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International Journal of Fluid Mechanics Research
ESCI SJR: 0.206 SNIP: 0.446 CiteScore™: 0.9

ISSN Print: 2152-5102
ISSN Online: 2152-5110

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International Journal of Fluid Mechanics Research

DOI: 10.1615/InterJFluidMechRes.v39.i6.30
pages 494-520

Magnetic and Permeability Effects on a Weakly Nonlinear Magneto-Convective Flow in an Active Mushy Layer

Dambaru Bhatta
School of Mathematical and Statistical Science, University of Texas Rio Grande Valley, Edinburg, Texas 78539, USA
S. Mallikarjunaiah Muddamallappa
Department of Mathematics, Texas A&M University College Station, Texas
Daniel N. Riahi
School of Mathematical and Statistical Science, University of Texas Rio Grande Valley, Edinburg, Texas 78539, USA

ABSTRACT

Here we consider a mushy layer which is formed during solidification of binary alloys in presence of a magnetic field. The mushy layer is treated as active. The original boundary value problem consisting of five partial differential equations with five unknowns are converted to four partial differential equations with four unknowns after eliminating the pressure variable. A Landau type nonlinear evolution equation for the amplitude based on weakly nonlinear theory is derived. We also present computational results for marginal stability curves and other dependent variables for different permeability parameter and Chandrasekhar number. These results suggest that higher permeability parameter and Chandrasekhar number enhance the marginal stability. This analysis also indicates a possible slow transition to turbulence in such flow system since the computed Landau constants are positive.


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