Hi everyone,

Can you help me in this "near to CDF" topic?

I search for explicit expressions (formulas, laws) for both the viscosity and thermal conductivity in fluids (incompressible in general, but particularly air, water,other nearly incompressible), I mean, for instance, "exp^{T_0}*K_0.

Until now, I have only found (in Handbooks) tables with different values for these quantities for different temperatures, but I want to have something like:

"Arrhenius Law"= \mu=\mu_0*exp{T-T_0} (Valid for ???? in range of????)

Or others viscosity and thermal conductivity laws, and the fluids which can be modelised with this law.

I will need also some bibliographical references for put them in my report (Because I can't write in the Bibliography, Even if this is the truth, "Founded in the CFD Forum" .

Thank you very much for your help

CPW

There really isn't any general formula. Since you have tables, why not just fit those with polynomials, splines, or Pade approximants? Or one could simply input the tables and interpolate using your favorite method. For gases, the Sutherland formula often works well for fitting:

mu = A T^n / (T + B)

where mu is the coefficient of viscosity or thermal conductivity, and A, n, and B are constants that depend on which fluid you are considering. The Sutherland formula is discussed in many of the standard textbooks on fluids.

I have heared of exponentially Laws for the viscosity, and linear laws for the thermal conductivity, so these polynomials laws seems new to me. Can you give me a reference more precisely?

Thank you

This is curve fitting, not physics, and you can use whatever functions you find useful and sufficiently accurate. The "best" choice will depend upon the fluid you are modeling and the flow conditions. You might want to start with the classic "Transport Theory" by Bird, Stewart, and Lightfoot. You will find it helpful to learn some of the basic kinetic theory. Good luck with your research.