Thermocapillary-buoyancy flow of silicon melt in a shallow annular pool

In order to understand the nature of surface spoke patterns on silicon melt in industrial Czochralski furnaces, a series of unsteady three-dimensional numerical simulations were conducted for thermocapillary-buoyancy flow of silicon melt in annular pool (inner radius r(i)=15 mm, outer radius r(o)=50 mm, depth d=3mm). The pool is heated from the outer cylindrical wall and cooled at the inner wall. Bottom and top surfaces either are adiabatic or allow heat transfer in the vertical direction. Results show that a small temperature difference in the radial direction generates steady roll-cell thermocapillary-buoyancy flow. With large temperature difference, the simulation can predict three-dimensional oscillatory flow, which is characterized by spoke patterns traveling in the azimuthal direction. The small vertical heat flux (3W/cm(2)) does not have significant effects on the characteristics of this oscillatory flow. Details of the flow and temperature disturbances are discussed and the critical conditions for the onset of the oscillatory flow are determined.