A similarity solution for phase change of binary alloy with shrinkage or expansion

Explicit solutions related to the Rubinstein binary‐alloy solidification problem with a heat flux or a convective condition at the fixed face

“…A study of binary-alloy problems can be seen in [5][6][7][8][9][10][11][12]. Recent works on the solidification of a binary alloy are [6,8,[13][14][15][16][17][18][19][20][21][22][23][24].…”

Explicit solutions related to the Rubinstein binary-alloy solidification problem with a heat flux or a convective condition at the fixed face

“…Proof. By (8) we have that M (λ) = φ(T k ). Taking into account that T1 = T1 is given by ( 24), we have…”

“…A study of binary-alloy problems can be seen in [2,5,8,12,16,17,24,25]. Recent works on the solidification of a binary alloy are [1,3,5,6,7,9,10,11,12,14,21,22,23,28].…”

“…In Section 2 we obtain the necessary and sufficient condition (2) for problem (P1) in order to obtain the explicit solution (3)- (8). In Section 3 we deduce the inequality (38) for the coefficient µ that characterizes the Rubinstein free boundary x = s(t) for problem (P1) defined in (3).…”

Mathematical modelling of macrosegregation in binary alloys induced by convection

“…Moreover, this configuration is believed to permit a similarity solution to the governing equations (CHAKRABORTY;DUTTA, 2002;JAKHAR;RATH;MAHAPATRA, 2016;VOLLER, 1997;WACLAWCZYK;SCHäFER, 2018), which can then be used as a benchmark for testing higher-dimensional numerical codes. Furthermore, the fact that there is relative motion between solid and liquid phases in the so-called mushy zone, where the two phases coexist, leads to the possibility of macrosegregation (CHEN;DIAO;TSAI, 1993a;DIAO;TSAI, 1993b;MINAKAWA;SAMARASEKERA;WEINBERG, 1985;MO, 1993).…”