Unterschiede

Hier werden die Unterschiede zwischen zwei Versionen angezeigt.

--- en:grundlagenhandbuch:scale-up:modelluebertragung:konstanter_waermestrom [2025/06/22 11:08] – deppe2
+++ en:grundlagenhandbuch:scale-up:modelluebertragung:konstanter_waermestrom [2026/01/21 08:46] (aktuell) – gelöscht admin
@@ Zeile 1: / Zeile 1: @@
-====== Constant Heat Flow ======
-===== Constant Heat Flow =====
-Based on the energy balance of the melt zone for the heating capacity results
-$$\Pi_6 = \frac{\dot{q} L_{sz} \left(1 - \frac{\beta}{\pi}\right)}{h v \rho c_v \Delta T_{sz}} \tag{1}$$
-The expression in brackets in Equation 6 can be considered as an approximately constant value [3]. Are, furthermore, constant material values assumed and is the velocity replaced, the ratio of heat flow densities of the model design and the main design derive:
-$$\frac{\dot{q}}{\dot{q}_0} = \frac{L_{sz,0} h D N}{L_{sz} h_0 D_0 N_0} = \frac{\Delta T_{sz}}{\Delta T_{sz,0}} = \left(\frac{D}{D_0}\right)^{1-\psi-\chi} \frac{\Delta T_{sz}}{\Delta T_{sz,0}} \tag{2}$$
-By assuming a constant melt temperature at the screw tip for both the model design and the main design, it consequently has to apply
-$$\chi = \psi - \omega \tag{3}$$
-to obtain identical heat flow densities. The melt flow, which is to be metered, derives as before by inserting the exponent into the throughput equation $\frac{\dot{m}}{\dot{m}_0} = \frac{\dot{V}}{\dot{V}_0} = \left(\frac{D}{D_0}\right)^{2+\psi-\chi}$.