# Steady-State Heat Conduction in a Cylinder

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This Demonstration shows graphically an analytical solution for steady-state two-dimensional heat conduction in a cylinder.

Contributed by: Jorge Gamaliel Frade Chávez (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The equation for steady-state heat conduction (or momentum transfer) in a cylinder is

, (1)

with these boundary conditions:

at ,

at ,

at ,

at .

The analytic solution is given by:

,

where is the Bessel function of order 0.

Reference: R. B. Bird, W. E. Stewart, and E. N. Lightfoot, *Transport Phenomena*, 2nd ed., New York: John Wiley and Sons, 2007.

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