Stagnation-flow solidification on a finite thickness substrate

Asymptotic solutions for a time-dependent, axisymmetric directional solidification system

“…There exists an extensive amount of literature on sharp-interface, Stefan-type problems and various directional solidification configurations [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Mathematically, exact solutions to corresponding classes of problems are generally restricted to unbounded domains and are subject to limitations on possible boundary conditions.…”

An asymptotic analysis for directional solidification of a diffusion-dominated binary system

“…Numerical simulations of Yao et al [31] suggest that this regime is valid when gravity is less than 10 À5 g. Following Brattkus and Davis [10], we treat the heat transfer at the left and right ampoule walls as Oðe 2 Þ-quantities as defined in Table 4 and reflected in Eqs. (8) and (10). However, unlike these authors, we assume that the parameter M is also small ( Table 4 and Eq.…”

“…Since there is a close relationship between growth conditions and the microstructure and properties of solidified materials, there has been an extensive amount of investigation [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] of sharp-interface, Stefan-type problems and directional solidification configurations. Exact solutions to these classes of problems are generally restricted to unbounded domains and are subject to limitations on the boundary conditions.…”

“…Analytical approaches have generally been concerned with one-dimensional, planar interface, time-dependent models, or higher-dimensional, steady-state models. To solve the problems in the former category, recent investigations have used series expansion [4], similarity solution [6,8], Laplace transform [7], and Green's function techniques [5]. Quasi-steady models [2,3] have also been used by employing perturbation expansions in powers of a small parameter, which is inversely proportional to the latent heat, and small in magnitude due to the relatively large value of the latent heat.…”