An Analytical Investigation of Steady Convection in an
Active Mushy Layer

Prof. Dr. P.K.Srimani; Prof. R.Parthasarathi

doi:https://doi.org/10.14445/22315373/IJMTT-V23P509

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 23 | Number 1 | Year 2015 | Article Id. IJMTT-V23P509 | DOI : https://doi.org/10.14445/22315373/IJMTT-V23P509

An Analytical Investigation of Steady Convection in an Active Mushy Layer

Prof. Dr. P.K.Srimani, Prof. R.Parthasarathi

Citation :

Prof. Dr. P.K.Srimani, Prof. R.Parthasarathi, "An Analytical Investigation of Steady Convection in an Active Mushy Layer," International Journal of Mathematics Trends and Technology (IJMTT), vol. 23, no. 1, pp. 62-70, 2015. Crossref, https://doi.org/10.14445/22315373/IJMTT-V23P509

Abstract

In the present work, we consider the solidification of a binary alloy and analytically analyse the linear stability of the quiescent state by considering the basic, first and second order systems of the governing differential equations. The specific interest with which the study is carried out is to identify a model and the corresponding parametric values which could suppress the formation of chimney convection and annihilate the formation of freckles which cause imperfections in the resulting solid. The asymptotic limits considered here are a near-eutectic approximations, large far-field temperature and variable permeability. The consideration of large Stefan number incorporates a key balance for the existence of compositional convection. The important results of the present study are, (i) an active mushy layer is more stable than a passive mushy layer, (ii) the far-field temperature has a destabilising effect on the marginal stability curves as expected, (iii) there is a reduction in the mushy layer thickness for large far-field temperature, and (iv) the influence of the governing parameters is remarkable on the vertical velocity component, temperature and local solid fraction profiles. Finally it is concluded that, through an analytical approach it is possible to determine the accurate solutions which could control or supress the chimney formation during the solidification process which is a burning problem in the areas like metal casting, sea dynamics etc. It is found that the results of the present study are very much closer to the experimental results,

Keywords

Mushy layer, Solidification, Compositional convection, Chimney formation, Variable permeability, Analytical.

References

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