72
Views
14
CrossRef citations to date
0
Altmetric
Original Articles

Solidification of Double-Diffusive Flows Using Thermo-Magneto-Hydrodynamics and Optimization

&
Pages 594-606 | Received 01 Aug 2006, Accepted 12 Jan 2007, Published online: 30 May 2007

REFERENCES

  • Cao , W.Z. ; Poulikakos , D. Solidification of an alloy in a cavity cooled through its top surface . Int. J. Heat Mass Transfer 1990 , 33 , 427 – 434 .
  • Chellaiah , S. ; Waters , R.A. Solidification of an aqueous salt solution in the presence of thermosolutal convection . Proceedings of the third ASME-JSME Thermal Engineering Conference, 2 , 1991 , pp. 165 – 174 .
  • Beckermann , C. ; Viskanta , R. An experimental study of melting of binary mixtures with double-diffusive convection in the liquid . Experimental Thermal and Fluid Science 1989 , 2 ( 1 ), 17 – 26 .
  • Skudarnov , P.V. ; Lin , C.X. ; Wang , M.H. ; Pradeep , N. Ebadian , M.A. Evolution of convection pattern during the solidification process of a binary mixture: Effect of initial solutal concentration . Int. J. Heat and Mass Transfer 2002 , 45 , 5191 – 5200 .
  • Ghenai , C. ; Mudunuri , A. ; Lin , C.X. ; Ebadian , M.A. Double-diffusive convection during solidification of a metal analog system (NH4Cl–H2O) in a differentially heated cavity . Experimental Thermal and Fluid Science 2003 , 28 , 23 – 35 .
  • Mergui , S. ; Feroual , B. ; Gobin , D. ; Benard , C. Solidification of a binary mixture in a shear flow . Int. J. Heat and Mass Transfer 2004 , 47 , 1423 – 1432 .
  • Chakraborty , S. ; Dutta , P. An analytical solution for conduction-dominated unidirectional solidification of binary mixtures . Applied Mathematical Modeling 2002 , 26 , 545 – 561 .
  • Fleming , M.C. ; Nereo , G.E. Macrosegregation, Part 1 . Trans. AIME 1967 , 239 , 50 – 55 .
  • Kaviany , M. Principles of Heat Transfer in Porous Media ; Springer-Verlag : New York , 1991 .
  • Ni , J. ; Beckermann , C. A volume-averaged two-phase model for transport phenomena during solidification . MetaN. Trans. B 1991 , 22B , 349 – 361 .
  • Ni , J. ; Incropera , F.P. Extension of the continuum model for transport phenomena occurring during metal alloy solidification-I. The conservation equations . J. Heat and Mass Transfer 1995 , 38 ( 7 ), 1271 – 1284 .
  • Ni , J. ; Incropera , F.P. Extension of the continuum model for transport phenomena occurring during metal alloy solidification-II. Microscopic considerations . J. Heat and Mass Transfer 1995 , 38 , 1285 – 1296 .
  • Bennon , W.D. ; Incropera , F.P. Numerical simulation of binary solidification in a vertical channel with thermal and solutal mixed convection . Int. J. Heat Mass Transfer, 1988 , 31 ( 10 ), 2147 – 2160 .
  • Sampath , R. ; Zabaras , N. Numerical study of convection in the directional solidification of a binary alloy driven by the combined action of buoyancy, surface tension, and electromagnetic forces . J. Comp. Physics 2001 , 168 ( 2 ), 384 – 411 .
  • Heinrich , J.C. ; Poirier , D.R. Convection modeling in directional solidification . Comptes Rendus Mecanique 2004 , 332 ( 5–6 ), 429 – 445 .
  • Motakeff , S. Magnetic field elimination of convective interference with segregation during vertical-Bridgman growth of doped semiconductors . J. of Crystal Growth 1990 , 104 , 833 – 850 .
  • Hirtz , J.M. ; Ma , N. Dopant transport during semiconductor crystal growth: Axial versus transverse magnetic field . J. Crystal Growth 2000 , 210 , 554 – 572 .
  • Ghosh , A. Segregation in cast products . Sadhana 2001 , 26 , 5 – 24 .
  • Dulikravich , G.S. ; Colaco , M.J. ; Martin , T.J. ; Lee , S.-S. Magnetized fiber orientation and concentration control in solidifying composites . J. of Composite Materials 2003 , 37 ( 15 ), 1351 – 1366 .
  • Colaço , M.J. ; Dulikravich , G.S. A multilevel hybrid optimization of magnetohydrodynamic problems in double-diffusive fluid flow . Proceedings of the Third Meeting of the Study of Matter at Extreme Conditions (SMEC) ; Saxena , S. , Ed., Miami Beach , FL , April 17–21 , also in J. Physics and Chemistry of Solids 2005 , 67 , 1965 – 1972 .
  • Colaço , M.J. ; Dulikravich , G.S. Obtaining pre-specified concentration profiles in thermosolutal flows by applying magnetic fields having optimized intensity distribution . Int. Conf. on Computational Methods for Coupled Problems in Science and Engineering, COUPLED PROBLEMS 2005 ; Papadrakakis , M. , Oñate , E. , Schrefler , B. , Eds.; Santorini : Greece , 2005 .
  • Dulikravich , G.S. Electro-magneto-hydrodynamics and solidifi-cation . Advances in Flow and Rheology of Non-Newtonian Fluids, Part B ; Siginer , D.A. , De Kee , D. , Chhabra , R.P. , Eds.; Rheology Series, 8 ; Elsevier Publishers , 1999 ; Chapter no. 9 , 677 – 716 .
