Question

A brick oven of 20 cm thick has the following temperature profile at initial time. (from inside to outside) ?=2?+25 ? [?:?? ??]

Suddenly the inside surface (Left) of the brick oven is being contacted with 1000C and the other side (Right) is being contacted with 300C. The model equation is given as follows:

?.?? (?²?/??²)=??/??

M Make the required corrections and modifications in the following function to Find the temperature profile of the brick oven (for t=20 min, Δx=4 cm and Δt=5)

Note : Give your calculated temperature profile, your command function lines and your modified codes

function CrankNicholson(Tinitial, t, delx, delt, walllength, a)

stability = a*delt/delx^2;

nt=t/delt+1;

x = 0:delx:walllength;

nx = length(x);

Td(1:nt,1)=Tinitial;

Td(1,1:nx)=2*x;

for j=1:nt-1

for k=1:nx-1

   if k == 1

     M(k, k) = -1-stability;

     M(k, k+1) = stability/2;

    elseif k > 1 && k <= nx-2

      M(k, k-1) =stability/2;

      M(k, k) = -1-stability;

      M(k, k+1) = stability/2;

    else

      M(k, k-1) = 2*stability/2;

      M(k, k) = -1-stability;

   end

    if k+2 <= nx

      S(k) =-stability/2*Td(j, k)+(stability-1)* Td(j, k+1)-stability/2* Td(j, k+2);  

    else

      S(k) =-stability*Td(j, k)+(stability-1)* Td(j, k+1);

   end

end

aa = inv(M) * S';

end

disp(aa);

end