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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.
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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. |
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.
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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> |
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
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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
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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
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Re: equations for viscosity and thermal conductivi
thanks Zlatko.
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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.
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