00:01
So this is a finite volume method for diffusion problems.
00:05
And let's start.
00:08
So here is our governing equation.
00:14
Kappa, delta t over delta x, which is our thermal gradient, plus heat equals to zero.
00:24
So here is how to solve this.
00:32
So our boundary conditions are at the end of the two places.
00:36
We got a hundred degrees celsius and then 200 degrees celsius at the other end and the length of the domain is l which is two centimeters okay so the first step is to integrate you know the equation well first of all case constant and because of that, our equation becomes t squared where x squared plus q is equal to zero.
01:21
Excuse me.
01:22
That's because k is constant.
01:26
Now, by integrating once, we get the following result.
01:33
It goes to minus qx plus c1.
01:37
We get a constant of integration, c1.
01:41
We integrate again and we get an equation for our temperature, which is q over 2k, x squared plus c1x, plus our constant integration for the second integration.
01:59
Now, we use our battery conditions, so at zero, this is equal to a, it's equal to 100...