Calculate Nusselt Number: Free Convection Air Vertical Channel Different Temps

In summary, the conversation discusses various equations and situations for calculating the Nusselt number for free convection in a vertical channel with walls at different temperatures. The speakers consider the Bar-Cohen and Rohsenow equations and discuss the implications of symmetric vs asymmetric heating. They also mention using the enclosure equations as an approximation, but note that this may not accurately represent the situation. The conversation ends with a discussion on the flow pattern in an "infinite" parallel plate setup and how it may affect the Nusselt number calculation.
  • #1
engineer23
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What expression should be used to calculate Nusselt number for free convection (of air) in a vertical channel with walls at different temperatures?

I have the Bar-Cohen and Rohsenow equations, but I am unsure which situation this corresponds to (and thus which constants to use).
Symmetric isothermal plates (wouldn't this imply Ts,1 = Ts,2 which is not the case?)
Symmetric isoflux
Isothermal/adiabatic (I am leaning towards this)
Isoflux/adiabatic
 
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  • #2
Wow...I think we're looking at the same book, and I'm surprised this isn't in here. They have good relations for a fully enclosed cavity, which I'm sure you've seen in the next section. They also have a case for flow between concentric cylinders, but nothing about asymmetric heating.

This led me to literature, and I was more surprised on how little I find even in journal papers. The closest I've found so far is FORCED convection between asymmetrically heated plates. I'm going to keep looking for you though.

boy there are a LOT of different types of uniform heating though isn't there?
 
  • #3
Maybe I can use the enclosure equations as an approximation.
 
  • #4
That's what I was originally thinking, however the computed Nusselt number can very quite a bit if you assume L/H = 100:1, or 1000:1, etc. This of course affects the convection coefficient. Also, the enclosed space assumes that there will be a complete convection current. In your case of "infinte" parallel plates, I would think that there would be none. There will probably be some swirl, but I wouldn't think that the flow would come "down", so long as both wall temps are higher than the incoming temp.
 

1. What is the Nusselt number?

The Nusselt number is a dimensionless number used in heat transfer calculations to determine the convective heat transfer coefficient. It represents the ratio of convective to conductive heat transfer in a fluid flow.

2. How is the Nusselt number calculated?

The Nusselt number can be calculated using the equation Nu = hL/k, where h is the convective heat transfer coefficient, L is the characteristic length, and k is the thermal conductivity of the fluid.

3. What is free convection?

Free convection is a type of heat transfer that occurs when a fluid, such as air, is heated and rises due to its lower density. This creates a circulation of the fluid, which results in convective heat transfer.

4. What is a vertical channel?

A vertical channel refers to a confined space through which a fluid can flow vertically, such as a chimney or a pipe. In the case of calculating the Nusselt number, it would be a channel through which air is flowing vertically.

5. How does temperature difference affect the Nusselt number in free convection?

The Nusselt number is directly proportional to the temperature difference between the heated surface and the surrounding fluid. As the temperature difference increases, so does the Nusselt number, resulting in a higher convective heat transfer coefficient and greater heat transfer.

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