# Homework Help: Heat flow equation: solid

1. Dec 9, 2007

### plmokn2

1. The problem statement, all variables and given/known data
If temperature T in a solid is constant over any x,y plane show that the temperature and heat flow Q normal to x,y planes both satisfy the equation:
del^2 T=D dT/dt where D is a constant.

How would you expect the differential equations to be modified if it were necessary to take account of the finite speed at which mechanical energy is transmitted in a solid?

2. Relevant equations
div J + C dT/dt =0

3. The attempt at a solution
It's easy to combine the two equations above to get the first part of the solution. However I don't reallty have a clue about the second part. I think the key point is that we're dealing with a solid not a gas like I'm used to, but I don't know what to do next.

Maybe the finite speed puts a delay in the heat flux occuring relative to the gradient existing, but I'm not sure how to make this exact.

Any help appreciated,
Thanks

Last edited: Dec 9, 2007