Derive the heat equation for a rod assuming constant thermal properties with variable

Chapter 1, Problem 1.2.3

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QUESTION:

Derive the heat equation for a rod assuming constant thermal properties with variable cross-sectional area A(x) assuming no sources by considering 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 with variable cross-sectional area A(x) assuming no sources by considering the total thermal energy between x = a and x = b.

ANSWER:

Step 1 of 8

Since we have constant thermal properties we know that equation for the heat energy density.

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