# Brinkman number

The Brinkman number is a dimensionless number related to heat conduction from a wall to a flowing viscous fluid, commonly used in polymer processing. There are several definitions; one is

$$N_{Br} = \frac {\mu U^2}{\kappa(T_w-T_0)},$$

where

• NBr is the Brinkman number;
• μ is the fluid's dynamic viscosity;
• U is the fluid's velocity;
• κ is the thermal conductivity of the fluid;
• T0 is the bulk fluid temperature;
• Tw is the wall temperature.

In, for example, a screw extruder, the energy supplied to the polymer melt comes primarily from two sources:

• viscous heat generated by shear between parts of the flow moving at different velocities;
• direct heat conduction from the wall of the extruder.

The former is supplied by the motor turning the screw, the latter by heaters. The Brinkman number is a measure of the ratio of the two.

## References

bs:Brinkmanov broj