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Reducing Convection Effects in Solidification by Applying Magnetic Fields Having Optimized Intensity Distribution

[+] Author Affiliations
Marcelo J. Colaço

Federal University of Rio de Janeiro, Rio de Janeiro, RJ, Brazil

George S. Dulikravich

University of Texas at Arlington, Arlington, TX

Thomas J. Martin

Pratt & Whitney Engine Company, East Hartford, CT

Paper No. HT2003-47308, pp. 199-209; 11 pages
doi:10.1115/HT2003-47308
From:
  • ASME 2003 Heat Transfer Summer Conference
  • Heat Transfer: Volume 3
  • Las Vegas, Nevada, USA, July 21–23, 2003
  • Conference Sponsors: Heat Transfer Division
  • ISBN: 0-7918-3695-9 | eISBN: 0-7918-3679-7
  • Copyright © 2003 by ASME

abstract

This paper presents a numerical procedure for achieving desired features of a melt undergoing solidification by applying an external magnetic field whose intensity and spatial distribution are obtained by the use of a hybrid optimization algorithm. The intensities of the magnets along the boundaries of the container are described as B-splines. The inverse problem is then formulated as to find the magnetic boundary conditions (the coefficients of the B-splines) in such a way that the gradients of temperature along the gravity direction are minimized. For this task, a hybrid optimization code was used that incorporates several of the most popular optimization modules; the Davidon-Fletcher-Powell (DFP) gradient method, a genetic algorithm (GA), the Nelder-Mead (NM) simplex method, quasi-Newton algorithm of Pshenichny-Danilin (LM), differential evolution (DE), and sequential quadratic programming (SQP). Transient Navier-Stokes and Maxwell equations were discretized using finite volume method in a generalized curvilinear non-orthogonal coordinate system. For the phase change problems, an enthalpy formulation was used. The code was validated against analytical and numerical benchmark results with very good agreements in both cases.

Copyright © 2003 by ASME

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