Index in position 2 exceeds array bounds (must not exceed 1)

I am solving a I D transient heat conduction equation (given below) and I keep getting this error, I am unable to resolve it.

ANY HELP IS APPRECIATED

u_c = zeros(n+1,1);

u_p = zeros(n+1,1);

for i = 1:n+1

u_c(i+1,1) = U_i;

end

for m = 2:T+1 % Time Loop

for i = 2:n % Space Loop

u_c(m,i+1) = u_p(m,i+1) + 0.5*(u_p(m+1,i+1)-(2*u_p(m,i+1))+u_p(m-1,i+1)) ;

end

u_p = u_c;

u_c(1,i) = ((k*u_p(1,i)) + (dx*h*U_f))/(k+(dx*h));

u_c(n,i) = ((k-(dx*h))*u_p(n-1,i))+(U_f*dx)/k;

end

Answer 1

[meghannmarie]

The variables u_c and u_p are vectors or the size of the second dimension is 1. Then you try to set these variables with i in the second dimension which is more than 1. Maybe first 2 lines should be this:

u_c = zeros(n+1,T+2);
u_p = zeros(n+1,T+2);

Hard to tell without the data.

[Aditya Sonwane]

I understand, I have made some changes in the matrix formation of u_c and u_p and am providing ,my overall code please take a look and let me know.

%% MAIN FUNCTION %%

clc

clear all

%thickness of strip = L = 120mm = 0.12m

%u_p = previous temperature

%u_c = current temperature

%total time = T in sec

%timesteps = ts

U_i = 673; %initial medium temperature

U_f = 298; %quenching medium temperature

h = 3000; %in W/m^2-K

rho = 2.7889*10^3; %in kg/m^3

Cp = 0.7639*10^3; %in J/kg-K

k = 0.2473*10^3; %in W/m-K

lamda = k/(rho*Cp); %= (0.2473*10^3)/(2.7889*10^3*0.7639*10^3) = 0.1161*10^-3

T = 200;

L = 0.12;

n = 50;

dx = L/n;

%dt = (0.5/lamda)*dx^2;

ts = 500;

dt = T/ts;

%%%%%%%%%% END OF INPUT %%%%%%%%%%

u_p = zeros(1,n+1);%n+1 is for space and ts is for space

u_c = zeros(1,n+1);

w = solver(i, n, T, dx, h, k, U_f, U_i);

%plot(ts, w')

clc

clear all

%thickness of strip = L = 120mm = 0.12m

%u_p = previous temperature

%u_c = current temperature

%total time = T in sec

%timesteps = ts

U_i = 673; %initial medium temperature

U_f = 298; %quenching medium temperature

h = 3000; %in W/m^2-K

rho = 2.7889*10^3; %in kg/m^3

Cp = 0.7639*10^3; %in J/kg-K

k = 0.2473*10^3; %in W/m-K

lamda = k/(rho*Cp); %= (0.2473*10^3)/(2.7889*10^3*0.7639*10^3) = 0.1161*10^-3

T = 200;

L = 0.12;

n = 50;

dx = L/n;

%dt = (0.5/lamda)*dx^2;

ts = 500;

dt = T/ts;

%%%%%%%%%% END OF INPUT %%%%%%%%%%

u_p = zeros(1,n+1);%n+1 is for space and ts is for space

u_c = zeros(1,n+1);

w = solver(i, n, T, dx, h, k, U_f, U_i);

%plot(ts, w')

%% SOLVER %%

function u_c = solver(i, n, T, dx, h, k, U_f, U_i)

u_c = zeros(1,n+1);

u_p = zeros(1,n+1);

for i = 1:n+1

u_c(i+1,1) = U_i;

end

for ts = 2:T+1 % Time Loop

for i = 2:n % Space Loop

u_c(i+1) = u_p(i+1) + 0.5*(u_p(i+1)-(2*u_p(i+1))+u_p(i+1)) ;

end

u_p = u_c;

u_c(i) = ((k*u_p(i)) + (dx*h*U_f))/(k+(dx*h));

u_c(i) = ((k-(dx*h))*u_p(i))+(U_f*dx)/k;

end

end

%% PLOTTEMP %%

function plottemp(ts, u_c)

plot(ts,u_c)

title('Temperature Distribution in the aluminum strip')

xlabel('length of strip')

ylabel('temp')

end

END