Water vs. Wood, grudge match

Ever wonder about the mathematics of drying wood? Look no further!

Lost Art Press

Chris gives you geometry homework; I give you partial differential equations:


This is the diffusion equation. It’s often called the heat equation, because it also models the diffusion of heat through a solid. And you’ll sometimes see it as Fick’s Second Law, after Adolf Fick, who first formulated it around 150 years ago. (The Wikipedia article on Fick’s Laws is a good introduction to diffusion from a physical, rather than abstract math, point of view.)

In our case, the quantity of interest, symbolized by u in the equation, is the moisture content of the wood. While it looks formidable, the interpretation of the diffusion equation is actually fairly simple:


Gradient: You have more “stuff” in one place than another, and stuff tends to move from high concentration to low concentration; the gradient measures the steepness of the slope.

Diffusivity: Also known as the diffusion…

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