PDE conversion

To convert to a PDE, we again proceed as we did for the continuity and momentum equations.

First write out the energy equation in index notation, including the expressions for and in the left hand side:

Using the divergence theorem:

The conservation form of the energy equation is therefor:

The usual nonconservative form can be derived as before, and is:

In terms of a Lagrangian derivative,

You should now be able to do questions 5.8