Numerical Investigation on Marginal Stability and Convection with and without Magnetic Field in a Mushy Layer |
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Authors: | Mallikarjunaiah S Muddamallappa Dambaru Bhatta Daniel N Riahi |
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Institution: | (1) Department of Mathematics, The University of Texas-Pan American, 1201 West University drive, Edinburg, TX 78539-2999, USA |
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Abstract: | In this article, an investigation is conducted to analyze the marginal stability with and without magnetic field in a mushy
layer. During alloy solidification, such mushy layer, which is adjacent to the solidification front and composed of solid
dendrites and liquid, is known to produce vertical chimneys. Here, we carry out numerical investigation for particular range
of parameter values, which cover those of available experimental studies, to determine the convective flow at the onset of
motion. The governing coupled non-linear partial differential equations are non-dimensionalised and solved to get the steady
basic-state solution. The thickness of the mushy layer is determined as a part of the solution. Using multiple shooting technique,
we determine the steady-state solutions in a range of critical Rayleigh number. We analyse the effect of several parameters,
Chandrasekhar number Q, and Robert’s number τ on the problem. It was found that an increase in Q has a stabilizing effect on solidification and the critical Rayleigh number increases on increasing Q. It was also found that for moderate or small values of Robert’s number τ the critical Rayleigh number is mostly insensitive. |
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Keywords: | Convection Convective flow Magneto-convection Mushy layer Hydromagnetic flow |
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