germblaster
Dec11-08, 12:49 AM
1. The problem statement, all variables and given/known data
How many non-homogeneities can appear in the conduction equation for a quenching, such as a hot machine tool immersed in cold water?
2. Relevant equations
\partial^2T/\partialx^2 + \partial^2T/\partialy^2+ \partial^2T/\partialz^2 + q/k = 1/\alpha \partialT/\partialt
3. 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?
How many non-homogeneities can appear in the conduction equation for a quenching, such as a hot machine tool immersed in cold water?
2. Relevant equations
\partial^2T/\partialx^2 + \partial^2T/\partialy^2+ \partial^2T/\partialz^2 + q/k = 1/\alpha \partialT/\partialt
3. 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?