The Brinkman number is a dimensionless number related to heat conduction from a wall to a flowing viscous fluid

Viscosity

Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...

, commonly used in polymer

Polymer

A polymer is a large molecule composed of repeating structural units. These subunits are typically connected by covalent chemical bonds...

 processing. There are several definitions; one is



where

• N_Br is the Brinkman number;
• μ is the fluid's dynamic viscosity;
• U is the fluid's velocity;
• κ is the thermal conductivity
  Thermal conductivity
  In physics, thermal conductivity, k, is the property of a material's ability to conduct heat. It appears primarily in Fourier's Law for heat conduction....
  
   of the fluid;
• T₀ is the bulk fluid temperature;
• T_w 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.