# Dictionary:Diffusion equation

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1. A simplification of the wave equation for EM-waves in a good conductor:

${\displaystyle \nabla ^{2}{\textbf {E}}\approx j\omega \mu \sigma {\textbf {E}}}$ or ${\displaystyle \nabla ^{2}{\textbf {H}}\approx j\omega \mu \sigma {\textbf {H}}}$.

where ${\displaystyle \omega }$=angular frequency, ${\displaystyle \mu }$=magnetic permeability, and ${\displaystyle \sigma }$=electric conductivity.

2. An equation for the rate of temperature change as a consequence of heat diffusion:

${\displaystyle {\frac {\partial T}{\partial t}}={\frac {k}{\rho c_{p}}}\nabla ^{2}T}$,

where T=temperature, t=time, k=thermal diffusivity, ${\displaystyle \rho }$=density, and cp=specific heat at constant pressure. See Fowler (1990, 222–223).