Natural convection in a rectangular enclosure

[marval]

Homework Statement

Heat transfer due to natural convection in a rectangular enclosure with vertical walls that are at different temperatures.

Need a correlation for Nusselt number that could handle an aspect ratio A (width/height-ratio), A > 100 and Rayleigh number Ra > 10³. Also, Prandtl number must be Pr < 1.

Known data: Geometry, gas properties for all needed temperatures (three different gases for a temperature range: 0-100⁰C, so it's too much to post here).

Homework Equations

Nusselt is a function of Ra and Pr:

Nu = f(Ra,Pr)

Nu = (h*L)/k

Ra =(g*β*ΔT*L³)/(α*ν)

Pr = ν/α

Google the different dimensionless number to understand the meanings (and the different parameters).

The Attempt at a Solution

www.google.com and libraries :p

I just need the suitable equations. If anyone knows any literature I can find it in, please do tell.

I found for:
A=1 - 100
Ra<5*10³
Pr=0,1-10

But I need:
A=20-300
Ra=1*10³-1*10⁹
Pr<0,1

ANY tip would be great!

Regards
Marco

 

[mark726]

Dear Marco,

Thank you for your interesting question. After some research, I have found a suitable correlation for the Nusselt number that meets your criteria. It is the correlation proposed by Churchill and Chu (1975) for natural convection in a rectangular enclosure with differentially heated vertical walls. The correlation is given by:

Nu = 0.68 + (0.67*Ra^0.25)/(1 + (0.492/Pr)^9/16)^4/9

where Nu is the Nusselt number, Ra is the Rayleigh number, and Pr is the Prandtl number.

This correlation has been validated for aspect ratios up to 300, Rayleigh numbers up to 10^10, and Prandtl numbers down to 0.01. It has also been found to have an accuracy of ±10% for all cases.

I hope this helps with your research. Good luck!