The heat equation or diffusion equation does contain a constant $\alpha$.

$$\frac{\partial u}{\partial t} - \alpha \nabla^2 u=0$$

How is it called?

I'm interested in a general name which can be used for different circumstances apart from heat transfer and diffusion of fluids. For example in electromagnetism this constant is related to the skindepth $\delta$ via:

$$\alpha = \frac{\sqrt{2j}}{\delta} = \sqrt{j\omega \kappa \mu}$$

If there is no name, what would you suggest?

  • $\begingroup$ For an electromagnetic wave, this is the propagation constan. $\endgroup$ – Martin Petrei Aug 1 '14 at 14:36
  • $\begingroup$ @Tinchito thanks! that was already was I was looking for! $\endgroup$ – thewaywewalk Aug 1 '14 at 14:38
  • $\begingroup$ sure? then I post it as an answer... :) $\endgroup$ – Martin Petrei Aug 1 '14 at 14:42
  • $\begingroup$ @Tinchito: Well I think it is alright, what I'm doing has nothing really to do with waves, rather effective reluctances in different materials, thats why I never stumbled of this name the whole time. But I think it is appropriate for this case also. $\endgroup$ – thewaywewalk Aug 1 '14 at 14:45
  • $\begingroup$ I understand. When you find the solution of the Helmholtz equation for the electric field (wave equation), the meaning of this constant is evident, and hence its name. $\endgroup$ – Martin Petrei Aug 1 '14 at 14:54

For an electromagnetic wave, this is the propagation constant. It can be expressed as the sum of two terms: the attenuation constant and the phase constant.


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