Brinkmann number

Physical key figure
Surname	Brinkmann number
Formula symbol	${\displaystyle {\mathit {Br}}}$
dimension	dimensionless
definition	${\displaystyle {\mathit {Br}}={\frac {\eta \cdot U^{2}}{k\cdot \Delta T}}}$
${\displaystyle \eta }$ dynamic viscosity ${\displaystyle U}$ Flow velocity ${\displaystyle k}$ Thermal conductivity ${\displaystyle \Delta T}$ Temperature difference
Named after	Henri Brinkman
scope of application	viscous currents

The Brinkmann number ( symbol :) is a dimensionless number in physics . It describes the relationship between the heat generated by friction and the fluid's ability to dissipate this heat. It is named after the Dutch physicist Henri Coenraad Brinkman (1908–1961). ${\displaystyle {\mathit {Br}}}$

The usual definition corresponds to the product of the Prandtl and Eckert numbers : ${\displaystyle {\mathit {Pr}}}$ ${\displaystyle {\mathit {Ec}}}$

${\displaystyle {\mathit {Br}}={\frac {\eta \cdot U^{2}}{k\cdot \left(T_{\mathrm {U} }-T_{\mathrm {L} }\right)}}={\mathit {Pr}}\cdot {\mathit {Ec}}}$

The heat generated by friction flows in as a product of the dynamic viscosity and the characteristic flow velocity , the dissipated heat as a product of the thermal conductivity and the temperature difference between the fluid and the vessel wall. Alternatively, the dissipated heat can also be formulated as the product of the characteristic heat flow density and the hydraulic diameter as the characteristic length : ${\displaystyle \eta }$ ${\displaystyle U}$ ${\displaystyle k}$ ${\displaystyle T_{\mathrm {U} }-T_{\mathrm {L} }}$ ${\displaystyle {\dot {q}}}$ ${\displaystyle d_{\mathrm {h} }}$

${\displaystyle {\mathit {Br}}={\frac {\eta \cdot U^{2}}{{\dot {q}}\cdot d_{\mathrm {h} }}}}$

Individual evidence

1. ^ R. Bryon Bird: Who was who in transport phenomena. Retrieved August 4, 2014 . 
2. ↑ LP Yarin, A. Mosyak, G. Hetsroni: fluid flow, heat transfer and Boiling in Micro-Channels . Springer Science & Business Media, 2008, ISBN 3-540-78755-0 , pp. 161 ( limited preview in Google Book search).
3. ↑ Michael M. Khonsari, E. Richard Booser: Applied Tribology: Bearing Design and Lubrication . John Wiley & Sons, 2008, ISBN 0-470-05944-3 , pp. 125 ( limited preview in Google Book Search).