Section 26.6
Non-Homogeneous BCs
What if the ends are held at 100 degrees instead of 0?
1
Introduction
Separation of variables requires homogeneous BCs ().
If , we decompose into steady state + transient.
2
The Method
Steady + Transient
Let .
- satisfies the steady problem () matches the non-zero BCs.
- solves the Heat Equation with zero BCs.
- The initial condition for becomes .
3
Worked Examples
Example 1: Fixed Ends
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Find line connecting (0,10) to (10,30).
.
Then solve for with .
Example 2: Insulated End
(Insulated right end).
.
.
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Steady state is constant .
Example 3: Visual Shift
The sine wave "rides" on top of the steady state line.
4
Practice Quiz
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