# Adding buoyancy to 3D integration of diffusion equation

1. Jan 17, 2006

### dangerousdave

I have managed to create a simple CFD model to integrate in 3D the heat/diffusion equation, namely dT/dt = k d2T/dx2.

This works fine, but I would now like to add the effect of 'less dense rising' assuming the gas is operating in air -- I think I'm right in saying that's called buoyancy (I'm not a physicist).

SO my question is, can someone post a (hopefully) simple extension to this nice little equation that includes the buoyancy effect. I would assume it involves divT dot g, (where g is a vector of gravity), but thats as far as I can fathom.

Any help much appreciated,
Dave.