| (3.7) |
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This equation is non-homogeneous. Let us make it homogeneous by the change of variable
| (3.10) |
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Click here for Math Link 2, a discussion
of second order linear DE's, homogeneous and non-homogeneous.
Then equation (3.7) becomes
| (3.11) |
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for which the boundary conditions are
| (3.12) |
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The general solution to equation (3.11) is (see Boyce and Di Prima)
| (3.13) |
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Inserting the boundary condition at z = 0, we have
| (3.14) |
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The boundary condition at z = L requires
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Solving for c1, we have
| (3.15) |
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Using equations (3.14), (3.15) and (3.10) we can write (3.13) in the form
| (3.16) |
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Solving for T = T(z), we have the temperature distribution in the rod.
Explore this distribution in the next discover section.