Anisotropic heat diffusion in gas streams with shear?

AI Thread Summary
In a heat transfer problem involving a gas stream in a small tube, the flow exhibits a parabolic velocity profile with a mean radial velocity of zero, treated as purely diffusion for heat transfer. The discussion raises a question about whether the radial component of the diffusion rate is influenced by the decreasing gas velocities. It is clarified that in laminar, fully developed, steady flow, the diffusion term is independent of velocity magnitudes, while the dissipation term depends on velocity gradients and acts as a heat source. Understanding these dynamics is crucial for accurately modeling heat transfer in such systems. The conversation emphasizes the importance of distinguishing between diffusion and dissipation in heat transfer analysis.
Mike_In_Plano
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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
 
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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.
 
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