Dr. Jyotirmay Banerjee
  Associate Professor, Department of Mechanical Engineering,
  S V National Institute of Technology, Surat 395007, Gujarat, India.
Degree |
College/University |
Year |
---|---|---|
Ph D |
Indian Institute of Technology, Kanpur |
Jan 2005 |
Ph D Thesis on
Czochralski Growth of Oxide Crystals: Numerical Simulation and Experiments
The problem involves modeling of fluid flow and heat transfer in a domain consisting of solid, liquid and gas phases separated by their respective phase boundaries. Since the interfaces separating the different phases are influenced by the flow and thermal field in the adjacent phases, the interface specific equations needed to be solved simultaneously and iteratively along with the conservation equations in all phases. The interface in the present formulation is tracked as an (n-1) dimensional entity in an n-dimensional Euclidian space. Thus the interfaces are surfaces of sharp discontinuity and are followed by assigning a fixed grid line to them. Grids are regenerated with every new location of the interface using numerically determined coordinate transformation. The conservation equations for all three phases are jointly represented with the understanding that velocity is zero in the solid phase. The computations are done in an axi-symmetric configuration. The flow in the liquid phase involved the effects of Buoyancy, Marangoni and rotation. An equation for conservation of angular momentum is solved to take care of rotation. A bulk radiation module is incorporated to account for internal emission, absorption and scattering in the melt as well as the crystal phase. This called for solution of Radiative Transfer Equation (RTE) simultaneously with the conservation of energy. RTE is solved using Discrete Ordinates method. Liquid Crystal thermography (LCT) tracers are used to visualize the temperature field in a low Temperature Czochralski setup prepared in the laboratory. The images captured by a high resolution CCD camera are suitably calibrated via Hue to obtain the thermal field in the natural, mixed and forced convection regime. The numerical results are validated with these processed images.