equations for viscosity and thermal conductivity

Светлана · November 22, 2000, 14:14

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.

Светлана · November 22, 2000, 18:03

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.

Светлана · November 23, 2000, 16:28

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.

Светлана · November 24, 2000, 01:51

<!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: ******* C1=1.458E-06kgm/s^3K^(3/2) ******* C2=110.4K ******* C3=2.495E-03kgm/s^3K^(3/2) ******* C4=194K
[1] Tannehil J.C., Anderson D.A., Pletcher R.H.: Computational Fluid Mechanics and Heat Transfer, **** Taylor & francis, 1997, p. 259. </body> </html>

Светлана · November 24, 2000, 05:45

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

November 24, 2000, 10:05

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

November 24, 2000, 10:34

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

Светлана · November 25, 2000, 20:26

thanks Zlatko.

Светлана · November 27, 2000, 17:45

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, 07:24

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?

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

November 22, 2000, 14:14	equations for viscosity and thermal conductivity	#1
clifford bradford Guest Posts: n/a	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. Светлана likes this.

November 22, 2000, 18:03	Re: equations for viscosity and thermal conductivi	#2
A. Taurchini Guest Posts: n/a	Hi, here's what you requested: mu=mu_0 [(T/T_0)^1.5] [(T_0+SUT)/(T+SUT)] (viscosity). k=(mucp) / 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. Светлана and ronithstanly like this.

November 23, 2000, 16:28	Re: equations for viscosity and thermal conductivi	#3
clifford bradford Guest Posts: n/a	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. Светлана likes this.

November 24, 2000, 01:51	Re: equations for viscosity and thermal conductivi	#4
Zlatko Rek Guest Posts: n/a	<!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=C1T^(3/2)/(T+C2) k=C3T^(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> Светлана likes this.

November 24, 2000, 05:45	Re: equations for viscosity and thermal conductivi	#5
A. Taurchini Guest Posts: n/a	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 Светлана likes this.

November 24, 2000, 10:05	Re: equations for viscosity and thermal conductivi	#6
rodolphe bolot Guest Posts: n/a	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

November 24, 2000, 10:34	Re: equations for viscosity and thermal conductivi	#7
rodolphe bolot Guest Posts: n/a	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-6T^1.5/(110.4+T) if T<1500K

November 25, 2000, 20:26	Re: equations for viscosity and thermal conductivi	#8
clifford bradford Guest Posts: n/a	thanks Zlatko. Светлана likes this.

November 27, 2000, 17:45	Re: equations for viscosity and thermal conductivi	#9
clifford bradford Guest Posts: n/a	sorry I didn't write my message properly. I meant that I didn't want to use Pr=const to solve for k. Светлана likes this.

March 21, 2014, 07:24		#10
Daniel_P New Member Join Date: Dec 2013 Posts: 11 Rep Power: 12	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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