I want to ask two things in this post: 1

^{st}theories to calculate the tip undercooling and 2

^{nd}solutions to the theories to calculate the tip undercooling.

1)

In order to calibrate the numerical parameter (kinetic coefficient), I need to approximate before the tip temperature (undercooling). For this, one could use the theory developed by Kurz Giovanola and Trivedi KGT

^{1}. Another possibility is to use the model developed by Hunt

^{2}. The key difference between the two - afaik - is that they assume a different growth condition to determine the amount of undercooling. KGT: marginal stable. Hunt: maximum growth rate. I have trouble identifying, which of two theories would be suitable for a laser welding / slm solidification sceneario. Or do I compare pears with apples?

2)

As far as I understand KGT theory correctly, I need to numerically solve for a given temperature gradient the unique pair of tip radius R and growth rate V. With this information I get the Peclet Number and can solve the super saturation assumed to be equal to Ivantsov's solution. Lastly, I can calculate the solutal undercooling with that last puzzle piece. Values for Ivantsov's solution can be found in

*Fundamentals of Solidification*by Kurz and Fisher. I wondered that I am probably not the first one trying to implement such a code: do any of you know a python/matlab/octave code for solving this, given the physical properties of the alloy?

I am looking forward for your answers. Thanks.

^{1}https://doi.org/10.1016/0001-6160(86)90056-8

^{2}https://doi.org/10.1016/0022-0248(74)90127-4