NEWTON METHOD FOR SOLVING HEAT-TRANSFER, FLUID-FLOW AND INTERFACE SHAPES IN A FLOATING MOLTEN ZONE

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Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/26682

Title:	NEWTON METHOD FOR SOLVING HEAT-TRANSFER, FLUID-FLOW AND INTERFACE SHAPES IN A FLOATING MOLTEN ZONE
Authors:	LAN,CW
Contributors:	化學工程與材料工程學系
Keywords:	RADIAL DOPANT SEGREGATION;CRYSTAL-GROWTH;THERMOCAPILLARY CONVECTION;SURFACE-TENSION;FINITE-ELEMENT;LINEAR-SYSTEMS;NORMAL GRAVITY;DRIVEN FLOW;ROTATION;STEADY
Date:	1994
Issue Date:	2010-06-29 17:34:09 (UTC+8)
Publisher:	中央大學
Abstract:	Newton's method is applied to the finite volume approximation for the steady state heat transfer, fluid flow and unknown interfaces in a floating molten zone. The streamfunction/vorticity and temperature formulation of the Navier-Stokes and energy equations and their associated boundary conditions are written in generalized curvilinear co-ordinates and conservative law form with the Boussinesq approximation. During Newton iteration the ILU(0) preconditioned GMRES matrix solver is applied for solving the linear system, where the sparse Jacobian matrix is estimated by finite differences. Nearly quadratic convergence of the method is observed. Sample calculations are reported for sodium nitrate, a high-Prandtl-number material (Pr = 9.12). Both natural convection and thermocapillary flow as well as an overall mass balance constraint in the molten zone are considered. The effects of convection and heat input on the flow patterns, zone position and interface shapes are illustrated. After the lens effect due to the molten zone is considered, the calculated flow patterns and interface shapes are compared with the observed ones and are found to be in good agreement.
Relation:	INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
Appears in Collections:	[National Central University Department of Chemical & Materials Engineering] journal & Dissertation

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