Heat Transfer coefficient calculation for hot air flow inside rectangular duct

Question

I am working on modeling of air-heater component. A simplified representation of system is as follows:

Cold air flow enters steel duct at one end. Inside duct is Calrod heating element shaped as ellipse. Follwing heat transfer occur simulteneously:-

1. Air gains heat from surface of heated calord.
2. Air also exchanges heat with duct inner surface.
3. Calrod element radiates heat to duct inner surface.
4. Duct loses heat by radiation to surroundings as well as convection.

System is solved by taking energy balance equations on Air mass, Duct mass and Heater element mass.

My question is in regards to convection between air and duct. In model, I have considered whole assembly to be made of 5 parts along duct length. In each part respective thermal balance on air, duct and heated element mass is taken. In each part, I consider air to be lump-sum mass. Entering air gains heat from calrod and gains some temperature ( which would in real world be average temperature). Problem occurs when that temperature is used for convection transfer with duct. In actual process, air flow is fast enough (0.013 $\frac{m^3}{sec}$) so that air that actually is in contact with heater element doesn't reach duct surface. So air that exchanges heat with duct inner surface is at lower temperature than average air's temperature. This gives incorrect duct temperature predictions. How can I properly set $\Delta T$ for convection heat exchange with duct?

Answer 1

There are several issues going on that I believe are making the model not very accurate. They all in some way relate to your question about the convection:

1. Breaking up the flow into 5 discrete chunks is a good start, but probably not a sufficient number. Keep increasing the number of nodes in your model until the answer stops changing.

2. The next thing to check is the Reynold number of your flow and the length it will take to become fully developed. If your flow is fully developed for most of the length, the heat transfer coefficient will do a good job modeling the problem you are describing with the air not contacting the wall. If the flow is not fully developed (which is my gut guess) then the heat transfer coefficient won't do a good job.

3. In general, you should consider the high level thermal resistances between the coil and the duct wall. Since air is such a poor conductor and has such a low density, it is a poor heat transfer medium. Since the heat transfer coefficient on the surface of the coil to the air will be similar to the heat transfer coefficient from the air to duct, the extreme difference in dT between the coil and air and the air and wall will result in a very large Q to the air and a very small Q to the duct wall from the air. It is not impossible that the air actually cools the duct wall instead of heating. If you work out the air-to-duct heat transfer coefficient you may find that it is so trivial that it is likely not the source of error in your model.

4. Without numbers I can't really say for sure, but my guess is that the air in your model is not actually the primary means of heat from the coil to the wall. Instead, the radiation in dominant. Thus, I would look to improve the accuracy of that calculation first if you want to predict wall temperature. For example, what emissivity are you using for the duct wall? How are you calculating the view factor between the coil's interior edge and the wall? Etc etc.

Hope this helps and that this is still even remotely relevant 1 year late.