Thermosolutal transport and macrosegregation during freeze coating of a binary substance on a continuous moving object

Abstract The process of freeze coating of a binary substance on a continuous moving plate is investigated theoretically. A comprehensive model describing the momentum, heat, and mass transport in the freeze-coating system has been developed that accounts for the coupling between the macroscopic and microscopic aspects of the process. The problem is formulated using the single-domain approach and the governing equations are solved by the finite difference method. Effects of various controlling parameters on the freeze-coat thickness and the macrosegregation pattern have been determined. It is found that macrosegregation could be important in the freeze-coating process. As the distance from the surface of the plate is increased, the solid species concentration considerably decreases, reaching a minimum value and rising toward the ambient concentration. The macrosegregation pattern appears to be most sensitive to the equilibrium partition ratio. As the latter is increased, the difference between the solid and liquid species concentrations tends to decrease, leading to a substantial reduction of macrosegregation within the freeze coat.

[1]  A. V. Kuznetsov.  Investigation of the coupled heat transfer, fluid flow and solute transport during the strip casting process , 1997 .

[2]  H. Kuiken.  Solidification of a liquid on a moving sheet , 1977 .

[3]  A. Kuznetsov.  Parametric study of macrosegregation in the horizontal strip casting process for different cooling rates and different casting speeds , 1999 .

[4]  C. Prakash,et al.  TWO-PHASE MODEL FOR BINARY SOLID-LIQUID PHASE CHANGE, PART I: GOVERNING EQUATIONS , 1990 .

[5]  P. Weidman,et al.  Calculation of dendrite settling velocities using a porous envelope , 1993 .

[6]  D. Poulikakos,et al.  Heat and fluid flow processes during the coating of a moving surface , 1991 .

[7]  Christoph Beckermann,et al.  Equiaxed dendritic solidification with convection: Part I. Multiscale/multiphase modeling , 1996 .

[8]  Frank P. Incropera,et al.  A continuum model for momentum, heat and species transport in binary solid-liquid phase change systems. II: Application to solidification in a rectangular cavity , 1987 .

[9]  R. Pletcher,et al.  Computational Fluid Mechanics and Heat Transfer. By D. A ANDERSON, J. C. TANNEHILL and R. H. PLETCHER. Hemisphere, 1984. 599 pp. $39.95. , 1986, Journal of Fluid Mechanics.

[10]  F. Cheung,et al.  Solidified Layer Growth and Decay Characteristics During Freeze Coating of Binary Substance , 2002 .

[11]  C. Beckermann,et al.  Multiparticle interfacial drag in equiaxed solidification , 1995 .

[12]  F. Cheung,et al.  FINITE-DIFFERENCE ANALYSIS OF GROWTH AND DECAY OF A FREEZE COAT ON A CONTINUOUS MOVING CYLINDER , 1987 .

[13]  F. Cheung,et al.  Behavior of the Two-Phase Mushy Zone During Freeze Coating on a Continuous Moving Plate , 2002 .

[14]  J. Ni,et al.  A volume-averaged two-phase model for transport phenomena during solidification , 1991 .

[15]  M. K. Moallemi,et al.  Numerical simulation of hot-dip metallic coating process , 1995 .

[16]  V. Voller,et al.  The modelling of heat, mass and solute transport in solidification systems , 1989 .

[17]  Christoph Beckermann,et al.  A numerical study of the combined effects of microsegregation, mushy zone permeability and fllow, caused by volume contraction and thermosolutal convection, on macrosegregation and eutectic formation in binary alloy solidification , 1995 .

[18]  D. R. Poirier.  Permeability for flow of interdendritic liquid in columnar-dendritic alloys , 1987 .

[19]  C. Prakash.  TWO-PHASE MODEL FOR BINARY SOLID- LIQUID PHASE CHANGE, PART II: SOME ILLUSTRATIVE EXAMPLES , 1990 .

[20]  F. Incropera,et al.  A continuum model for momentum, heat and species transport in binary solid-liquid phase change systems—I. Model formulation , 1987 .

[21]  D. Poulikakos,et al.  Freeze coating of a moving substrate with a binary alloy , 1991 .

[22]  Masahiko Yamada,et al.  Solidification of Pure Liquids and Liquid Mixtures Inside Ducts and Over External Bodies , 1994 .

[23]  R. Grugel.  Composite growth in hypermonotectic alloys , 1991 .

[24]  F. Incropera,et al.  Extension of the continuum model for transport phenomena occurring during metal alloy solidification-II. Microscopic considerations , 1995 .

[25]  S. Patankar.  Numerical Heat Transfer and Fluid Flow , 2018, Lecture Notes in Mechanical Engineering.

[26]  K. Mahmoud.  Numerical analysis of freeze coating on a two-dimensional moving plate , 1994 .

[27]  R. D. Jackson,et al.  Heat Transfer 1 , 1965 .

[28]  F. Incropera,et al.  Extension of the continuum model for transport phenomena occurring during metal alloy solidification—I. The conservation equations , 1995 .

[29]  F. Cheung.  Thermal boundary layer on a continuous moving plate with freezing , 1987 .

[30]  Christoph Beckermann,et al.  Equiaxed dendritic solidification with convection: Part II. Numerical simulations for an Al-4 Wt pct Cu alloy , 1996 .

[31]  R. Seeniraj,et al.  Freeze-coating on a continuous moving sheet and on an axially moving cylinder , 1981 .