Derive the heat equation for a rod assuming constant thermal properties and no sources

Chapter 1, Problem 1.2.2

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QUESTION:

Derive the heat equation for a rod assuming constant thermal properties and no sources. (a) Consider the total thermal energy between x and x + x. (b) Consider the total thermal energy between x = a and x = b.

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QUESTION:

Derive the heat equation for a rod assuming constant thermal properties and no sources. (a) Consider the total thermal energy between x and x + x. (b) Consider the total thermal energy between x = a and x = b.

ANSWER:

Step 1 of 9

Since we are told that there are constant thermal properties, we know the equation for the heat energy density.

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