Abstract
The current article devoted to study a moving boundary problem describing freezing of a eutectic system in a semi-infinite medium in cylindrical symmetry. The solidification of the material is considered by a line heat sink of strength Q place at r = 0. The heat transfer is considered due to both mechanism, conduction and convection driven by fluid motion in the liquid region, mushy region and possibly in porous solid phase. The analysis is concerned with extended freezing temperature range between solidus and liquidus temperatures respectively. The solid fraction is considered to have a linear relationship with temperature within the mushy zone. A direct integration method is used to solve the mathematical model, resulting an exact solution of the problem is obtained. To illustrate the application of current study and validity of mathematical model, a numerical example of freezing of an Al–Cu alloy with 5% Cu is presented. In addition, the temperature distribution in each region and position of moving interfaces is shown for different Peclet number. In this work, we obtained that the process of freezing becomes fast in the presence of convection. Moreover, it is shown that for a large value of Q, strength of line heat sink, the freezing of a eutectic alloy increases rapidly. Both eutectic and solid solution alloys come under the application of current study.
Funding source: Banaras Hindu University
Award Identifier / Grant number: Unassigned
Acknowledgment
Vikas Chaurasiya, one of the authors is grateful to DST (INSPIRE)-New Delhi (India) for the Senior Research Fellowship vide Ref. No. DST/INSPIRE/03/2 017/000 184 (i) Ref. no/Math/2017-18/March 18/347 and also to the Department of Mathematics (Institute of Science), Banaras Hindu University (BHU), Varanasi (U.P), India, for providing necessary facilities.
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Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: None declared.
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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