[Hohenheim92]

Goodmorning everyone,
I'm a chemical eng student and I would like to ask you a problem about natural convection. I read an article ("Trapping and manipulation of micro particles using laser-induced convection currents and photophoresis")(you can find the free pdf online if you want) where there is a thin enclosed layer of water between two glasses, and on the bottom glass there is a layer of silicon. The system is heated with a laser vertically and the silicon is then heated locally and transfers heat to the water solvent creating convection flows which form two symmetric convective rolls. The Rayleigh number of the system is << 1 and the convective flow is said to be a non Rayleigh flow (at page 5). My question is: is it possible to have convective rolls with a Rayleigh number which is lower than the critical one? Is it a different type of natural convection with respect to the Rayleigh-Bènard convection?
Thank you very much 

[Enthalpy]

Good luck...

If you read French you may check Sacadura's
Initiation aux transferts thermiques
which has a section just for natural convection heat transfers.

[Hohenheim92]

I've read the book you suggest me, thank you, but my problem is that I don't know what happens if the Rayleigh number is below 1700 (critical Ra number in the case of  fixed boundaries). I thought that under this number no convective rolls could appear, but in the article I've mentioned, the Rayleigh number is much lower than 1, and they have two symmetric convective rolls in their system. My question is, if the Rayleigh number is so low, is this possible?

[Hohenheim92]

Maybe the reason is that the heating from below is not uniform? The 1700 critical Rayleigh number is referred to a uniform heating condition, so maybe there is a different critical number for a non-uniform heating?

[Enthalpy]

If heat isn't uniform you'll get convection necessarily. The point is rather whether convection is more efficient than heat diffusion in transporting heat.