(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Gas with thermal conductivity κ fills the space between two coaxial cylinders

(inner cylinder radius a, outer cylinder inner radius b). A current I is passed through

the inner cylinder, which has resistivity ρ. Derive an expression for the equilibrium temperature of the inner cylinder Ta when the outer cylinder is held at a constant temperature Tb.

2. Relevant equations

3. The attempt at a solution

so for the equilibrium case we have ##\frac{\partial T}{\partial t} =0##

Solving the heat diffusion equation in cylindrical coordinates with a heat source H we get

##T=-\frac{Hr^2}{4\kappa}+c_1 \ln{r} +c_2## where ##H=\frac{I^2\rho}{A^2}## where A is the C.S.A of the inner cylinder.

I can see that we have one boundary condition, namely ##T=T_b## at r=b but i cannot see the second boundary condition.

Many thanks

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# Homework Help: Thermal diffusion equation

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