Challenges in Solving Poisson's Equation in Polar Coordinates with a Heat Source

[sachi]

I have to solve 1/r*d/dr(r*dT/dr) + 1/(r^2)*(d^2)T/(d theta)^2 = q(r) where all derivatives are partials. N.b this is just poisson's equation in plane polar co-ordinates. A heat source of form q(r) = K/(r^2) where K is a constant i applied to a olis between coaxial cylinders of radius a and b.

I have tried using the separation of variables method, but I can't get the r terms and the theta terms to separate. Thanks very much.

 

[quantumdude]

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