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Thomas P. Abraham March 26, 1999 09:13

Rayleigh Number
 
Hello Everyone:

I was trying to get a good definition of Rayleigh number and its physical significance.

I understand that Rayleigh number gives the dominance of free convection. If the Rayleigh number is high, the turbulent effects are dominant too. I was told that if the Rayleigh number is more than 1.0e+07, turbulent effects need to be accounted. Am I right about this?

I am trying to check out some basic text books. Unfortunately, all these text boks are checked from the library. I need to wait tiil they are returned.

Till then, all your comments are appreciated,

Thomas

Heinz Wilkening March 26, 1999 10:58

Re: Rayleigh Number
 
Hi,

The Raylaigh number kann be calculated as:

Ra = Re*Re*Ar*Pr

Re: Reynolds number

Ar: Arcimendes number

Pr: Prandtl number

It is a seminarity number for the natural convective heat transfer. It includes efects of turbulence, buoyancy and heattransfer.

You may calculate it as

Ra = g*rho*l*l*l*(T-T0)*cp/(mu*lambda)

You may think of a flow in a 2D box/room one side wall high temperature over side low temperature. Top and bottom adiabatic.

For such asituation the flow in the boundary layer along the sidefwall will become turbulent if Ra>10^7, as you mentioned.

Ciao Heinz

Thomas P. Abraham March 26, 1999 11:25

Re: Rayleigh Number
 
Hi Heinz,

Thanks for your nice definition. It was well defined.

I never heard of Arcimedes number. How is that defined? It seems to give the strength of buoyancy.

Thanks,

Thomas

Heinz Wilkening March 26, 1999 11:49

Re: Rayleigh Number
 
Hi,

the Archimedes Number should be something like the ratio of the strength of the buoyancy to the strength of inertia on a fluid partricle, as you mentioned.

You can calculate it like:

Ar = g*beta*l*(T-T0)/(U*U)

See also the posting by Erich: Isobaric compressibility of Air

Ciao Heinz

Thomas P. Abraham March 27, 1999 07:39

Re: Rayleigh Number
 
Hi Heinz,

Thanks for your definitions.

Thanks,

Thomas

ViLaks November 13, 2017 02:55

Hello,

Sorry for starting the thread again, I need to know the significance of Ra.

For my natural convection problem, my Ra is around 129120.

In this case, I wanted to know if the heat transfer occurs due to Conduction or conduction and convection. It is mentioned in wikipedia that when the Rayleigh number is below a critical value for that fluid, heat transfer is primarily in the form of conduction; when it exceeds the critical value, heat transfer is primarily in the form of convection. But what is that critical value?? My working fluid here is air

Thanks
Vignesh

FMDenaro November 13, 2017 04:16

Quote:

Originally Posted by ViLaks (Post 671441)
Hello,

Sorry for starting the thread again, I need to know the significance of Ra.

For my natural convection problem, my Ra is around 129120.

In this case, I wanted to know if the heat transfer occurs due to Conduction or conduction and convection. It is mentioned in wikipedia that when the Rayleigh number is below a critical value for that fluid, heat transfer is primarily in the form of conduction; when it exceeds the critical value, heat transfer is primarily in the form of convection. But what is that critical value?? My working fluid here is air

Thanks
Vignesh


To understand the role, just see where the Ra number enters into the equations. It is a measure of the relevance of the term it multiplies.

ViLaks November 13, 2017 04:23

Quote:

Originally Posted by FMDenaro (Post 671447)
To understand the role, just see where the Ra number enters into the equations. It is a measure of the relevance of the term it multiplies.

Dear Filippo Maria Denaro,

Thanks for your reply. But, Im sorry, how could I check that?

With Regards
Vignesh


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