Heat transfer problem using FDM

I'm attempting to find the heat distribution and time required to reach steady state for a 1d rod using a finite difference method (explicit), which has fixed temperature on both its left and right hand sides

I'm having problems trying to write a loop to calculate (and replace) the elements of my matrix using my function which is New temperature= Current temperature at point +alpha*dt((T(j+1)-2*T(j)+T(j-1))/dx^2)

What I have so far:

TR=25 %Temperature (right side)

TL=100 %temperature (left side)

TM=20 %temperature across rod

k=54; %thermal conductivity of slab

rho=7800; %density

c=490; %specific heat

alpha=k/(rho*c);

W=0.05 %width of rod

dx=0.01 %space between grid points

dt=3 %change in time

nx=6;

ny=1

T(1:ny,1:nx)=TM; %make all values of grid =TM can also use TM*ones(26,51)

T(:,nx)=TR; % change values of last column to TR

T(:,1)=TL; %change values of first column to TL

tstart=0 %start time

I also want to calculate the time required for my rod to achieve the steady state condition

How could I go about doing this?

Answer 1

[Torsten]

Use two arrays for T (e.g. Told and T), one for the old and one for the new temperatures.

Best wishes

Torsten.