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Old Mar 20th 2017, 03:20 PM   #1
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Natural convection: turbulent or laminar?

Hello everyone,

I am modelling an inclined rectangular cavity and got confused with Grashof and Rayleigh number. I've reviewed many research papers - some researchers use Rayleigh, some Grashof number to determine the type of flow.

This is probably very simple but I can't find where my mistake lies...

I get 10^6 for Rayleigh which indicates Laminar flow and I also get 10^12 for Grashof which indicates Turbulent flow. This got me confused.


My problem involves upper wall exposed to a heat flux, bottom wall and side walls adiabatic. Heat flux warms up the upper wall and the fluid inside. The conditions become:

Tupper = 306 K (average)
Tbottom = 303 K (average)
Tfluid = 300 K (average)

Dimensions: L=2m, W=1m, H=0.007m (space between plates)

From literature and texbooks, I use the following formulas:

Ra=( g*B* (Tu-Tf)*L^3 ) / (v*a)
Gr = (g*B (Tu-Tf)*H^3) / (v^2)

where Tu - upper plate temperature
Tf - fluid temperature
L - Length of the cavity
g - 9.81m/s
B - thermal expansion coeff for WATER @ 20C (0.0033 [1/K])
v - kinematic viscosity 1x10e-7 m/s2
a - thermal diffusivity 1x10e-7 mē/s

Thank you for you help.

Last edited by Artis; Mar 20th 2017 at 03:27 PM. Reason: added values for v and a
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Old Mar 20th 2017, 03:52 PM   #2
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7mm is a very narrow slot.

http://naca.central.cranfield.ac.uk/...rc/cp/0013.pdf
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Old Mar 20th 2017, 04:06 PM   #3
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Originally Posted by studiot View Post
Thanks for the reply and the link. However, there is no information on neither Rayleigh or Grashof numbers in it...
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Old Mar 21st 2017, 02:30 AM   #4
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Originally Posted by Artis View Post
Thanks for the reply and the link. However, there is no information on neither Rayleigh or Grashof numbers in it...
No but there is a derivation from first principles of the conditions for both laminar and turbulent flow.

You need to understand the physics behind a model not just blindly apply formulae.
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Old Mar 21st 2017, 05:21 AM   #5
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Originally Posted by studiot View Post
No but there is a derivation from first principles of the conditions for both laminar and turbulent flow.

You need to understand the physics behind a model not just blindly apply formulae.
Yes, it's true. I tried to understand it but it is still confusing and does not help me to determine the type of flow. How would you interpret the flow based on the boundary conditions provided above?
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Old Mar 21st 2017, 05:46 AM   #6
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You said the cavity was inclined, but were not clear if this was flow thrrough a rectangular duct or if the 'cavity' is blanked off?

Further you said it is inclined, but not by how much (unless I missed that bit)

I have gathered that the fluid is water and that the crossectional boundary temperature differences are small and the longitudinal ones zero.

So are there any other causes of flow?
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Old Mar 21st 2017, 07:21 AM   #7
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Originally Posted by studiot View Post
You said the cavity was inclined, but were not clear if this was flow thrrough a rectangular duct or if the 'cavity' is blanked off?

Further you said it is inclined, but not by how much (unless I missed that bit)

I have gathered that the fluid is water and that the crossectional boundary temperature differences are small and the longitudinal ones zero.

So are there any other causes of flow?
Yes, sorry, I will make it more clear (see the attached picture).
It's a natural convection flow, induced due to density differences in water inside the cavity between two hot plates. I am not certain if the flow inside the cavity is laminar or turbulent.

Thanks for helping me.

Natural convection: turbulent or laminar?-physics-forum.png
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Old Mar 21st 2017, 01:48 PM   #8
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Artis, Some time ago (maybe 40 years past) I spent a week on your "enclosed space ~ laminar/turb" issue. I had a wall of books, data. I was looking at the "R-value" of ceramic-barrel tiled roofs in south Florida. "Turb vrs Laminar" within a small space is a very esoteric topic. LOL means "lots of luck" in your search... JP

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