Karl-Heinz Spitzer

Application of rotating magnetic fields in Czochralski crystal growth

The physical principles of electromagnetic stirring with a rotating magnetic field are explained and a mathematical model to calculate the electromagnetic volume force, the fluid flow and the transport of heat and solutes is outlined. For the electromagnetic volume force and for the order of magnitude of the flow velocities approximative analytical expressions are given. A high flexibility in configuring the volume force in order to achieve a desired flow distribution is obtained by multi-frequency stirring that is by superposition of two or several magnetic fields with different frequencies and/or sense of rotation. Results of experimental investigation and mathematical simulation of multi-frequency stirring are given. Numerical simulation of the fluid flow, the temperature and the oxygen distribution in a Czochralski process crucible was performed including the effect of single mode and multi-frequency stirring. The results indicate that electromagnetic stirring should offer large potentials for the optimization of the flow configuration in a Czochralski process crucible. Finally examples from literature of practical application of rotating magnetic fields in crystal growth are presented.

Spray Cooling Heat Transfer and Calculation of Water Impact Density for Cooling of Steel Sheet Materials by Inverse Process Modelling

Modern steel grades require accurate temperature control during processing. The cooling section technology has to deliver prescribed cooling rates while fulfilling specific constraints, e.g. on the minimum surface temperature. For all material thicknesses, numerical cooling system set value prediction is advantageous and above 10 mm, the possible cooling rates and the experimental parameter determination are limited by physical constraints. Laboratory measurements provide quantitative experimental data on the heat transfer coefficient (HTC) depending on the cooling system parameter water impact density and the temperature difference. The desired final material properties determine temperature control and cooling rate. This information is used to predict the optimum cooling section set values for a specific cooling task. The inverse modelling calculations use a simple cooling section process model. Illustrative examples for optimum cooling of strip or sheet material using water spray cooling demonstrate the approach. Additionally, the physical limitations due to the finite heat conductivity of the strip are calculated and discussed.

Spray water cooling heat transfer under oxide scale formation conditions

Spray water cooling is an important technology used for the cooling of materials from temperatures up to 1800K. The heat transfer coecient (HTC) in the so-called steady film boiling regime is known to be a function of the water mass flow density. Below a specific surface temperature TL, film boiling becomes unstable and the HTC shows a strong dependence on temperature (Leidenfrost eect). The HTC was measured by an automated cooling test stand (instationary method). Compared to the previous state-of-the-art, an additional temperature dependency in the high temperature regime was found. A new analytic fit formula for the dependence of the heat transfer coecient on temperature and water impact density is proposed and discussed.