The following cylinder has a temperature inside Ti and temperature outside To. Using the general equation for heat conduction in a cylinder, write the temperature distribution equation as a function of the radius T(r). What is the temperature midway at r=a? (Take the heat conductivity = k, and length of cylinder is L).
Assume no convection and constant temperature across the length of the cylinder.
Fourier's Law in cylindrical coordinates: q''= -k (dT/dr)
The Attempt at a Solution
So integrating Fourier's equation with these boundary points I get:
To-Ti= -roq'' ln(ro/ri)
I think this gives the temperature difference though, not the distribution and I also have the q'' (flux term) still in the equation as an unknown. How would I find the temperature distribution and T(r=a)?
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