Explicit method- Error

My script to find the temperature distrubution by varying the number of nodes and time step is below, I don't know what the error is on line 32:

k = 14.0;
density = 7650;
c = 513;
h_oil = 40;
h_a = 10; 
T_oil = 515;
T_inf = 298;
T_air=298;
T_initial = 298; %(initial temperature of entire chopstick)
L = 0.33; %(total length of chopstick)
L_ex = 0.16; %(total part length of chopstick in air)
r_tip = 0.005;  %(the end of chopstick immersed in the oil)
beta=0.01;
x=1;
r = r_tip + beta*x;
V=pi*(r^2)*L; %Assume the chopstick is cylindrical

delta_t= input('Enter time step');
n_oil=input ('Enter the number of nodes in oil');
n_air=input('Enter the number of nodes in air');
delta_x1=L/n_oil;
delta_x2=L/n_air;
for x= 0:0.1:L
for j=0:delta_t
     for i=1:n_oil
         for h=1:n_air
      T1(1,j)=T_initial;
      T2(1,j)=T_initial;
      T3(1,j)=T_initial;
      T4(1,j)=T_initial;
   %line 31%
  T1(i+n_oil,j+1)=(delta_t*density*c*V)*(T1(i,j)+h_oil*delta_x1*pi*r*k*(T_oil-T1(i,j))+k*pi*r*(4/3)*(T2(i,j)-T1(i,j));
    T2(i+n_oil,j+1)=(dleta_t*density*c*V)*(T2(i,j)+h_oil*2*pi*r*delta_x1*(T_oil-T2(i,j))+(8/3)*k*pi*r*(T1(i,j)-T2(i,j))+2*pi*r*k(T3(h,j)-T2(i,j));
    T3(h+n_air,j+1)=(dleta_t*density*c*V)*(T3(h,j)+h_air*2*pi*r*delta_x2*(T_air-T3(1,j))+2*pi*r*k(T2(i)-T1(i,j)+(8/3)*pi*r*k(T4(h,j)-T3(i,j));
    T4(h+n_air,j+1)=(dleta_t*density*c*V)*(T4(h,j)+h_air*pi*r*delta_x2*(T_air-T4(h,j))+(8/3)*pi*r*k(T3(h,j)-T4(h,j));
      
     end
     end
end
     
if T1=>0.001 & T2=>0.001 & T3=>0.001 & T4=>0.001
    
    printf('Steady State has been reached')
end
      
        
        

end

Answer 1

[Walter Roberson]

for j=0:delta_t

j starts at 0

     for i=1:n_oil
         for h=1:n_air
      T1(1,j)=T_initial;

You try to use j as a subscript, but j is 0 and 0 is not a valid subscript.

You would never have reached line 32.

T2(i+n_oil,j+1)=(dleta_t*density*c*V)*(T2(i,j)+h_oil*2*pi*r*delta_x1*(T_oil-T2(i,j))+(8/3)*k*pi*r*(T1(i,j)-T2(i,j))+2*pi*r*k(T3(h,j)-T2(i,j));
                 ^^^^^^^

You have not defined any variable named dleta_t only delta_t

[Abdulrahman Emad Al-Badawi]

I fixed the variable name for delta_t and the error lies in the temperature equations. Also, how would I used j as a subscript if delta_t is a defind variable?

[Walter Roberson]

  T1(i+n_oil,j+1)=(delta_t*density*c*V)*(T1(i,j)+h_oil*delta_x1*pi*r*k*(T_oil-T1(i,j))+k*pi*r*(4/3)*(T2(i,j)-T1(i,j));
    1           0 1                   0 1  2   1                       2        3   21        2   1 2  3   2   3   21

Bracket mismatch.

[Abdulrahman Emad Al-Badawi]

How do I fix this?

[Walter Roberson]

You look carefully at your expressions and add in a ) where one is missing, or you remove an extra one you do not need.

When you start getting a line long enough that the position of the brackets is not obvious, then it is time to start breaking the line into multiple assignments.

Exception: there are some cases involving complex conjugates transpose or transpose where you should not break a * or / or \ operator. Those are matrix algebra operations and it happens that A/B' can be implemented more efficiently than calculating B' and using A/result.