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
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
- 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 978-0849320187.
- Stephen M. Richardson. Fluid mechanics.
- L. P. Yarin, A. Mosyak, Gad Hetsroni. Fluid flow, heat transfer and boiling in micro-channels.
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