Heat flux as boundary condition in 2D transient heat conduction equation

Hello,

I have a question regarding the 2D transient heat conduction equation:

clc
clear all
close all
length_x=0.2;
length_y=0.2;
nx=4;% Number of Grid Points in x
ny=4;% Number of Grid Points in y
nt=1000; 
x=linspace(0,length_x,nx);% Method to Create The Grid Points in x
y=linspace(0,length_y,ny);% Method to Create The Grid Points in y

dx=x(2)-x(1);
dy=y(2)-y(1);

error=9e9;
tolerance=1e-4;
dt=1e-3; 
omega=1.1;

T_L=150; %Left side of domain 
T_R=150; %Right side of domain 
T_T=300; %Top side of domain 
T_B=77; %Botom side of domain 

T=300*ones(nx,ny); %Defining the Inital Condition
T(2:ny-1,1)=T_L;
T(2:ny-1,nx)=T_R;
T(1,2:nx-1)=T_T;
T(ny,2:ny-1)=T_B;

% assign the T value at corner
T(1,1)=(T_L+T_T)/2;
T(nx,ny)=(T_R+T_B)/2;
T(1,ny)=(T_T+T_R)/2;
T(nx,1)=(T_L+T_B)/2;

% keeping the Back Up of T 
T_ini=T;
T_old=T;
T_end=T;

% Calculation of 2D Transient Heat Conduction Equation by Explicit
k1=1.1*(dt/(dx^2));
k2=1.1*(dt/(dy^2));
is=1;

fc=1;
if fc==1
    gs=1;
for k=1:nt
    error=9e9;
    
    while(error>tolerance)
        
        for i=2:nx-1
            
            for j=2:ny-1
                t1=T_old(i,j);
                t2=k1*(T_old(i+1,j)-2*T_old(i,j)+(T_old(i-1,j)));
                t3=k2*(T_old(i,j+1)-2*T_old(i,j)+(T_old(i,j-1)));
                T(i,j)=t1+t2+t3;
            end
        end
        error=max(max(abs(T_old-T)));
        T_old=T;
        gs=gs+1;
           
    end
end
end 

figure(1)

contourf(x,y,T)
clabel(contourf(x,y,T))
colorbar
colormap(jet)
set(gca,'ydir','reverse')

xlabel('X -Axis')
ylabel('Y -Axis')

Is it possible to change the code to insert a variable temperatur boundary conditions (T=f(x,y,t), like Temperature graph/function instead a constant temperature at the boundarys?

and can the code altered to use a time dependent heat flux at the bottom instead a Temperature boundary condtion like:

-lambda*dT/dx = 10

Maybe someone has a clue

Best regards

Steffen

[Torsten]

Why don't you use the pde toolbox if you have no experience with discretization and coding ? No license ?