# Heat Transfer along a Rod

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This Demonstration shows the solution to the heat equation for a one-dimensional rod. The rod is initially submerged in a bath at 100 degrees and is perfectly insulated except at the ends, which are then held at 0 degrees. This is a a Sturm–Liouville boundary value problem for the one-dimensional heat equation

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Contributed by: Stephen Wilkerson (April 2011)

(Department of Mathematical Sciences at the United States Military Academy, West Point, NY)

Open content licensed under CC BY-NC-SA

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References:

[1] R. Haberman, *Applied Partial Differential Equations with Fourier Series and Boundary Value Problems,* 4th ed., Saddle River, NJ: Prentice Hall, 2003.

[2] J. R. Brannan and W. E. Boyce, *Differential Equations with Boundary Value Problems: An Introduction to Modern Methods and Applications*, New York: John Wiley and Sons, 2010.

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