The Heat Equation

PDEs · Axiom Academy

Discover how heat spreads through space and time, governed by one of the most fundamental partial differential equations in mathematics! Imagine a metal rod where one end is heated. Heat doesn't stay put—it spreads from hot regions to cold regions. Let's watch this happen! Let's look at the temperature distribution along the rod and watch how it evolves. The profile starts sharp and gradually smooths out. Rate of Change Depends on Curvature Here's the key insight: how fast the temperature changes at a point depends on the curvature of the temperature profile at that point! The Role of Thermal Diffusivity The constant k (thermal diffusivity) controls how fast heat spreads. Different materials have different values of k ! A Parabolic Partial Differential Equation

This is the written version of the interactive lesson above. See the full PDEs course.