CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Forums > Main CFD Forum

equations for viscosity and thermal conductivity

Register Blogs Members List Search Today's Posts Mark Forums Read

Reply
 
LinkBack Thread Tools Display Modes
Old   November 22, 2000, 15:14
Default 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.
  Reply With Quote

Old   November 22, 2000, 19:03
Default 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=(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.

  Reply With Quote

Old   November 23, 2000, 17:28
Default 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.
  Reply With Quote

Old   November 24, 2000, 02:51
Default 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> =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>
  Reply With Quote

Old   November 24, 2000, 06:45
Default 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
  Reply With Quote

Old   November 24, 2000, 11:05
Default 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
  Reply With Quote

Old   November 24, 2000, 11:34
Default 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-6*T^1.5/(110.4+T) if T<1500K
  Reply With Quote

Old   November 25, 2000, 21:26
Default Re: equations for viscosity and thermal conductivi
  #8
clifford bradford
Guest
 
Posts: n/a
thanks Zlatko.
  Reply With Quote

Old   November 27, 2000, 18:45
Default 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.
  Reply With Quote

Old   March 21, 2014, 08:24
Default
  #10
New Member
 
Join Date: Dec 2013
Posts: 7
Rep Power: 3
Daniel_P is on a distinguished road
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
Daniel_P is offline   Reply With Quote

Reply

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On


Similar Threads
Thread Thread Starter Forum Replies Last Post
Constant velocity of the material Sas CFX 15 July 13, 2010 08:56
mass flow in is not equal to mass flow out saii CFX 2 September 18, 2009 08:07
Two-Phase Buoyant Flow Issue Miguel Baritto CFX 4 August 31, 2006 12:02
Porous Media Effective Thermal Conductivity Greg Perkins FLUENT 3 August 5, 2001 21:53
Info: Short Course On Thermal Design of Electronic Equipment Arnold Free Main CFD Forum 0 August 10, 1999 10:18


All times are GMT -4. The time now is 05:07.