Practice One-dimensional Diffusion (heat) Equation (11) - Partial Differential Equations

Practice: One-Dimensional Diffusion (Heat) Equation

Lesson 11Partial Differential Equations

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8 questions

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2 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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Quiz
2 questions · about 1 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is the general form of the one-dimensional diffusion equation?
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Recall how heat diffusion is expressed mathematically.
Question 2.
What does the symbol 'α' represent in the diffusion equation?
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Think about what dictates how fast heat spreads.
3Question 3.
What is the one-dimensional diffusion equation?
- ∂u/∂t = α²∂²u/∂x²
- ∂u/∂x = β∂²u/∂t²
- ∂u/∂t = 0
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Recall the relationship between temperature, time, and space.
4Question 4.
True or False: Neumann boundary conditions specify the value of the function at the boundaries.
- True
- False
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Consider what Neumann actually indicates for boundary conditions.
Question 5.
Consider a metal rod of length L with fixed temperatures at both ends. Derive the series solution using separation of variables.
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Begin with simplifications based on known boundary values.
Question 6.
A rod with one end maintained at 100°C and the other at 0°C is cooled down. Formulate the boundary-value problem using suitable boundary conditions.
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Consider how to express temperature changes over the defined domain.

4 more questions in this section. Enroll free to practise them all.