# Aerospace Anisotropic heat diffusion in gas streams with shear?

1. Nov 17, 2012

### Mike_In_Plano

Hi all,

I'm working on a heat transfer problem with a gas stream in a tiny tube. At my dimensions and flow rates, the flow still has a parabolic velocity profile. The mean radial velocity of the gas is zero, and I've treated the radial aspect of the heat transfer as strictly diffusion.

My question is this:

Given that the gas velocity is decreasing, from inside to out, is the radial component of the diffusion rate now dependent upon the changing velocities the heat must transition through? If so, does anyone have some equations or online references to aid me in understanding this?

Thanks and happy holidays :)

Mike

2. Nov 19, 2012

### RandomGuy88

Is the flow laminar or turbulent? I ask because you say the "mean" radial velocity is zero.

If you look at the energy equation for a fluid, in a laminar fully developed and steady flow you should only have radial diffusion and a dissipation term. The diffusion term is independent of the velocity but the dissipation term depends on the square of the velocity gradients. The friction converts the kinetic energy of the fluid into heat. So dissipation is a heat source. The diffusion does not depend on the actual velocity magnitudes but rather the gradients.