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Old   March 26, 1999, 09:13
Default Rayleigh Number
  #1
Thomas P. Abraham
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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
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Old   March 26, 1999, 10:58
Default Re: Rayleigh Number
  #2
Heinz Wilkening
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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
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Old   March 26, 1999, 11:25
Default Re: Rayleigh Number
  #3
Thomas P. Abraham
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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
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Old   March 26, 1999, 11:49
Default Re: Rayleigh Number
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Heinz Wilkening
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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
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Old   March 27, 1999, 07:39
Default Re: Rayleigh Number
  #5
Thomas P. Abraham
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Hi Heinz,

Thanks for your definitions.

Thanks,

Thomas
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