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equations for viscosity and thermal conductivity

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  • 1 Post By clifford bradford
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Old   November 22, 2000, 15:14
Default equations for viscosity and thermal conductivity
  #1
clifford bradford
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hello all. I'm interested in getting equations for the dynamic viscosity of air (Sutherland's law) and the thermal conductivity of air as a function of temperature. Please include the reference values. I know these equations are both in Tannehill, Anderson, and Pletchers CFD book so if you have it could you please let me know what they are? Thanks.
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Old   November 22, 2000, 19:03
Default Re: equations for viscosity and thermal conductivi
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A. Taurchini
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Hi, here's what you requested:

mu=mu_0 [(T/T_0)^1.5] *[(T_0+SUT)/(T+SUT)] (viscosity).

k=(mu*cp) / Pr (thermal conductivity).

where mu_0 = 1.789 * 10^-5 Kg/(ms) and T_0 = 288.16 K are calculated at standard sea level conditions, SUT = 110.4 K. Pr = 0.72 is Prandtl number, cp is the specific heat for p=const. Note that second relationship is valid only if Pr is assumed constant (air as calorically perfect gas). Bye.

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Old   November 23, 2000, 17:28
Default Re: equations for viscosity and thermal conductivi
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clifford bradford
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thamks for the answer. there's a formula similar in form to sutherland's formula that doesn't require the assumption of a calorically perfect gas (ie constant Pr). However I've only seen it in print once (in Tannehill, Anderson, and Pletcher), unfortunately I no longer have a copy of that book.
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Old   November 24, 2000, 02:51
Default Re: equations for viscosity and thermal conductivi
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Zlatko Rek
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<!doctype html public "-//w3c//dtd html 4.0 transitional//en"> <html> <head>

<meta name="GENERATOR" content="Mozilla/4.76 [en] (X11; U; Linux 2.2.17 i686) [Netscape]"> </head> <body> µ=C1*T^(3/2)/(T+C2)
k=C3*T^(3/2)/(T+C4)
C1-C4 are constants for a given gas . Air at modest temperatures: ******* <font color="#3366FF">C1=1.458E-06kgm/s^3K^(3/2)</font> <font color="#3366FF">******* C2=110.4K</font> <font color="#3366FF">******* C3=2.495E-03kgm/s^3K^(3/2)</font> <font color="#3366FF">******* C4=194K</font>
[1] Tannehil J.C., Anderson D.A., Pletcher R.H.: Computational Fluid Mechanics and Heat Transfer, **** Taylor & francis, 1997, p. 259. </body> </html>
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Old   November 24, 2000, 06:45
Default Re: equations for viscosity and thermal conductivi
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A. Taurchini
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Pay attention : Sutherland law for viscosity doesn't require Pr=const, second formula does. First formula given by Zlatko is equal to mine but in a different form (just constants). Second is usuallly referred to as Sutherland law for thermal conductivity, but if your problem range of temperature variation is not too wide (o[100K]) you can surely use the simpler formula for conductivity. Bye
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Old   November 24, 2000, 11:05
Default Re: equations for viscosity and thermal conductivi
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rodolphe bolot
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Hi, I developped a code in order to compute thermodynamic properties and transport coefficients of combustion products. In a first step, a gibbs free energy minimization method is used in order to determine the chemical equilibrium composition versus temperature. In a second step, a Lennard-Jones potential is used for each species and the Wilke mixing rule is used to compute the mixture viscosity and thermal conductivity. Since my code includes C-H-O-N elements, it may be used to compute air properties (the results compare well with the just given formula) ... but species dissociation occurs at high temperature. I can give you my results if your temperature range is large ... A T^0.65 formula may also be used to fit the viscosity curve. Bye
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Old   November 24, 2000, 11:34
Default Re: equations for viscosity and thermal conductivi
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rodolphe bolot
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My equation for air dynamic viscosity: Viscosity=2.6134e-5*(T/500)^0.6514 (obtained from a linear fit of ln(viscosity)) It is quite similar to 1.458e-6*T^1.5/(110.4+T) if T<1500K
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Old   November 25, 2000, 21:26
Default Re: equations for viscosity and thermal conductivi
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clifford bradford
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thanks Zlatko.
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Old   November 27, 2000, 18:45
Default Re: equations for viscosity and thermal conductivi
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clifford bradford
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sorry I didn't write my message properly. I meant that I didn't want to use Pr=const to solve for k.
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Old   March 21, 2014, 08:24
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Hej everyone!

Sorry for reactivating this old post, but I have a question with respect to the same topic and was wondering if you could help me with it.

I use chtMultiRegionSimpleFoam (OF 2.2.x) and experimented with the transport models in thermophysicalProperties of a fluid region. The thermo model I set is heRhoThermo and the fluid is air.

When I set transport to "const", I define a constant dynamic viscosity mu and the Prandtl number Pr. The thermal conductivity k is then calculated by Pr=mu*cp/k.

In a second example I set transport to "sutherland". Now I define only the two input parameters As=1.4792e-06 and Ts=116 for Sutherland's law and nothing more.
How does the solver calculate the thermal conductivity then?

I read about Sutherland's law for thermal conductivity but then I would need to define four constants, right?


Thank you for any help,
Daniel
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