)+bpe(2))-(lat(1)+cp(1)*T(1)))*1000; j(1,8)=0; j(1,9)=0; j(1,10)=0;
j(1,11)=0;j(1,12)=0;j(1,13)=0;j(1,14)=0;j(1,15)=0;
j(2,1)=-lat0*1000; j(2,2)=-U(1)*A(1); j(2,3)=0; j(2,4)=0; j(2,5)=0; j(2,6)=0; j(2,7)=0; j(2,8)=0; j(2,9)=0; j(2,10)=0;j(2,11)=0;j(2,12)=0;j(2,13)=0;
j(2,14)=0;j(2,15)=0;
j(3,1)=0; j(3,2)=0; j(3,3)=(-(L(3)-L(2))*cp(2)-L(2)*cp(2))*1000; j(3,4)=L(3)*cp(3)*1000; j(3,5)=0; j(3,6)=-lat(1)*1000;
j(3,7)=(lat(1)+lat(2)+cp(2)*T(2)-cp(2)*(T(2)+bpe(2)))*1000; j(3,8)=(cp(3)*(T(3)+bpe(3))-(lat(2)+cp(2)*T(2)))*1000; j(3,9)=0; j(3,10)=0;
j(3,11)=-lat(1)*1000;j(3,12:15)=0;
j(4,1)=0; j(4,2)=U(2)*A(2); j(4,3)=-U(2)*A(2); j(4,4)=0; j(4,5)=0; j(4,6)=lat(1)*1000; j(4,7)=-lat(1)*1000; j(4,8)=0; j(4,9)=0; j(4,10)=0;
j(4,11)=lat(1)*1000;j(4,12:15)=0;
j(5,1)=0; j(5,2)=0;j(5,3)=0; j(5,4)=(-(L(4)-L(3))*cp(3)-L(3)*cp(3))*1000; j(5,5)=L(4)*cp(4)*1000; j(5,6)=0;
j(5,7)=-lat(2)*1000; j(5,8)=(lat(2)+lat(3)+cp(3)*T(3)-cp(3)*(T(3)+bpe(3)))*1000; j(5,9)=(cp(4)*(T(4)+bpe(4))-(lat(3)+cp(3)*T(3)))*1000; j(5,10)=0;
j(5,11)=0;j(5,12)=-lat(2)*1000; j(5,13:15)=0;
j(6,1)=0; j(6,2)=0; j(6,3)=U(3)*A(3); j(6,4)=-U(3)*A(3); j(6,5)=0; j(6,6)=0; j(6,7)=lat(2)*1000; j(6,8)=-lat(2)*1000; j(6,9)=0; j(6,10)=0;
j(6,11)=0; j(6,12)=lat(2)*1000;j(6,13:15)=0;
j(7,1)=0; j(7,2)=0; j(7,3)=0; j(7,4)=0; j(7,5)=(-(L(5)-L(4))*cp(4)-L(4)*cp(4))*1000; j(7,6)= 0; j(7,7)=0;
j(7,8)=-lat(3)*1000;j(7,9)=(lat(3)+lat(4)+cp(4)*T(4)-cp(4)*(T(4)+bpe(4)))*1000;j(7,10)=(cp(5)*(T(5)+bpe(5))-(lat(4)+cp(4)*T(4)))*1000;j(7,11)=0;
j(7,12)=0; j(7,13)=-lat(3)*1000; j(7,14)=0; j(7,15)=0;
j(8,1)=0; j(8,2)=0; j(8,3)=0; j(8,4)=U(4)*A(4); j(8,5)=-U(4)*A(4); j(8,6)=0; j(8,7)=0; j(8,8)=lat(3)*1000; j(8,9)=-lat(3)*1000; j(8,10)=0;j(8,11)=0;
j(8,12)=0;j(8,13)=lat(3)*1000;j(8,14)=0;j(8,15)=0;
j(9,1)=0; j(9,2)=0; j(9,3)=0; j(9,4)=0; j(9,5)=0; j(9,6)=0; j(9,7)=0; j(9,8)=0;
j(9,9)=-lat(4)*1000; j(9,10)=(lat(4)+cp(5)*T(5)+lat(5)-cp(5)*(T(5)+bpe(5)))*1000;j(9,11:13)=0; j(9,14)=-lat(4)*1000;j(9,15)=0;
