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

• N_Br 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;
• 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.

References

• J. D. Huba. NRL Plasma Formulary. Naval Research Laboratory, 1994.
• Carl W. Hall. Laws and Models: Science, Engineering and Technology. — CRC Press, Boca Raton, 2000. ISBN 978-0-8493-2018-7.
• Stephen M. Richardson. Fluid mechanics.
• L. P. Yarin, A. Mosyak, Gad Hetsroni. Fluid flow, heat transfer and boiling in micro-channels.

bs:Brinkmanov broj