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# Brinkman number

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

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

Where

• NBr = the Brinkman Number
• η = fluid viscosity
• U = fluid velocity
• κ = thermal conductivity of fluid
• T0 = bulk fluid temperature
• Tw = wall temperature

In, for example, a screw extruder, the energy supplied to the polymer melt comes primarily from two sources (i) viscous heat generated by shear between parts of the flow moving at different velocities (ii) 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.