Analytical and numerical simulations for the kinetics of phase separation in iron (Fe–Cr–X (X=Mo,Cu)) based on ternary alloys

D. Lu, M.S. Osman, M.M.A. Khater, R.A.M. Attia and D. Baleanu

Physica A: Statistical Mechanics and its Applications, 2020, vol. 537, issue C

Abstract: In this paper, we investigate the physical behavior of the basic elements that related to phase decomposition in ternary alloys of (Fe–Cr–Mo) and (Fe–Cr–Cu) according to analytical and approximate simulation. We study the dynamic of the separation phase for the ternary alloys of iron. The dynamical process of this separation has been described in a mathematical model called the Cahn–Hilliard equation. The minor element behavior in the process has been described by the Cahn–Hilliard equation. It describes the process of phase separation for two components of a binary fluid in ternary alloys of (Fe–Cr–Mo) and (Fe–Cr–Cu). We implement a modified auxiliary equation method and the cubic B-spline scheme on this mathematical model to show the dynamical process of phase separation and the concentration of one of two components in a system. We try obtaining the solitary and approximate solutions of this model to show the relation between the components in this phase. We discuss our solutions in view of a Stefan, Thomas-Windle, and Navier–Stokes models. Whereas, these models describe the motion of viscous fluid substance.

Keywords: Convective–diffusive Cahn–Hilliard equation; Modified auxiliary equation method; Cubic B-spline scheme; Solitary wave solutions (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:537:y:2020:i:c:s0378437119315055

DOI: 10.1016/j.physa.2019.122634

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