# Conduction PDE

## Homework Statement

How many non-homogeneities can appear in the conduction equation for a quenching, such as a hot machine tool immersed in cold water?

## Homework Equations

$$\partial$$^2T/$$\partial$$x^2 + $$\partial$$^2T/$$\partial$$y^2+ $$\partial$$^2T/$$\partial$$z^2 + q/k = 1/$$\alpha$$ $$\partial$$T/$$\partial$$t

## The Attempt at a Solution

There are two boundary conditions for each coordinate direction (2x3 = 6) any or all of which can be non-homogenous. The initial condition T(t=0) can be non-homogeneous. And the generation term makes the PDE nonhomogeneous. So 8 possible.

Can I simplify the equation for a quenching process (which would change the number of possible non-homogeneities). I know quenching is transient conduction, so we cannot assume steady-state conditions. But can any other terms be eliminated?