Browsing by Author "Myers, Timothy G"
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- ItemOpen AccessMathematical modelling of the Czochralski crystal growth process(2006) Brakel, Thomas W; Myers, Timothy GIn this document a mathematical model for the Czochralski crystal growth process is developed. The trend in current research involves developing cumbersome numerical simulations that provide little or no understanding of the underlying physics. We attempt to review previous research methods, mainly devoted to silicon, and develop a novel analytical tool for indium antimonide (lnSb) crystal growth. This process can be subdivided into two categories: solidification and fluid mechanics. Thus far, crystal solidification of the Czochralski process has been described in the literature mainly qualitatively. There has been little work in calculating actual solidification dynamics. Czochralski crystal growth is a very sensitive process, particularly for lnSb, so it is crucial to describe the system as accurately as possible. A novel ID quasi-steady method is proposed for the shape and temperature field of an lnSb crystal, incorporating the effects of the melt. The fluid mechanics of the Czochralski melt have been modelled by numerous researchers,with calculations performed using commercial software. However, a descriptionof the buoyancy and rotation interaction in the melt has not been adequatelyperformed. Many authors have presented flow patterns but none have indicated either: melt conditions preferential for crystal growth or at least a description of a typical melt structure. In this work, a scale analysis is performed that implies an idealized flow structure. An asymptotic model is then derived based on this order of magnitude analysis, resulting in a fast and efficient fluid flow calculation. The asymptotic model is validated against a numerical solution to ensure that the macroscopic features of the flow structure are present. The asymptotic model does not show exact agreement, but does provide an estimate of the melt heat flux that is necessary for the solidification calculation. The asymptotic model is also used to predict macroscopic changes in the melt due to rotation.
- ItemOpen AccessMathematical modelling of unsteady contact melting(2008) Muchatibaya, Gift; Myers, Timothy G; Mitchell, S LThe work in this thesis deals with the heat transfer and fluid flow problem encountered in the analysis of an unsteady contact melting process. Chapters 2 and 3 deal with only the heat transfer problem without fluid flow. In Chapter 2 the pre-melting problem is treated. The focus is to obtain the best approximate analytical solution to be used in the melting phase where there are no known exact solutions. The approximate solutions are constructed using the heat balance integral method.
- ItemOpen AccessA numerical investigation of the linear hydrodynamic stability of Newtonian and weakly non-Newtonian channel flows as described by the Orr-Sommerfeld equation(2009) Van der Fort, Zareer; Laurie, H; Myers, Timothy GThe Orr-Sommerfeld equation describes the growth of infinitesimal disturbances to laminar solutions of the Newtonaian Navier-Stokes equations. In this dissertation we consides in part idealised flows between two parallel planes of infinite extent and a finite distance apart. They are referred to as closed channel flows.
- ItemOpen AccessSpin coating of Newtonian and non-Newtonian fluids(2006) Lombe, Mubanga; Myers, Timothy GThe work in this thesis deals with the axisymmetric flow of a thin fluid layer on a rotating substrate.
- ItemOpen AccessTwo dimensional flow of variable viscosity fluids(2009) Tshehla, Maashutha Samuel; Myers, Timothy GIncludes abstract. Includes bibliographical references (p. 207-218).