The Unsteady Problems

We shall now discuss how to handle a transient, heat conduction problem.

The governing equation for the problem is:

(23.1)

The residue equation can be set up as

Expanding temperature as within each element and proceeding as before, we get:

(23.2)

where the heat-flux integral for a known temperature boundary has been ignored, since it does not make any difference to our nodal equations.