Find the temperature distribution T(x,t) in a long thin bar with given initial temperature
The side walls of the bar are insulated, while heat radiates from the ends into the surrounding medium whose temperature is .
The radiation at the ends is taken to obey Newton's Law.
In particular, find the Fourier coefficients in terms of
Here's what I did so far:
I set the boundary condition to be , initial condition to be .
I am not sure what to do with the "radiation" part of the problem, and thus i don't really know what my partial differential equation should look like...
A wave system that includes damping and dispersion is represented by
where are positive constants.
Solve by separation of variables
For simplicity assume that .
And again here's what I did:
Please help...and in the mean time, I'll try to work something out with my classmates...
Thank you very much.