Equations · equation
Fourier's Law of Heat Conduction
Heat Transfer · 1822
- Equation
- q = −k·∇T
- Field
- Heat Transfer
- Named After
- Joseph Fourier
- Year
- 1822
Symbols
q heat flux, energy crossing unit area per second · k thermal conductivity of the material · ∇T the temperature gradient · the minus sign: heat runs downhill
Significance
Heat flows from hot to cold at a rate set by the steepness of the temperature slope and the material's conductivity — copper's k is 400, wool's 0.04. The constitutive law of conduction; combined with energy conservation it yields the heat equation, and it's the template Fick copied for diffusion and Ohm for current.
Referenced by
element
equation
skill
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