# Need help solving this PDE

1. Mar 21, 2013

### mehsus

I have a circular heat source of inner radius r1 and r2=r1+Δr on top of a pcb board. This heat source is transferring heat along the radius and the length of the beaker which is say L. I have to find temperature distribution along the length of the beaker so T(r.z). The beaker is filled with water till the bottom of the pcb.

I considered a differential element of radius Δr and thickness Δz at a distance z from the bottom of the pcb. Now once I write the energy balance equation on the basis of steady state as:

Qz-Qz+Δz+Qr-Qr+Δr=0

There is no convection taking place.

I come to the PDE:

d^2T/dz^2+1/r(dt/dr)+d^2T/dr^2=0

I am stuck here in solving this PDE...plz help

2. Mar 21, 2013

### fzero

Have you tried separation of variables? I.e., try to find solutions of the form $T(r,z) = R(r) Z(z)$.

3. Mar 22, 2013

### HallsofIvy

Staff Emeritus
It looks to me that after you separate variables, you will get Bessel's equation in r.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook