Heat transfer analysis for the solidification of a binary eutectic system under imposed movement of the material

Abstract

The current article deals with a moving boundary problem describing solidification of a eutectic alloy in a semi-infinite medium. The process of solidification of a eutectic alloy is considered under imposed movement of material in the mushy zone in place of liquidus zone due to imposing an insulated boundary condition at liquidus front. It is assumed that solid fraction fs has a linear, quadratic and cubic relationship with distance within the mushy zone between the solidus and liquidus. An exact solution of the problem is obtained with the help of similarity transformation. A numerical example of the solidification of Al–Cu alloy is presented to demonstrate the application of the current analysis. Solidification of eutectic system is discussed in the absence of material movement and in the presence of material movement in each case of solid fraction distribution. Thus, the temperature profile and moving interfaces in each region are shown for different Peclet numbers Pe. In addition, heat extraction Q from the surface x= 0 is shown with respect to the time for different Pe. The novelty of the current study is transition process becomes fast when material moves in the direction of freeze and hence time for complete freezing of the alloy reduces. Moreover, mushy zone becomes thinner when material moves in the direction of freeze. A comparative study and error analysis between the present work and Tien and Geiger (ASME J Heat Transf 89:230–233, 1967)[9] in linear case of solid fraction are presented in figure and tables. The application of the present analysis is useful for both eutectic and solid solution alloys. © 2021, Akadémiai Kiadó, Budapest, Hungary.