## 8.4.2 Viscosity as a Function of Temperature

If you are modeling a problem that involves heat transfer, you can define the viscosity as a function of temperature . Five types of functions are available:

• piecewise-linear:

 (8.4-1)

• piecewise-polynomial:

 (8.4-2) (8.4-3)

• polynomial:

 (8.4-4)

• Sutherland's law

• power law

 The power law described here is different from the non-Newtonian power law described in Section  8.4.5.

For one of the first three, select piecewise-linear, piecewise-polynomial, polynomial in the Viscosity drop-down list and then enter the data pairs ( ), ranges and coefficients, or coefficients that describe these functions Section  8.2. For Sutherland's law or the power law, choose sutherland or power-law respectively in the drop-down list and enter the parameters.

Sutherland Viscosity Law

Sutherland's viscosity law resulted from a kinetic theory by Sutherland (1893) using an idealized intermolecular-force potential. The formula is specified using two or three coefficients.

Sutherland's law with two coefficients has the form

 (8.4-5)

where,

 = the viscosity in kg/m-s = the static temperature in K and = the coefficients = the mass fraction of species = the molecular weight of species = the Operating Pressure

For air at moderate temperatures and pressures, kg/m-s-K , and K.

Sutherland's law with three coefficients has the form

 (8.4-6)

where,

 = the viscosity in kg/m-s = the static temperature in K = reference value in kg/m-s = reference temperature in K = an effective temperature in K (Sutherland constant)

For air at moderate temperatures and pressures, kg/m-s, = 273.11 K, and = 110.56 K.

Inputs for Sutherland's Law

To use Sutherland's law, choose sutherland in the drop-down list to the right of Viscosity. The Sutherland Law panel will open, and you can enter the coefficients as follows:

1.   Select the Two Coefficient Method or the Three Coefficient Method.

 Use SI units if you choose the two-coefficient method.

2.   For the Two Coefficient Method, set C1 and C2. For the Three Coefficient Method, set the Reference Viscosity , the Reference Temperature , and the Effective Temperature .

Power-Law Viscosity Law

Another common approximation for the viscosity of dilute gases is the power-law form. For dilute gases at moderate temperatures, this form is considered to be slightly less accurate than Sutherland's law.

A power-law viscosity law with two coefficients has the form

 (8.4-7)

where is the viscosity in kg/m-s, is the static temperature in K, and is a dimensional coefficient. For air at moderate temperatures and pressures, , and .

A power-law viscosity law with three coefficients has the form

 (8.4-8)

where is the viscosity in kg/m-s, is the static temperature in K, is a reference value in K, is a reference value in kg/m-s. For air at moderate temperatures and pressures, kg/m-s, K, and .

 The non-Newtonian power law for viscosity is described in Section  8.4.5.

Inputs for the Power Law

To use the power law, choose power-law in the drop-down list to the right of Viscosity. The Power Law panel will open, and you can enter the coefficients as follows:

1.   Select the Two Coefficient Method or the Three Coefficient Method.

 Note that you must use SI units if you choose the two-coefficient method.

2.   For the Two Coefficient Method, set B and the Temperature Exponent . For the Three Coefficient Method, set the Reference Viscosity , the Reference Temperature , and the Temperature Exponent .

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