2D heat transfer equation with matlab

Good day all!

I'm solly for my bad english language. I trying to solve the heat transfer equation with matlab in 2D. I have time dependent equation with linear coefficient lambda, Cp, rho. I turned this code. The problem is that the values of Nnew(i, j) filled just over the border and inside equal to H0(i,j). Please, see my code and edit.

    clc
clear all
global t Tbf Cth Cf L Wtot Ww V tend dt lamda rho Cp T0 a TU TD TR TL H0
t=0;
Tbf=-0.47+273.15;
Cth=2845;
Cf=1899;
L=45000;
Wtot=0.25;
Ww=0.12;
V=Ww/Wtot;
tend=1000;
dt=0.1;
lamda=57;
rho=7900;
Cp=450;
T0=270.15;
Lx=20;
Nx=20;
Ly=20;
Ny=20;
dx=Lx/(Nx-1);
dy=Ly/(Ny-1);
a=lamda/(rho*Cp);
Kx=(dx)^2/(a*dt);
Ky=(dy)^2/(a*dt);
TU=-12+273.15; %temp up
TD=-3.5+273.15; %temp down
TL=-2.5+273.15; %temp left
TR=60+273.15; %temp right
T=zeros(Nx,Ny);
H=zeros(Nx,Ny);
H0=Cf*(T0-Tbf);
Hnew=H0;

for i=1:1:Nx for j=1:1:Ny H(i,j)=H0; end end

for i=1:1:Nx for j=1:1:Ny T(i,j)=T0; end end

    for j=1;
        for i=1;
            Hnew(i,j)=H(i,j)+Kx*(T(i+1,j)-2*T(i,j)+TL)+Ky*(T(i,j+1)-2*T(i,j)+TD);
        end
    end

    for j=Ny;
        for i=1;
            Hnew(i,j)=H(i,j)+Kx*(T(i+1,j)-2*T(i,j)+TL)+Ky*(TU-2*T(i,j)+T(i,j-1));
        end
    end

    for j=1;
        for i=Nx;
            Hnew(i,j)=H(i,j)+Kx*(TR-2*T(i,j)+T(i-1,j))+Ky*(T(i,j+1)-2*T(i,j)+TD);
        end
    end

    for j=Ny;
        for i=Nx;
            Hnew(i,j)=H(i,j)+Kx*(TR-2*T(i,j)+T(i-1,j))+Ky*(TU-2*T(i,j)+T(i,j-1));
        end
    end

    for i=1;
        for j=2:1:Ny-1
            Hnew(i,j)=H(i,j)+Kx*(T(i+1,j)-2*T(i,j)+TL)+Ky*(T(i,j+1)-2*T(i,j)+T(i,j-1));
        end
    end

    for i=Nx;
        for j=2:1:Ny-1
            Hnew(i,j)=H(i,j)+Kx*(TR-2*T(i,j)+T(i-1,j))+Ky*(T(i,j+1)-2*T(i,j)+T(i,j-1));
        end
    end

    for j=1;
        for i=2:1:Nx-1
            Hnew(i,j)=H(i,j)+Kx*(T(i+1,j)-2*T(i,j)+T(i-1,j))+Ky*(T(i,j+1)-2*T(i,j)+TD);
        end
    end

    for j=Ny;
        for i=2:1:Nx-1
            Hnew(i,j)=H(i,j)+Kx*(T(i+1,j)-2*T(i,j)+T(i-1,j))+Ky*(TU-2*T(i,j)+T(i,j-1));
        end
    end

while t<tend t=t+dt; for i=2:1:Nx-1 for j=2:1:Ny-1 Hnew(i,j)=H(i,j)+Kx*(T(i+1,j)-2*T(i,j)+T(i-1,j))+Ky*(T(i,j+1)-2*T(i,j)+T(i,j-1)); end end H=Hnew; end

http://pastebin.com/h1hFnYqa

Best Regards, Alexey Ishkov

Answer 1

[Hadj Merad]

clc

clear all

global t Tbf Cth Cf L Wtot Ww V tend dt lamda rho Cp T0 a TU TD TR TL H0

t=0;

Tbf=-0.47+273.15;

Cth=2845;

Cf=1899;

L=45000;

Wtot=0.25;

Ww=0.12;

V=Ww/Wtot;

tend=1000;

dt=0.1;

lamda=57;

rho=7900;

Cp=450;

T0=270.15;

Lx=20;

Nx=20;

Ly=20;

Ny=20;

dx=Lx/(Nx-1);

dy=Ly/(Ny-1);

a=lamda/(rho*Cp);

Kx=(dx)^2/(a*dt);

Ky=(dy)^2/(a*dt);

TU=-12+273.15; %temp up

TD=-3.5+273.15; %temp down

TL=-2.5+273.15; %temp left

TR=60+273.15; %temp right

T=zeros(Nx,Ny);

H=zeros(Nx,Ny);

H0=Cf*(T0-Tbf);

Hnew=H0;

for j=1;

for i=1;

Hnew(i,j)=H(i,j)+Kx*(T(i+1,j)-2*T(i,j)+TL)+Ky*(T(i,j+1)-2*T(i,j)+TD);

end

end

for j=Ny;

for i=1;

Hnew(i,j)=H(i,j)+Kx*(T(i+1,j)-2*T(i,j)+TL)+Ky*(TU-2*T(i,j)+T(i,j-1));

end

end

for j=1;

for i=Nx;

Hnew(i,j)=H(i,j)+Kx*(TR-2*T(i,j)+T(i-1,j))+Ky*(T(i,j+1)-2*T(i,j)+TD);

end

end

for j=Ny;

for i=Nx;

Hnew(i,j)=H(i,j)+Kx*(TR-2*T(i,j)+T(i-1,j))+Ky*(TU-2*T(i,j)+T(i,j-1));

end

end

for i=1;

for j=2:1:Ny-1

Hnew(i,j)=H(i,j)+Kx*(T(i+1,j)-2*T(i,j)+TL)+Ky*(T(i,j+1)-2*T(i,j)+T(i,j-1));

end

end

for i=Nx;

for j=2:1:Ny-1

Hnew(i,j)=H(i,j)+Kx*(TR-2*T(i,j)+T(i-1,j))+Ky*(T(i,j+1)-2*T(i,j)+T(i,j-1));

end

end

for j=1;

for i=2:1:Nx-1

Hnew(i,j)=H(i,j)+Kx*(T(i+1,j)-2*T(i,j)+T(i-1,j))+Ky*(T(i,j+1)-2*T(i,j)+TD);

end

end

for j=Ny;

for i=2:1:Nx-1

Hnew(i,j)=H(i,j)+Kx*(T(i+1,j)-2*T(i,j)+T(i-1,j))+Ky*(TU-2*T(i,j)+T(i,j-1));

end

end