  • Ko , H.-J. ; Dulikravich , G.S. A fully non-linear model of electro-magneto-hydrodynamics . Int. J. Non-Linear Mechanics 2000 , 35 ( 4 ), 709 – 719 .
  • Dulikravich , G.S. ; Lynn , S.R. Unified electro-magneto-fluid dynamics (EMFD): Introductory concepts . Int. J. Non-Linear Mechanics 1997 , 32 ( 5 ), 913 – 922 .
  • Dulikravich , G.S. ; Lynn , S.R. Unified electro-magneto-fluid dynamics (EMFD): A survey of mathematical models . Int. J. Non-Linear Mechanics 1997 , 32 ( 5 ), 923 – 932 .
  • Bennacer , R. ; Gobin , D. Cooperating thermosolutal convection in enclosures – I. Scale analysis and mass transfer . Int. J. Heat Mass Transfer 1996 , 39 ( 13 ), 2671 – 2681 .
  • Gobin , D. ; Bennacer , R. Cooperating thermosolutal convection in enclosures – II. Scale analysis and mass transfer . Int. J. Heat Mass Transfer 1996 , 39 ( 13 ), 2683 – 2697 .
  • Voller , V.R. ; Brent , A.D. ; Prakash , C. The modeling of heat, mass and solute transport in solidification systems . Int. J. Heat Mass Transfer 1989 , 32 , 1719 – 1731 .
  • Zabaras , N. ; Samanta , D. A stabilized volume-averaging finite element method for flow in porous media and binary alloy solidification processes . Int. J. for Numerical Methods in Eng. 2004 , 60 , 1103 – 1138 .
  • Rappaz , M. Modelling of microstructure formation in solidification processes . Int. Materials Review 1989 , 34 , 93 – 123 .
  • Ghosh , A. Principles of Secondary Processing and Casting of Liquid Steel ; Oxford and IBH : New Delhi , 1990; Chapters 6, 7, and 9.
  • Van Doormal , J.P. ; Raithby , G.D. Enhancements of the SIMPLE method for predicting incompressible fluid flow . Numerical Heat Transfer 1984 , 7 , 147 – 163 .
  • Raithby , G.D. ; Torrance , K.E. Upstream-weighted differencing schemes and their application to elliptic problems involving fluid flow . Computers and Fluids 1974 , 2 , 191 – 206 .
  • Saad , Y. ; Schultz , M. Conjugate gradient-like algorithms for solving non-symmetric linear systems . Mathematics of Computation 1985 , 44 , 170 .
  • Colaço , M.J. ; Orlande , H.R.B. Inverse problem of simultaneous estimation of two boundary heat fluxes in parallel plate channels . J. of the Brazilian Society of Mechanical Sciences 2001 , 23 ( 2 ), 201 – 215 .
  • Colaço , M.J. ; Orlande , H.R.B. Inverse forced convection problem of simultaneous estimation of two boundary heat fluxes in irregularly shaped channels . Numerical Heat Transfer – Part A 2001 , 39 , 737 – 760 .
  • Colaço , M.J. ; Orlande , H.R.B. Inverse convection problems in irregular geometries . Proc. of the 21st Southeastern Conference on Theoretical and Applied Mechanics , Orlando , Florida , USA , 2002 .
  • Dulikravich , G.S. ; Colaço , M.J. ; Dennis , B.H. ; Martin , T.J. ; Lee , S. Optimization of intensities and orientations of magnets controlling melt flow during solidification . J. of Materials and Manufact. Processes 2004 , 19 ( 4 ), 695 – 718 .
  • Colaço , M.J. ; Dulikravich , G.S. ; Martin , T.J. Control of unsteady solidification via optimized magnetic fields, Materials and Manufacturing Processes 2005 , 20 ( 3 ), 435 – 458 .
  • Patankar , S.V. Numerical Heat Transfer and Fluid Flow ; John Benjamins Publishing Co , 1980 .
  • Broyden , C.G. Quasi-Newton methods and their applications to function minimization . Math. Comp. 1987 , 21 , 368 – 380 .
  • Kennedy , J. ; Eberhart , R.C. Particle swarm optimization . Proc. of the 1995 IEEE Int. Conf. on Neural Networks 1995 , 4 , 1942 – 1948 .
  • Storn , R. ; Price , K.V. Minimizing the real function of the ICEC'96 contest by differential evolution . Proc. of IEEE Conf. on Evolutionary Comput. 1996 , 842 – 844 .
  • Hardy , R.L. Multiquadric equations of topography and other irregular surfaces . J. of Geophysics Res. 1971 , 176 , 1905 – 1915 .
  • Kansa , E.J. Multiquadrics – A scattered data approximation scheme with applications to computational fluid dynamics – II: Solutions to parabolic, hyperbolic and elliptic partial differential equations . Comput. Math. Applic. 1990 , 19 , 149 – 161 .
  • Leitão , V.M.A. A mesheless method for Kirchhoff plate bending problems . Int. J. of Numerical Methods in Eng. 2001 , 52 , 1107–1130.
  • Colaço , M.J. ; Dulikravich , G.S. ; Orlande , H.R.B. ; Martin , T.J. Hybrid optimization with automatic switching among optimization algorithms . In: Evolutionary Algorithms and Intelligent Tools in Engineering Optimization ; W. Annicchiarico ; J. Periaux ; M. Cerrolaza ; G. Winter , Eds.; WIT Press : UK , 2005 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.