# 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.