Graez number

For reactive extrusion the Damkohler IV number, the Brinkmann number, and the Graez number can conveniently be rewritten as... 

If the Brinkmann number is much smaller than the Damkohler IV number (or Daiv/Br 1), the heat released by viscous dissipation can be neglected with respect to the heat of reaction. If the Graez number is small, the heat removed by the cooled wall will be negligible, and the process is nearly adiabatic. This will generally be the case in situations where large extruders are used. 

These relations show that in large-scale equipment, where the Graez number is generally small, the process is almost adiabatically, whereas in small-scale equipment, with larger Graez numbers, the influence of the wall can be a dominating factor in the process, especially at low throughput. 

Forot Fourier number related to the revolution time Gr Graez number... 

If the equations above are made dimensionless there remain two important dimensionless numbers that govern the heat balances in the extruder the Graez number and the Brinkmann number. 

The Graez number accounts for the development of the temperature profile, whereas the Brinkmann number signifies the ratio between viscous dissipation and heat conduction to the wall. 

Three different dimensionless groups are of importance for estimating this temperature rise in reactive extrusion the Damkohler IV (Daiv) number, the Brinkmann (Br) number, and the Graez (Gz) number. The Damkohler IV number gives the ratio between the heat released by the... 

From the dimensionless energy equation it follows that thermal similarity can be attained if the dimensionless numbers of Graez and Brinkmann are the same for both sizes of machines. 

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