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 clifford bradford November 22, 2000 15:14

equations for viscosity and thermal conductivity

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.

 A. Taurchini November 22, 2000 19:03

Re: equations for viscosity and thermal conductivi

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.

 clifford bradford November 23, 2000 17:28

Re: equations for viscosity and thermal conductivi

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.

 Zlatko Rek November 24, 2000 02:51

Re: equations for viscosity and thermal conductivi

<!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>

 A. Taurchini November 24, 2000 06:45

Re: equations for viscosity and thermal conductivi

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

 rodolphe bolot November 24, 2000 11:05

Re: equations for viscosity and thermal conductivi

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

 rodolphe bolot November 24, 2000 11:34

Re: equations for viscosity and thermal conductivi

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

 clifford bradford November 25, 2000 21:26

Re: equations for viscosity and thermal conductivi

thanks Zlatko.

 clifford bradford November 27, 2000 18:45

Re: equations for viscosity and thermal conductivi

sorry I didn't write my message properly. I meant that I didn't want to use Pr=const to solve for k.

 Daniel_P March 21, 2014 08:24

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? :confused:

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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