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| The '''Brinkman number''' ('''Br''') is a [[dimensionless]] number related to heat conduction from a wall to a flowing [[viscosity|viscous fluid]], commonly used in [[polymer]] processing. There are several definitions; one is
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| <math> \mathrm{Br} = \frac {\mu U^2}{\kappa(T_w-T_0)} = \mathrm{Pr} \, \mathrm{Ec}</math>
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| where
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| * ''μ'' is the fluid's [[dynamic viscosity]];
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| * ''U'' is the fluid's velocity;
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| * ''κ'' is the [[thermal conductivity]] of the fluid;
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| * ''T<sub>0</sub>'' is the bulk fluid temperature;
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| * ''T<sub>w</sub>'' is the wall temperature;
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| * Pr is the [[Prandtl number]]
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| * Ec is the [[Eckert number]]<ref name="KhonsariBooser2008">{{cite book|author1=Michael M. Khonsari|author2=E. Richard Booser|title=Applied Tribology: Bearing Design and Lubrication|url=http://books.google.com/books?id=_EcQZJIyjpcC&pg=PA125|accessdate=19 July 2012|date=28 July 2008|publisher=John Wiley & Sons|isbn=978-0-470-05944-9|page=125}}</ref>
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| 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 the value of it, the lesser will be the conduction of heat produced by viscous dissipation and hence larger the temperature rise.<ref name="BrodkeyHershey1988">{{cite book|author1=Robert S. Brodkey|author2=Harry C. Hershey|title=Transport Phenomena: A Unified Approach|url=http://books.google.com/books?id=CjBTMYXM7ccC&pg=PA333|accessdate=19 July 2012|year=1988|publisher=Brodkey Publishing|isbn=978-0-9726635-9-5|page=333}}</ref><ref name="Pontes">{{cite book|author=José Pontes|title=COMPUTATIONAL HEAT AND MASS TRANSFER – CHMT 2001-|url=http://books.google.com/books?id=zQx3U7_73-oC&pg=PA113|accessdate=19 July 2012|publisher=Editora E-papers|isbn=978-85-87922-44-1|pages=113–}}</ref>
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| In, for example, a [[screw extruder]], the energy supplied to the polymer melt comes primarily from two sources:
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| * viscous heat generated by shear between parts of the flow moving at different velocities;
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| * direct heat conduction from the wall of the extruder.
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| 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.
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| ==References==
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| {{Reflist}}
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| * J. D. Huba. NRL Plasma Formulary. Naval Research Laboratory, 1994.
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| * Carl W. Hall. ''Laws and Models: Science, Engineering and Technology''. — CRC Press, Boca Raton, 2000. ISBN 978-0-8493-2018-7.
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| * Stephen M. Richardson. ''[http://books.google.com/books?id=ZY-mxKpagwAC&pg=PA73&dq=brinkman+number+Br&lr=&cd=1#v=onepage&q=brinkman%20number%20Br&f=false Fluid mechanics]''.
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| * L. P. Yarin, A. Mosyak, Gad Hetsroni. ''[http://books.google.com/books?id=puTM9KYgOEoC&lpg=PA164&dq=brinkman%20number%20Br&lr=&pg=PA165#v=onepage&q=brinkman%20number%20Br&f=false Fluid flow, heat transfer and boiling in micro-channels]''.
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| {{NonDimFluMech}}
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| [[Category:Dimensionless numbers of fluid mechanics]]
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| [[Category:Dimensionless numbers of thermodynamics]]
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| [[Category:Fluid dynamics]]
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| [[Category:Polymer chemistry]]
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