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## Homework Statement

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.

[PLAIN]http://img40.imageshack.us/img40/7344/radiusproblem.jpg [Broken]

## Homework Equations

Fourier's Law in cylindrical coordinates: q''= -k (dT/dr)

## The Attempt at a Solution

Boundary conditions:

r=r

_{i}, T=T

_{i}

r=r

_{o}, T=T

_{o}

So integrating Fourier's equation with these boundary points I get:

T

_{o}-T

_{i}= -r

_{o}q'' ln(r

_{o}/r

_{i})

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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