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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.

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)

Ciao Heinz

 Thomas P. Abraham March 27, 1999 07:39

Re: Rayleigh Number

Hi Heinz,