# Sutherland Viscosity Model and Specificiation of Thermal Conductivity

#1

I am using a convective heat transfer model to look at the wall heat transfer coefficient as a gas flows along a pipe.

The gas I’m using is a non-standard mixture and I can customise the Material by inputting a contant viscosity, specific heat capacity and through the Prandlt number, a fluid thermal conductivity. The results I get from doing this appear reasonable.

I am though looking at quite a large temperature range and would like to change the viscosity to use the Sutherland model so that it is temperature dependent. However, when I select this option I am no longer able to specify a Prandtl number, so how does the simulation know what the thermal conductivity of the fluid is? When I run the model it appears to be applying a thermal conductivity equivalent to ta Prandtl number of 0.7, but the fluid I’m using has quite a different Prandlt number.

Am I missing something or is this a bug in the input?

#2

If you change your settings to Sutherland the viscosity is no longer a constant but is a function of temperature assuming you know the Sutherland coefficient. For the thermal conductivity \kappa the Eucken approximation is used if I am not mistaken. @sjoshi and @dzivkovic might give you more information about the implementation and the approximation behind that. Any additional input from @1318980 and @Get_Barried is appreciated as well.

Best,

Jousef

#3

Thanks for the information. I was able to use it find a reference to the OpenFOAM code where this is implemented.

You are correct, it uses the Eucken approximation for the thermal conductivity but unfortunately, it doesn’t give a good value for the mixture I have. I’ll leave it with the constant viscosity then.

#4