Solidification of double-diffusive flows using thermo-magneto-hydrodynamics and optimization

Materials and Manufacturing Processes

Volumn 22, Issue 5, 2007, Pages 594-606

  Colaço, Marcelo J ^a   Dulikravich, George S ^b  

^a MILITARY INSTITUTE OF ENGINEERING   (Brazil)

^b Florida International University   (United States)

Author keywords

Flow control; Hybrid optimization; Inverse problems; Magnetohydrodynamics; Materials processing; Numerical methods; Smart manufacturing; Solidification; Solute transport

Indexed keywords

BOUNDARY CONDITIONS; DIFFUSION; FUNCTIONS; MAGNETOHYDRODYNAMICS; NUMERICAL METHODS; OPTIMIZATION; SOLIDIFICATION; SOLUTE TRANSPORT;

BASIS FUNCTION; HYBRID OPTIMIZER; MAGNETIC BOUNDARY CONDITIONS; MATERIALS PROCESSING; SMART MANUFACTURING; THERMOSOLUTAL FLOW;

FLOW OF FLUIDS;

EID: 34249852405     PISSN: 10426914     EISSN: 15322475     Source Type: Journal    
DOI: 10.1080/10426910701322583     Document Type: Article

References (47)

1. 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.
7. Chakraborty, S.; Dutta, P. An analytical solution for conduction-dominated unidirectional solidification of binary mixtures. Applied Mathematical Modeling 2002, 26, 545-561.
8. Fleming, M.C.; Nereo, G.E. Macrosegregation, Part 1. Trans. AIME 1967, 239, 50-55.
9. Kaviany, M. Principles of Heat Transfer in Porous Media; Springer-Verlag: New York, 1991.
10. Ni, J.; Beckermann, C. A volume-averaged two-phase model for transport phenomena during solidification. MetaN. Trans. B 1991, 22B, 349-361.
11. 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.
12. 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.
13. 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.
14. 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.
15. Heinrich, J.C.; Poirier, D.R. Convection modeling in directional solidification. Comptes Rendus Mecanique 2004, 332 (5-6), 429-445.
16. 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.
17. Hirtz, J.M.; Ma, N. Dopant transport during semiconductor crystal growth: Axial versus transverse magnetic field. J. Crystal Growth 2000, 210, 554-572.
18. Ghosh, A. Segregation in cast products. Sadhana 2001, 26, 5-24.
19. 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.
20. 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.
21. 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., Ofiate, E., Schrefler, B., Eds.; Santorini: Greece, 2005.
22. Dulikravich, G.S. Electro-magneto-hydrodynamics and solidification. 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.
23. 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.
24. Dulikravich, G.S.; Lynn, S.R. Unified electro-magneto-fluid dynamics (EMFD): Introductory concepts. Int. J. Non-Linear Mechanics 1997, 32 (5), 913-922.
25. 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.
26. 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.
27. 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.
28. 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.
29. 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.
30. Rappaz, M. Modelling of micro structure formation in solidification processes. Int. Materials Review 1989, 34, 93-123.
31. Ghosh, A. Principles of Secondary Processing and Casting of Liquid Steel; Oxford and IBH: New Delhi, 1990; Chapters 6, 7, and 9.
32. Van Doormal, J.P.; Raithby, G.D. Enhancements of the SIMPLE method for predicting incompressible fluid flow. Numerical Heat Transfer 1984, 7, 147-163.
33. 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.
34. Saad, Y.; Schultz, M. Conjugate gradient-like algorithms for solving non-symmetric linear systems. Mathematics of Computation 1985, 44, 170.
35. 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.
36. 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.
37. 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.
38. 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.
39. 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.
40. Patankar, S.V. Numerical Heat Transfer and Fluid Flow; John Benjamins Publishing Co, 1980.
41. Broyden, C.G. Quasi-Newton methods and their applications to function minimization. Math. Comp. 1987, 21, 368-380.
42. Kennedy, J.; Eberhart, R.C. Particle swarm optimization. Proc. of the 1995 IEEE Int. Conf. on Neural Networks 1995, 4, 1942-1948.
43. 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.
44. Hardy, R.L. Multiquadric equations of topography and other irregular surfaces. J. of Geophysics Res. 1971, 176, 1905-1915.
45. 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.
46. Leitão, V.M.A. A mesheless method for Kirchhoff plate bending problems. Int. J. of Numerical Methods in Eng. 2001, 52, 1107-1130.
47. 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.