Anisotropic heat diffusion in gas streams with shear?

In summary, the conversation discusses a heat transfer problem involving a gas stream in a tiny tube. The flow has a parabolic velocity profile and the mean radial velocity of the gas is zero. The question is whether the changing velocities affect the radial component of the diffusion rate. The answer is yes, as the diffusion process is dependent on the velocity of the gas. Resources such as Fick's law of diffusion and online materials on convective heat transfer can aid in understanding this concept.
  • #1
Mike_In_Plano
702
35
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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  • #2
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.
 
  • #3


Hi Mike,

Happy holidays to you too! Your heat transfer problem sounds interesting. To answer your question, yes, the radial component of the diffusion rate will be affected by the changing velocities of the gas. This is because the diffusion process is dependent on the velocity of the gas, and as the velocity decreases towards the outer edge of the tube, the diffusion rate will also decrease.

As for equations or references, I suggest looking into Fick's law of diffusion, which relates the diffusion rate to the concentration gradient and diffusion coefficient. You can also check out some online resources on convective heat transfer, which takes into account the velocity of the fluid.

I hope this helps and best of luck with your research! Let us know how it goes.
 

1. What is anisotropic heat diffusion in gas streams with shear?

Anisotropic heat diffusion refers to the transfer of heat in a gas stream that is not uniform in all directions. This can occur due to variations in the gas velocity, temperature, or composition, leading to differences in the rate of heat transfer in different directions. Shear refers to the movement of the gas stream in a specific direction.

2. How does anisotropic heat diffusion affect heat transfer in gas streams?

Anisotropic heat diffusion can significantly impact the rate of heat transfer in gas streams. In some cases, it can enhance heat transfer, while in others, it can hinder it. The direction and intensity of the shear, as well as the temperature and composition of the gas stream, all play a role in determining the overall effect on heat transfer.

3. What factors influence anisotropic heat diffusion in gas streams?

Several factors can influence anisotropic heat diffusion in gas streams, including the gas velocity, temperature, composition, and pressure. Additionally, the geometry and surface properties of the gas stream can also play a role in determining the direction and intensity of heat diffusion.

4. What are some real-world applications of anisotropic heat diffusion in gas streams?

Anisotropic heat diffusion is prevalent in many industrial processes, including combustion, chemical reactions, and heat exchangers. It also plays a crucial role in atmospheric science, such as in the study of weather patterns and climate change. Understanding anisotropic heat diffusion is essential for optimizing these processes and predicting their impact on the environment.

5. What are some methods used to study anisotropic heat diffusion in gas streams?

There are various experimental and computational methods used to study anisotropic heat diffusion in gas streams. These include laser-induced fluorescence, particle image velocimetry, and computational fluid dynamics simulations. Each method has its advantages and limitations, and a combination of approaches is often used to gain a comprehensive understanding of heat diffusion in gas streams.

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