Unterschiede

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--- en:grundlagenhandbuch:strangabkuehlung [2026/05/28 10:04] – [Convergence criterion] deppe2
+++ en:grundlagenhandbuch:strangabkuehlung [2026/08/17 11:01] (aktuell) – [Determination of the temperature field] paal
@@ Zeile 79: / Zeile 79: @@
 After a few simplifications, the following expression results:
-$$T_{i+1,j} = T_{i,j} + \frac{\Delta t \cdot a}{R^2} \left[(T_{i,j+1} - 2T_{i,j} + T_{i,j-1}) \cdot N^2 + \frac{N}{j} \cdot \frac{T_{i,j+1} - T_{i,j-1}}{2}\right] \tag{13}$$
+$$T_{i+1,j} = T_{i,j} + \frac{\Delta t \cdot a}{R^2} \left[(T_{i,j+1} - 2T_{i,j} + T_{i,j-1}) \cdot N^2 + \frac{N^2}{j} \cdot \frac{T_{i,j+1} - T_{i,j-1}}{2}\right] \tag{13}$$
 In addition, the time difference Δt can be described by the ratio of the length to the pull-off speed:
-$$T_{i+1,j} = T_{i,j} + \frac{\Delta x \cdot a}{v_{ab} \cdot R^2} \left[(T_{i,j+1} - 2T_{i,j} + T_{i,j-1}) \cdot N^2 + \frac{N^2 T_{i,j+1} - T_{i,j-1}}{j \cdot 2}\right] \tag{14}$$
+$$T_{i+1,j} = T_{i,j} + \frac{\Delta x \cdot a}{v_{ab} \cdot R^2} \left[(T_{i,j+1} - 2T_{i,j} + T_{i,j-1}) \cdot N^2 + \frac{N^2}{j} \cdot \frac{T_{i,j+1} - T_{i,j-1}}{2}\right] \tag{14}$$
 $$T_{i+1,j} = T_{i,j} + \frac{\Delta x \cdot a \cdot N^2}{v_{ab} \cdot R^2} \left[(T_{i,j+1} - 2T_{i,j} + T_{i,j-1}) + \frac{1}{j} \frac{T_{i,j+1} - T_{i,j-1}}{2}\right] \tag{14.1}$$
@@ Zeile 137: / Zeile 137: @@
 Core temperature:
-$$T_{i,Mitte} = T_{i,1} \tag{20}$$
+$$T_{i,Mitte} = T_{i,1} \tag{21}$$
 Surface temperature:
-$$T_{i,OF} = \frac{(T_{i,N} + T_{i,Hilfs.})}{2} \tag{Equation 19}$$
+$$T_{i,OF} = \frac{(T_{i,N} + T_{i,Hilfs.})}{2} \tag{22}$$
 Mean temperature:
-$$T_{i,Mittel} = \frac{2}{N^2 + N} \cdot \sum_{j=1}^N j \cdot T_{i,j} \tag{Equation 20}$$
+$$T_{i,Mittel} = \frac{2}{N^2 + N} \cdot \sum_{j=1}^N j \cdot T_{i,j} \tag{23}$$
 ===== References =====