j(10,1)=0; j(10,2)=0; j(10,3)=0; j(10,4)=0; j(10,5)=U(5)*A(5); j(10,6)=0; j(10,7)=0; j(10,8)=0; j(10,9)=lat(4)*1000; j(10,10)=-lat(4)*1000;
j(10,11:13)=0;j(10,14)=lat(4)*1000;j(10,15)=0;
j(11,1:14)=0;j(11,15)=lat(5)*1000;
j(12,1:4)=0; j(12,5)=-L(5)*cp(5)*1000;j(12,6:9)=0; j(12,10)=-cp(5)*(T(4)-5-(T(5)+bpe(5)))*1000;j(12,11:13)=0; j(12,14)=lat(4)*1000;j(12,15)=0;
j(13,1:3)=0; j(13,4)=-L(4)*cp(4)*1000;j(13,5)=L(4)*cp(4)*1000;j(13,6:8)=0; j(13,9)=-cp(4)*(T(3)-5-(T(4)+bpe(4)))*1000;j(13,10)=0;j(13,11:12)=0;
j(13,13)=lat(3)*1000;j(13,14:15)=0;
j(14,1:2)=0; j(14,3)=-L(3)*cp(3)*1000; j(14,4)=L(3)*cp(3)*1000; j(14,5:7)=0; j(14,8)=-cp(3)*(T(2)-5-(T(3)+bpe(3)))*1000; j(14,9:11)=0;j(14,12)=lat(2)*1000;
j(14,13:15)=0;
j(15,1)=0; j(15,2)=-L(2)*cp(2)*1000; j(15,3)=L(2)*cp(2)*1000;j(15,4:6)=0; j(15,7)=-cp(2)*(T(1)-5-(T(2)+bpe(2)))*1000;j(15,8:10)=0;
j(15,11)=lat(1)*1000;j(15,12:15)=0;
z=-inv(j)*f;
V0=0.1*V0+0.5*z(1);
T(1)=T(1)+z(2);
T(2)=T(2)+z(3);
T(3)=T(3)+z(4);
T(4)=T(4)+z(5);
L(1)=L(1)+z(6);
L(2)=L(2)+z(7);
L(3)=L(3)+z(8);
L(4)=L(4)+z(9);
L(5)=L(5)+z(10);
V1(1)=V1(1)+z(11);
V1(2)=V1(2)+z(12);
V1(3)=V1(3)+z(13);
V1(4)=V1(4)+z(14);
V1(5)=V1(5)+z(15);
V(1)=L(2)-L(1);
V(2)=L(3)-L(2);
V(3)=L(4)-L(3);
V(4)=L(5)-L(4);
V(5)=F-L(5);
x(i)=37.8*0.13/L(i);
cp(i)=4.19-2.35*x(i);
bpe(i)=1.78*x(i)+6.22*(x(i)^2);
lat(i)=2823.2-4.9783*T(i);
gamma(i)=L(i)/4;
phi(1)=V0*lat0/A(1);
phi(2)=(V(1)*lat(1))/A(2);
phi(3)=(V(2)*lat(2))/A(3);
phi(4)=(V(3)*lat(3))/A(4);
phi(5)=(V(4)*lat(4))/A(5);
fori=1:5;
hi(i)=218+24*phi(i)-37*100*x(i)+1090*gamma(i)+32*(T(i)+bpe(i));
U(i)=((1/hi(i))+(1/ho)+1/hd)^-1;
end

Alan Moses on 1 Jul 2021
Some variables in your code are not updated in every iteration. For example, the variable gamma depends on L. L is upated every iteration, but gamma is not updated every iteration element-wise.
Refer this video on vectorizing code in MATLAB to avoid looping through an array and doing the operations on the matrix level. You may also refer to the post here that explains vectorization.