Differential Equations › Section I · Partial differential equations › Topic I.6
Heat equation with nonzero boundaries
Real bars rarely have both ends in ice water: one end may sit on a hot plate while the other touches room-temperature air. A simple shift by the bar's eventual steady temperature turns such problems back into the zero-boundary problems already solved.
In this topic
- Why the ends cause trouble
- The equilibrium temperature
- Worked example: a steel rod in steady state
- Shifting by the equilibrium
- The full solution
- Worked example: a bar heated at both ends
- How fast equilibrium arrives
- Other boundary combinations
- Common mistakes to avoid
- Key takeaways
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