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

Practice - One-Dimensional Diffusion (Heat) Equation

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the general form of the one-dimensional diffusion equation?

💡 Hint: Recall how heat diffusion is expressed mathematically.

Question 2 Easy

What does the symbol 'α' represent in the diffusion equation?

💡 Hint: Think about what dictates how fast heat spreads.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the one-dimensional diffusion equation?

∂u/∂t = α²∂²u/∂x²
∂u/∂x = β∂²u/∂t²
∂u/∂t = 0

💡 Hint: Recall the relationship between temperature, time, and space.

Question 2

True or False: Neumann boundary conditions specify the value of the function at the boundaries.

True
False

💡 Hint: Consider what Neumann actually indicates for boundary conditions.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Consider a metal rod of length L with fixed temperatures at both ends. Derive the series solution using separation of variables.

💡 Hint: Begin with simplifications based on known boundary values.

Challenge 2 Hard

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.

💡 Hint: Consider how to express temperature changes over the defined domain.

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