Nonhomogeneous BC Heat Conduction

[obscure]

Homework Statement

A very long cylinder has temperature T1 impressed on half of its peripheral surface and
temperature T2 impressed on the other half. Find T(r, θ).

Homework Equations

governing eq 1/r ∂/∂r(r∂/∂r)+∂2T/∂z2

The Attempt at a Solution

I am right at r=0 ;T=T1 at r=r' T=T2
to make BC homog define new term Q=T-T1

I am confused while define BCs

 

[Chestermiller]

If T is a function of r and θ, why do you have the z term in your Laplace equation. You should have the θ term, not the z term.

 

[obscure]

I am always confused with cylindrical coordinates. I know how to solve this but I couldn't formulate the problem as you sad I added z term.

 

[Chestermiller]

I am always confused with cylindrical coordinates. I know how to solve this but I couldn't formulate the problem as you sad I added z term.

So what is the laplace equation when you include the theta dependence and omit the z dependence?