Nonhomogeneous BC Heat Conduction

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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
 

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Answers and Replies

  • #2
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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.
 
  • #3
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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.
 
  • #4
21,159
4,673
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?
 

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