Graetz number

Physical key figure
Surname	Graetz number
Formula symbol	${\displaystyle {\mathit {Gz}}}$
dimension	dimensionless
definition	${\displaystyle {\mathit {Gz}}={\frac {\omega D_{\mathrm {H} }^{2}}{aL}}}$
${\displaystyle \omega }$ Flow velocity ${\displaystyle D_{\mathrm {H} }}$ Hydraulic diameter ${\displaystyle a}$ Thermal diffusivity ${\displaystyle L}$ Characteristic length
Named after	Leo Graetz
scope of application	Forced convection

The Graetz number (according to Leo Graetz ) is a dimensionless number from the field of forced convection . In the case of a steady flow , where the dwell time in the pipe sections is constant, it is the reciprocal of the Fourier number : ${\displaystyle {\mathit {Gz}}}$ ${\displaystyle {\mathit {Fo}}}$

${\displaystyle {\mathit {Gz}}={\frac {1}{\mathit {Fo}}}}$

and thus expresses the ratio of convectively transferred to dissipated heat :

${\displaystyle {\mathit {Gz}}={\frac {Q_{\mathrm {konv} }}{Q_{\mathrm {leit} }}}}$

The higher the value of the Graetz number, the stronger the influence of convection on heat transfer compared to the heat conduction of the fluid . It can therefore be defined by the characteristic length , the hydraulic diameter of a pipe (corresponds to the diameter of a circular pipe), the flow velocity and the thermal diffusivity of the fluid: ${\displaystyle L}$ ${\displaystyle D_{\mathrm {H} }}$ ${\displaystyle \omega }$ ${\displaystyle a}$

${\displaystyle {\mathit {Gz}}={\frac {\omega D_{\mathrm {H} }^{2}}{aL}}}$

With the help of the Reynolds number , the Prandtl number or the Péclet number this can be written as: ${\displaystyle {\mathit {Re}}}$ ${\displaystyle {\mathit {Pr}}}$ ${\displaystyle {\mathit {Pe}}}$

${\displaystyle {\mathit {Gz}}={\frac {D_{\mathrm {H} }}{L}}\cdot {\mathit {Re}}\cdot {\mathit {Pr}}={\frac {D_{\mathrm {H} }}{L}}\cdot {\mathit {Pe}}}$

swell

• Dirk Flottmann, Ralph Gräf et al .: Paperback of mathematics and physics, Springer 2009, ISBN 978-3540786832
• Rudi Marek, Klaus Nitsche: Practice of heat transfer: Basics, applications, exercises, Hanser 2010, ISBN 978-3-446-42510-1

1. ^ Josef Kunes: Dimensionless Physical Quantities in Science and Engineering . Elsevier, 2012, ISBN 0-12-391458-2 , pp. 193 ( limited preview in Google Book search).