Conduction PDE

  • #1

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


[tex]\partial[/tex]^2T/[tex]\partial[/tex]x^2 + [tex]\partial[/tex]^2T/[tex]\partial[/tex]y^2+ [tex]\partial[/tex]^2T/[tex]\partial[/tex]z^2 + q/k = 1/[tex]\alpha[/tex] [tex]\partial[/tex]T/[tex]\partial[/tex]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?
 

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