Commun. Comput. Phys., 14 (2013), pp. 477-508.

Mathematical Modelling and Numerical Simulation of Dendrite Growth Using Phase-Field Method with a Magnetic Field Effect

A. Rasheed 1, A. Belmiloudi 2*

1 COMSATS-IIT, Quaid Avenue, Wah Cantt, Pakistan.
2 IRMAR-INSA de Rennes, 20 avenue des Buttes de Coesmes, CS 70839, 35708 Rennes Cedex 7, France.

Received 9 April 2012; Accepted (in revised version) 12 October 2012
Available online 4 January 2013


In this paper, we present a new model developed in order to analyze phenomena which arise in the solidification of binary mixtures using phase-field method, which incorporates the convection effects and the action of magnetic field. The model consists of flow, concentration, phase field and energy systems which are nonlinear evolutive and coupled systems. It represents the non-isothermal anisotropic solidification process of a binary mixture together with the motion in a melt with the applied magnetic field. To illustrate our model, numerical simulations of the influence of magnetic-field on the evolution of dendrites during the solidification of the binary mixture of Nickel-Copper (Ni-Cu) are developed. The results demonstrate that the dendritic growth under the action of magnetic-field can be simulated by using our model.

AMS subject classifications: 76W05, 35K55, 35R35, 74A50, 74N25, 65N30, 80A22

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Key words: Modelling, Phase-field method, dendritic solidification, binary alloys, convection, magnetic-field, Magnetohydrodynamics, numerical simulations.

*Corresponding author.
Email: (A. Rasheed),, (A. Belmiloudi)

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