[Bdew8556]

Hi all,

I was wondering if anyone could explain to me in a more intuitive/fundamental way what the diffusion term in the attached picture is saying.

Looks to me like it's a surface integral (if I'm not mistaken that's what that particular integral notation means) of some scalar's gradient multiplied by the circulation symbol?

https://ibb.co/2Z4X78j[IMG]
https://ibb.co/2Z4X78j[/IMG]

[sbaffini]

Originally Posted by Bdew8556

Hi all,

I was wondering if anyone could explain to me in a more intuitive/fundamental way what the diffusion term in the attached picture is saying.

Looks to me like it's a surface integral (if I'm not mistaken that's what that particular integral notation means) of some scalar's gradient multiplied by the circulation symbol?

https://ibb.co/2Z4X78j[IMG]
https://ibb.co/2Z4X78j[/IMG]

It's a surface integral of n (outward face normal) dot variable gradient times a generic diffusion coefficient, gamma, over the surface A. The vector area element in the integral actually is ndA.

[Bdew8556]

Thanks for that.

So the first character to the right hand side (Which is upper case gamma I believe) is meant to be some scalar quantity representing diffusion characteristic, not circulation as I thought it was?

B

[sbaffini]

Originally Posted by Bdew8556

Thanks for that.

So the first character to the right hand side (Which is upper case gamma I believe) is meant to be some scalar quantity representing diffusion characteristic, not circulation as I thought it was?

B

Exactly

Probably your confusion comes from how they wrote the surface integral symbol, with the circle on it (together with Gamma also being usually used in biot-savart like expressions). That symbol (the circle) is more commonly (and correctly) used, indeed, for circulation integrals, but it is not uncommon to find it used also for general higher dimensional integrals over closed curves/surfaces.

But, in the latter case, in my opinion, it is a useless misuse of symbols that, indeed, can generate confusion.