The Brinkman number (Br) is a
dimensionless
A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1) ...
number related to heat conduction from a wall to a flowing
viscous fluid
In condensed matter physics and physical chemistry, the terms viscous liquid, supercooled liquid, and glassforming liquid are often used interchangeably to designate liquids that are at the same time highly viscous (see Viscosity of amorphous m ...
, commonly used in
polymer
A polymer (; Greek '' poly-'', "many" + ''-mer'', "part")
is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic a ...
processing. It is named after the Dutch mathematician and physicist
Henri Brinkman. There are several definitions; one is
where
* ''μ'' is the
dynamic viscosity;
* ''u'' is the
flow velocity
In continuum mechanics the flow velocity in fluid dynamics, also macroscopic velocity in statistical mechanics, or drift velocity in electromagnetism, is a vector field used to mathematically describe the motion of a continuum. The length of the f ...
;
* ''κ'' is the
thermal conductivity
The thermal conductivity of a material is a measure of its ability to conduct heat. It is commonly denoted by k, \lambda, or \kappa.
Heat transfer occurs at a lower rate in materials of low thermal conductivity than in materials of high thermal ...
;
* ''T
0'' is the bulk fluid temperature;
* ''T
w'' is the wall temperature;
* Pr is the
Prandtl number
* Ec is the
Eckert number
It is the ratio between heat produced by viscous dissipation and heat transported by molecular conduction. i.e., the ratio of viscous heat generation to external heating. The higher its value, the slower the conduction of heat produced by viscous dissipation and hence the larger the temperature rise.
In, for example, a
screw extruder, the energy supplied to the polymer melt comes primarily from two sources:
* viscous heat generated by shear between elements of the flowing liquid 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
*
*
*
*
{{NonDimFluMech
Continuum mechanics
Dimensionless numbers of fluid mechanics
Dimensionless numbers of thermodynamics
Polymer chemistry