Fourier's Law of Heat Conduction

What is Fourier's Law of Heat Conduction?

q = −k dT/dx — conductive heat flux is proportional to the negative temperature gradient. It has the exact same mathematical shape as Ohm's law and Fick's law, and it's the starting point for essentially every steady-state conduction problem in engineering.

The five clues

Engineerdle #66 described Fourier's Law of Heat Conduction with five clues, revealed one at a time from hardest to most direct. Each clue points at a different property of the concept.

1. 01Same mathematical shape as Fick's and Ohm's laws.
2. 02Flux is proportional to a gradient, with a minus sign.
3. 03The constant of proportionality is a material property in W/mK.
4. 04Heat flows down the gradient, never up it unaided.
5. 05The gradient here is temperature.